VDI HeatAtlas

Kapil Hukkeri

VDI Heat Atlas Verein Deutscher Ingenieure VDI-Gesellschaft Verfahrenstechnik und Chemieingenieurwesen (GVC) Editor VDI Heat Atlas Second Edition With 1011 Figures and 539 Tables Editor VDI e. V. VDI-Gesellschaft Verfahrenstechnik und Chemieingenieurwesen (VDI-GVC) VDI-Platz 1 40468 Düsseldorf Germany 1st edition published in 1993 by VDI-Verlag GmbH, Düsseldorf. ISBN 978-3-540-77876-9 e-ISBN 978-3-540-77877-6 Print and electronic bundle ISBN 978-3-540-79999-3 DOI 10.1007/978-3-540-77877-6 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010924812 # Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface to the Second English Edition The VDI-Wärmeatlas or VDI Heat Atlas has a long-lasting history and it can be considered as a standard book for heat exchanger and process engineering equipment design. It is not conceived as a textbook presenting an overall view of the theoretical or experimental findings in heat transfer sciences. The aim was and is to present and explain the state of the art of engineering methods to solve industrially relevant heat transfer problems for apparatus design and process modeling. The first German edition was published in 1963. The sixth German edition was translated into English to meet the demands of the more and more internationally acting industry. This first English edition was published in 1992. Since then, the German edition was regularly updated until the tenth edition published in 2006. In view of today’s globally acting industry, the editorial board felt the necessity to revise the English edition in order to account for the most recent state of our knowledge. Instead of only translating the latest German edition, we preferred restructuring it at the same time because this also enabled us to include new subjects and to update methods according to the recent state of the art. This new structure will also serve as a basis for the forthcoming German edition. On behalf of the editorial board, I express my sincere thanks to the authors of the various sections for their contributions and kind cooperation. The editorial work was coordinated and assisted by Mrs. Sigrid Cuneus from Springer-Verlag, Berlin. We are indebted to her for the efficient work and pleasant collaboration. We are also grateful to Mrs. Tina Shelton from the Reference and Database Publishing group, Springer Reference Editorial, India, who handled the editorial workflow. Professor Dr.-Ing. Peter Stephan, Editor-in-Chief Darmstadt, May 2010 Editorial Board to the Second English Edition Prof. Dr.-Ing. Peter Stephan Technische Universität Darmstadt Fachbereich Maschinenbau Institut für Technische Thermodynamik Petersenstraße 30 64287 Darmstadt Germany pstephan@ttd.tu-darmstadt.de Prof. Dr.-Ing. Stephan Kabelac Helmut-Schmidt Universität Universität der Bundeswehr Hamburg Institut für Thermodynamik Holstenhofweg 85 22043 Hamburg Germany Kabelac@hsu-hh.de Prof. Dr.-Ing. Matthias Kind Karlsruher Institut für Technologie (KIT) Institut für Thermische Verfahrenstechnik Kaiserstraße 12 76131 Karlsruhe Germany matthias.kind@kit.edu Prof. Dr.-Ing. Holger Martin Karlsruher Institut für Technologie (KIT) Institut für Thermische Verfahrenstechnik Kaiserstraße 12 76131 Karlsruhe Germany holger.martin@kit.edu Prof. Dr.-Ing. Dr. h. c. Dieter Mewes Leibniz Universität Hannover Institut für Mehrphasenprozesse IMP Callinstraße 36 30167 Hannover Germany mewes@imp.uni-hannover.de Prof. Dr.-Ing. Karlheinz Schaber Karlsruher Institut für Technologie (KIT) Institut für Technische Thermodynamik und Kältetechnik ITTK Engler-Bunte-Ring 21 76131 Karlsruhe Germany Karlheinz.schaber@kit.edu Table of Contents List of Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii A Symbols, Units and Dimensionless Numbers A1 Symbols and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Matthias Kind . Holger Martin A2 Dimensionless Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Holger Martin B Fundamentals of Heat Transfer B1 Fundamentals of Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Peter Stephan C Fundamentals of Heat Exchanger Design C1 Thermal Design of Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Wilfried Roetzel . Bernhard Spang C2 Overall Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Wilfried Roetzel . Bernhard Spang C3 Typical Values of Overall Heat Transfer Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Wilfried Roetzel . Bernhard Spang C4 Fouling of Heat Exchanger Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Hans Müller-Steinhagen C5 Heat Exchanger Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Xing Luo . Wilfried Roetzel C6 Costs and Economy of Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Bernhard Spang . Wilfried Roetzel D Thermophysical Properties D1 Calculation Methods for Thermophysical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Michael Kleiber . Ralph Joh D2 Properties of Selected Important Pure Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 D2.1 Properties of Water and Steam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Wolfgang Wagner . Hans-Joachim Kretzschmar D2.2 Properties of Dry Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Roland Span x Table of Contents D2.3 Properties of Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Roland Span . Rolf Krauss D2.4 Properties of Carbon Dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Roland Span . Rolf Krauss D2.5 Properties of Oxygen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Roland Span . Rolf Krauss D2.6 Properties of Ammonia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Roland Span . Rolf Krauss D2.7 Properties of R134a (1,1,1,2-tetrafluoromethane) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 Roland Span . Rolf Krauss D3 Properties of Pure Fluid Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 D3.1 Liquids and Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 Michael Kleiber . Ralph Joh D3.2 Properties at Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 Roland Span D4 Properties of Industrial Heat Transfer Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 D4.1 Refrigerants: Regulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 Ewald Preisegger . Felix Flohr D4.2 Cryostatic Bath Fluids, Aqueous Solutions, and Glycols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Gernot Krakat D4.3 Oil-based and Synthetic Heat Transfer Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458 Andreas Glück . Dietmar Hunold D5 Properties of Multicomponent Fluid Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 D5.1 Calculation of Vapor–Liquid Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 Andreas Pfennig D5.2 Polymer Solutions: Vapor–Liquid Equilibrium and Diffusion Coefficients . . . . . . . . . . . . . . . . . . . . . . 527 Wilhelm Schabel D5.3 Vapor Pressures of Aqueous Salt Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534 Hartwig Wolf D6 Properties of Solids and Solid Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 D6.1 Thermodynamic Properties of Pure Metals and Metal Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 Matthias Neubronner . Thomas Bodmer D6.2 Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566 Christof Hübner . Paul Bernd Kempa D6.3 Thermal Conductivity of Packed Beds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570 Evangelos Tsotsas D6.4 Industrial Refractories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 Axel Eschner D6.5 Insulations Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591 Günther Kasparek Table of Contents D6.6 Thermal Conductivity of Insulation Materials Depending on Moisture Content and Temperature . . . 595 Fabian Ochs . Hans Müller-Steinhagen D6.7 Thermal Conductivity of Building Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601 Hans Werner . Martin H. Spitzner E Heat Conduction E1 Steady-State Heat Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617 Erich Hahne E2 Transient Conduction in Stagnant Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637 Holger Martin F Free Convection F1 Heat Transfer by Free Convection: Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663 André Thess F2 Heat Transfer by Free Convection: External Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667 Werner Kast . Herbert Klan . (Revised by André Thess) F3 Heat Transfer by Free Convection: Internal Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673 André Thess F4 Heat Transfer by Free Convection: Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681 Werner Kast . Herbert Klan . (Revised by André Thess) F5 Thermal Output of Heating Appliances Operating with Hot Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685 Werner Kast . Herbert Klan . (Revised by André Thess) G Forced Convection G1 Heat Transfer in Pipe Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693 Volker Gnielinski G2 Heat Transfer in Concentric Annular and Parallel Plate Ducts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701 Volker Gnielinski G3 Heat Transfer in Helically Coiled Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709 Volker Gnielinski G4 Heat Transfer in Flow Past a Plane Wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713 Volker Gnielinski G5 Heat Transfer to Single Cylinders, Wires, and Fibers in Longitudinal Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 717 Holger Martin . Bernhard Gampert G6 Heat Transfer in Cross-flow Around Single Tubes, Wires, and Profiled Cylinders . . . . . . . . . . . . . . . . . . . . . 723 Volker Gnielinski G7 Heat Transfer in Cross-flow Around Single Rows of Tubes and Through Tube Bundles . . . . . . . . . . . . . . . . 725 Volker Gnielinski G8 Shell-Side Heat Transfer in Baffled Shell-and-Tube Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 Edward S. Gaddis . Volker Gnielinski xi xii Table of Contents G9 Fluid-Particle Heat Transfer in Flow Through Packed Beds of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743 Volker Gnielinski G10 Impinging Jet Flow Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745 Wilhelm Schabel . Holger Martin H Boiling H1 Fundamentals of Bubble Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755 Karl Stephan H2 Pool Boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757 Dieter Gorenflo . David Kenning H3 Flow Boiling – An Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793 Matthias Kind H3.1 Flow Patterns in Evaporator Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796 Dieter Steiner . Matthias Kind H3.2 Pressure Drop in Evaporator Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 801 Jogindar Mohan Chawla . Matthias Kind H3.3 Subcooled Boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804 Matthias Kind . Jens-Jürgen Schröder H3.4 Saturated Flow Boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813 Matthias Kind . Yasushi Saito H3.5 Critical Boiling States in Flowing Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832 Hein Auracher . Oliver Herbst H3.6 Postdryout Heat Transfer in Flow Boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 870 Anastassios Katsaounis . Matthias Kind H3.7 Flow Boiling of Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887 Dieter Steiner . Matthias Kind . Yasushi Saito H3.8 Special Symbols and References Used and Cited in Subchaps. H3.1–H3.7 . . . . . . . . . . . . . . . . . . . . . 892 Matthias Kind J Condensation J1 Filmwise Condensation of Pure Vapors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905 Reiner Numrich . Jürgen Müller J2 Film Condensation of Binary Mixtures with and without Inert Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919 Ernst-Ulrich Schlünder J3 Dropwise Condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933 Alfred Leipertz J4 Mixing and Spray Condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 939 Ulrich Hochberg Table of Contents K Radiation K1 Radiation of Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 947 Stephan Kabelac . Dieter Vortmeyer K2 View Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 961 Dieter Vortmeyer . Stephan Kabelac K3 Gas Radiation: Radiation from Gas Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 979 Dieter Vortmeyer . Stephan Kabelac K4 Thermal Radiation of Gas–Solids–Dispersions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 989 Hans-Gerd Brummel K5 Heat Radiation in Furnaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1001 Wolfgang Richter . Klaus Görner K6 Superinsulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1013 Harald Reiss L Fluid Dynamics and Pressure Drop L1 Pressure Drop in Single Phase Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055 L1.1 Pressure Drop in Single Phase Flow in Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055 Werner Kast . (Revised by Hermann Nirschl) L1.2 Pressure Drop in Flow Through Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1057 Werner Kast . (Revised by Hermann Nirschl) L1.3 Pressure Drop in Flow Through Pipes of Changing Cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065 Werner Kast . (Revised by Hermann Nirschl) L1.4 Pressure Drop of Tube Bundles in Cross Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076 Edward S. Gaddis L1.5 Pressure Drop in the Outer Shell of Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1092 Edward S. Gaddis L1.6 Pressure Drop in Fixed Beds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1106 Karl-Ernst Wirth L1.7 Pressure Drop in Orifices and Column Trays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1111 Johann Stichlmair L2 Two-Phase Gas-Liquid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1117 L2.1 Prediction of Void Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1117 Holger Schmidt L2.2 Pressure Drop in Tubes, Valves, and Fittings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125 Anton Wellenhofer . Sebastian Muschelknautz L2.3 Sizing of Safety Devices for Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137 Jürgen Schmidt xiii xiv Table of Contents L2.4 Calculating Critical Mass Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1150 Florian Schmidt L2.5 Flooding and Pressure Drop of Counter Current Gas-Liquid Flow in Vertical Pipes . . . . . . . . . . . . . 1164 Dieter Mewes L2.6 Pressure Drop and Flooding in Packed Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1169 Alfons Mersmann L2.7 Pressure Drop and Operating Limits of Trays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1178 Johann Stichlmair L3 Two-Phase Gas-Solid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1181 L3.1 Particle Motion in Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1181 Martin Sommerfeld L3.2 Flow Patterns and Pressure Drop in Fluidized Beds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1197 Karl-Ernst Wirth L3.3 Pressure Drop in Pneumatic Conveying Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1207 Ulrich Muschelknautz L3.4 Cyclones for the Precipitation of Solid Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1226 Ulrich Muschelknautz L4 Bubble and Drops in Technical Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1239 L4.1 Formation and Movement of Bubbles and Drops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1239 Norbert Räbiger . Michael Schlüter L4.2 Production and Mechanical Destruction of Foams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1254 Alfons Mersmann L4.3 Droplet Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1264 Hans Detlef Dahl M Specific Heat Transfer Problems M1 Heat Transfer to Finned Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1273 Klaus Gerhard Schmidt M2 Heat Transfer to Walls with Welded Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1279 Wolfgang Heidemann M3 Heat Transfer to Falling Films at Vertical Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1287 Günter Schnabel M4 Heat Transfer to Non-Newtonian Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1295 Manfred H. Wagner M5 Heat Transfer in Fluidized Beds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1301 Holger Martin M6 Heat Transfer from a Wall to Stagnant and Mechanically Agitated Beds . . . . . . . . . . . . . . . . . . . . . . . . . . . 1311 Evangelos Tsotsas M7 Heat and Mass Transfer in Packed Beds with Fluid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1327 Evangelos Tsotsas Table of Contents M8 Humidifying and Drying of Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1343 Manfred Zeller . Ulrich Busweiler M9 Convective Heat Transfer at High Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1363 Bernhard Weigand . Nimai-Kumar Mitra M10 Heat Transfer and Momentum Flux in Rarefied Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1375 Arnold Frohn . Norbert Roth . Klaus Anders M11 Spontaneous Condensation and Cavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1391 Karlheinz Schaber . Günter H. Schnerr N Specific Heat Transfer Devices N1 Heat Transfer in Regenerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1423 Helmuth Hausen . (Revised by Wolfgang Bender) N2 Combined Heat and Mass Transfer in Rotating Regenerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1435 Gerd Gaiser N3 Heat Transfer and Power Consumption in Stirred Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1451 Edward S. Gaddis N4 Cooling Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1485 Paul J. Erens N5 Heat Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1503 Peter Stephan N6 Pressure Drop and Heat Transfer in Plate Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1515 Holger Martin O Construction of Heat Exchangers O1 Hints on the Construction of Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1525 Günther Kirchner O2 Vibration of Tube Bundles in Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1553 Horst Gelbe . Samir Ziada xv Contributors Klaus Anders, Dr.-Ing.{ Stuttgart Germany Hein Auracher, Prof. Dr.-Ing. Stuttgart Germany heinaur@gmx.de Wolfgang Bender, Dipl.-Ing. VDEh-Betriebsforschungsinstitut GmbH Düsseldorf Germany Thomas Bodmer, Dipl.-Ing. Marl Germany thomas.bodmer@eon-energie.com Hans-Gerd Brummel, Dr.-Ing. Siemens Power Generation Berlin Germany hans-gerd.brummel@siemens.com Ulrich Busweiler, Prof. Dr.-Ing. Sachverständigenbüro Darmstadt Germany ulrich.busweiler@mmew.fh-giessen.de Jogindar Mohan Chawla, Prof. Dr.-Ing.{ Ettlingen Germany Hans Detlef Dahl, Dr.-Ing. Marl Germany h-dahl@versanet.de Paul J. Erens, Dr. Private Consulting Engineer Stellenbosch Republic of South Africa paulerens@snowisp.com Axel Eschner, Dr. Osterode (Harz) Germany Axel.Eschner@t-online.de { Deceased Felix Flohr, Dipl.-Ing. Solvay Fluor GmbH Hannover Germany Felix.Flohr@solvay.com Arnold Frohn, Prof. Dr. Universität Stuttgart Stuttgart Germany arnold.frohn@t-online.de Edward S. Gaddis, Dr.-Ing. Technische Universität Clausthal Clausthal-Zellerfeld Germany Edward.Gaddis@t-online.de Gerd Gaiser, Dr.-Ing. Reutlingen Germany Gerd.Gaiser@eberspaecher.com Bernhard Gampert, Prof. Dr.-Ing. habil. Universität Duisburg-Essen Essen Germany bfjg2008@gmx.de Horst Gelbe, Prof. Dr.-Ing. Technische Universität Berlin Berlin Germany h.gelbe@gmx.de Andreas Glück, Dr. HTT Vertriebsbüro Süd GmbH Ebersbach Germany a.glueck@htt.de Volker Gnielinski, Prof. Dr.-Ing. Karlsruher Institut für Technologie (KIT) Karlsruhe Germany volker.gnielinski@tvt.uka.de Dieter Gorenflo, Prof. Dr.-Ing. Universität Paderborn Paderborn Germany digo@thet.uni-paderborn.de xviii Contributors Klaus Görner, Prof. Dr.-Ing. Universität Duisburg-Essen Essen Germany luat@uni-due.de Erich Hahne, Prof. Dr.-Ing. Universität Stuttgart Stuttgart Germany hahne@itw.uni-stuttgart.de Günther Kasparek, Dr.-Ing. Munich Germany guenther.kasparek@t-online.de Werner Kast, Prof. Dr.-Ing. Technische Universität Darmstadt Darmstadt Germany Helmuth Hausen, Dr.-Ing.{ Hannover Germany Anastassios Katsaounis, Prof. Dipl.-Ing. Beuth Hochschule für Technik Berlin Berlin Germany akatsaounis@arcor.de Wolfgang Heidemann, Dr.-Ing. Universität Stuttgart Stuttgart Germany heidemann@itw.uni-stuttgart.de Paul Bernd Kempa, Dr. Fraunhofer-Institut für Chemische Technologie (ICT) Pfinztal Germany paul-bernd.kempa@ict.fraunhofer.de Oliver Herbst, Dr. AREVA NP GmbH Erlangen Germany Oliver.Herbst@areva.com David Kenning, Prof. Dr. Brunel and Oxford Universities UK David.Kenning@brunel.ac.uk Ulrich Hochberg, Prof. Dr.-Ing. Hochschule Offenburg University of Applied Sciences Offenburg Germany Ulrich.Hochberg@FH-Offenburg.de Christof Hübner, Dr.-Ing. Fraunhofer-Institut für Chemische Technologie (ICT) Pfinztal Germany christof.huebner@ict.fraunhofer.de Dietmar Hunold, Dr.-Ing. HTT Energy Systems GmbH Herford Germany d.hunold@htt.de Ralph Joh, Dr. rer. nat. Siemens AG Frankfurt Germany ralph.joh@siemens.com Stephan Kabelac, Prof. Dr.-Ing. Helmut-Schmidt-Universität Universität der Bundeswehr Hamburg Hamburg Germany Kabelac@hsu-hh.de Matthias Kind, Prof. Dr.-Ing. Karlsruher Institut für Technologie (KIT) Karlsruhe Germany matthias.kind@kit.edu Günther Kirchner, Dipl.-Ing. BASF SE, Ludwigshafen Germany guenther.kirchner@basf.com Herbert Klan, Dr.-Ing. Technische Universität Darmstadt Darmstadt Germany Michael Kleiber, Dr.-Ing. Uhde GmbH Bad Soden Germany michael.kleiber@thyssenkrupp.com Gernot Krakat FRAGOL Schmierstoffe GmbH & Co. Mülheim (Ruhr), Germany g.krakat@fragol.de Rolf Krauss, Dipl.-Ing. Universität Stuttgart Stuttgart Germany krauss@itt.uni-stuttgart.de Contributors Hans-Joachim Kretzschmar, Prof. Dr.-Ing. habil. Hochschule Zittau/Görlitz University of Applied Sciences Zittau Germany HJ.Kretzschmar@hs-zigr.de Alfred Leipertz, Prof. Dr.-Ing. Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen Germany sek@ltt.uni-erlangen.de Xing Luo, Prof. Dr.-Ing. Helmut-Schmidt-Universität Universität der Bundeswehr Hamburg Hamburg Germany luoxing1122@hotmail.com Holger Martin, Prof. Dr.-Ing. Karlsruher Institut für Technologie (KIT) Karlsruhe Germany holger.martin@kit.edu Alfons Mersmann, Prof. Dr.-Ing. Technische Universität München Munich Germany alfons.mersmann@online.de Dieter Mewes, Prof. Dr.-Ing. Dr. h. c. Leibniz Universität Hannover Hannover Germany mewes@imp.uni-hannover.de Nimai-Kumar Mitra, Prof. Dr.-Ing{ Bochum Germany Matthias Neubronner, Dr.-Ing. EON Energie Munich Germany matthias.neubronner@eon-energie.com Hermann Nirschl, Prof. Dr.-Ing. habil. Karlsruher Institut für Technologie (KIT) Karlsruhe Germany hermann.nirschl@kit.edu Reiner Numrich, Prof. Dr.-Ing. Paderborn Germany r.numrich@numrich-gev.de Fabian Ochs, Dipl.-Ing. Universität Stuttgart Stuttgart Germany fabian.ochs@gmx.net Andreas Pfennig, Prof. Dr.-Ing. RWTH Aachen Aachen Germany andreas.pfennig@avt.rwth-aachen.de Ewald Preisegger, Dipl.-Ing. Solvay Fluor GmbH Hannover Germany familie.preisegger@gmx.de Norbert Räbiger, Prof. Dr.-Ing. Universität Bremen Bremen Germany nraebiger@iuv.de Jürgen Müller, Dr.-Ing. BASF AG Ludwigshafen Germany juergen.mueller@basf-ag.de Harald Reiss, Prof. Dr. rer. nat. Julius-Maximilians-Universität Würzburg Würzburg Germany Hans Müller-Steinhagen, Prof. D. Eng. Dr.-Ing. Universität Stuttgart Stuttgart Germany Hans.Mueller-Steinhagen@dlr.de Wolfgang Richter, Dr.-Ing.{ Essen Germany Sebastian Muschelknautz, Dr.-Ing. Linde AG, Pullach Germany sebastian.muschelknautz@linde-le.com Wilfried Roetzel, Prof. Dr.-Ing. Helmut-Schmidt-Universität Universität der Bundeswehr Hamburg Hamburg Germany Wilfried.Roetzel@hsu-hh.de Ulrich Muschelknautz, Prof. Dr.-Ing. MK Engineering Innsbruck Austria um@mkengineering.de Norbert Roth, Dr.-Ing. Universität Stuttgart Stuttgart Germany norbert.roth@itlr.uni-stuttgart.de xix xx Contributors Yasushi Saito, Dr. Eng. Kyoto University Osaka Japan ysaito@rri.kyoto-u.ac.jp Günter H. Schnerr, Prof. Dr.-Ing. habil. Technische Universität München Garching Germany Schnerr@flm.mw.tu – muenchen.de Wilhelm Schabel, Prof. Dr.-Ing. Karlsruher Institut für Technologie (KIT) Karlsruhe Germany wilhelm.schabel@kit.edu Jens-Jürgen Schröder, Dr.-Ing.{ Hannover Germany Karlheinz Schaber, Prof. Dr.-Ing. Karlsruher Institut für Technologie (KIT) Karlsruhe Germany Karlheinz.Schaber@KIT.edu Ernst-Ulrich Schlünder, Prof. Dr.-Ing. Dr. h. c. Karlsruher Institut für Technologie (KIT) Karlsruhe Germany Michael Schlüter, Prof. Dr.-Ing. Technische Universität Hamburg-Harburg Hamburg Germany michael.schlueter@tu-harburg.de Florian Schmidt, Dr.-Ing. Bayer Technology Services GmbH Krefeld Germany florian.schmidt@bayertechnology.com Holger Schmidt, Dr.-Ing. Areva NP GmbH Erlangen Germany Holger.Schmidt@areva.com Jürgen Schmidt, Prof. Dr.-Ing. BASF SE Ludwigshafen Germany juergen.schmidt@onlinehome.de Martin Sommerfeld, Prof. Dr.-Ing. habil. Martin-Luther-Universität Halle-Wittenberg Halle (Saale) Germany martin.sommerfeld@iw.uni-halle.de Roland Span, Prof. Dr.-Ing. Ruhr-Universität Bochum Bochum Germany roland.span@thermo.rub.de Bernhard Spang, Dr.-Ing. BUCO Wärmeaustauscher International GmbH Geesthacht Germany bernhard@spang-hh.de Martin H. Spitzner, Dr.-Ing. FIW München Gräfelfing Germany Dieter Steiner, Prof. Dr.-Ing.{ Karlsruhe Germany Karl Stephan, Prof. Dr.-Ing. Universität Stuttgart Stuttgart Germany stephan.karl1@gmx.de Peter Stephan, Prof. Dr.-Ing. Technische Universität Darmstadt Darmstadt Germany pstephan@ttd.tu-darmstadt.de Klaus Gerhard Schmidt, Prof. Dr.-Ing. Institut für Energie- und Umwelttechnik (IUTA) e.V. Duisburg Germany k.schmidt@iuta.de Johann Stichlmair, Prof. Dr.-Ing. Technische Universität München Garching Germany Johann.Stichlmair@apt.mw.tum.de Günter Schnabel, Dr.-Ing. BIDECO GmbH Biberach (Riss) Germany guenter.schnabel@bideco.de André Thess, Prof. Dr.-Ing. Technische Universität Ilmenau Ilmenau Germany tthess@tu-ilmenau.de Contributors Evangelos Tsotsas, Prof. Dr.-Ing. Otto-von-Guericke-Universität Magdeburg Magdeburg Germany evangelos.tsotsas@vst.uni-magdeburg.de Dieter Vortmeyer, Prof. Dr. Munich Germany Manfred H. Wagner, Prof. Dr.-Ing. Technische Universität Berlin Berlin Germany manfred.wagner@tu-berlin.de Wolfgang Wagner, Prof. Dr.-Ing. Ruhr-Universität Bochum Bochum Germany wagner@thermo.rub.de Bernhard Weigand, Prof. Dr.-Ing. Universität Stuttgart Stuttgart Germany itlr@itlr.uni-stuttgart.de Anton Wellenhofer, Dipl.-Ing. Linde AG, Pullach Germany anton.wellenhofer@linde-le.com Hans Werner, Prof. Dr.-Ing. Hochschule für Angewandte Wissenschaften (FH) München Germany dr.hans.werner@t-online.de Karl-Ernst Wirth, Prof. Dr.-Ing. Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen Germany k.e.wirth@lfg.uni-erlangen.de Hartwig Wolf, Dr.-Ing. Alstom Switzerland Ltd. Baden Switzerland hartwig.wolf@power.alstom.com Manfred Zeller, Prof. Dr.-Ing. RWTH Aachen Aachen Germany manfred.zeller@rwth-aachen.de Samir Ziada, Prof. Dr.-Ing. McMaster University Hamilton, ON Canada ziadas@mcmaster.ca xxi Part A Symbols, Units and Dimensionless Numbers A1 Symbols and Units A1 Symbols and Units Matthias Kind . Holger Martin Karlsruher Institut für Technologie (KIT), Karlsruhe, Germany 1 Introduction: Legal Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 SI Base Units of Base Quantities. . . . . . . . . . . . . . . . . . . . . . . 3 3 SI Derived Units with Special Names and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4 4.1 4.2 Quantities and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 Introduction: Legal Units ‘‘The International Committee for Weights and Measures’’ (BIPM, Paris) publishes the ‘‘SI Brochure’’ [1]. Most of the base and derived units used in this VDI-Heat Atlas are SI units and are assorted below. The SI units are the units that are recognized globally in order to establish a worldwide dialog 2 5 Non-SI Units Accepted for Use with the SI, and Units Based on Fundamental Constants . . . . . . . . . . . . . . . 7 6 Other Non-SI Units Not Recommended for Use . . . . . . . 7 7 SI Prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 8 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 and can be seen in the further reading. Although there are a variety of non-SI units for the same quantity in the literature, only some of them can be found below due to the fact that not all of them are widely used [2, 3]. As of October 2007, there are 51 Member States of the Metre Convention and 25 Associate States and Economies of the General Conference. SI Base Units of Base Quantities Quantity Symbol of the quantity Length L, x, y, z, r,. . . Meter m Mass M, m Kilogram kg Time t Second s Electric current I, i Ampere A Thermodynamic temperature T Kelvin K Amount of substance N Mol mol Luminous intensity Iv Candela cd 3 Unit Symbol of the unit SI Derived Units with Special Names and Symbols SI coherent derived unita Quantity Symbol of the quantity Symbol of Expressed in terms Expressed in terms the unit of other SI units of SI base units Plane angle a, b, g,. . . Solid angle a, b, g,. . . Steradian Frequency f Hertzc Hz Force F Newton N Unit Radianb rad b c sr 1b m/m 1b m2/m2 s1 m kg s2 2 m1 kg s2 Pressure, stress p, P, s, t Pascal Pa N/m Energy, work, amount of heat Joule J Nm m2 kg s2 Power, heat flow E, W, Q P, Q_ Watt W J/s m2 kg s3 Electric charge, amount of electricity Q Coulomb C VDI-GVC (ed.), VDI Heat Atlas, DOI 10.1007/978-3-540-77877-6_1, # Springer-Verlag Berlin Heidelberg 2010 sA 4 A1 Symbols and Units SI coherent derived unita Quantity Symbol of the quantity Symbol of Expressed in terms Expressed in terms the unit of other SI units of SI base units Electric potential U Volt V W/A m2 kg s3 A1 Capacitance C Farad F C/V m2 kg1 s4 A2 Electric resistance R Ohm O V/A m2 kg s3 A2 Electric conductance G Siemens S A/V m2 kg1 s3 A2 Magnetic flux F Weber Wb Vs Unit m2 kg s2 A1 kg s2 A1 2 Magnetic flux density B Tesla T Wb/m Inductance L Henry H Wb/A Celsius temperature # Degree Celsiusd Luminous flux I Lumen lm cd sre cd Illuminance E Lux lx lm/m2 m2 cd Activity referred to a radionuclide f Becquerel Absorbed dose, specific energy (imparted), kerma c Gray g m2 kg s2 A2 C K s1 Bq Gy J/kg m2 s2 J/kg m2 s2 Dose equivalent, ambient dose equivalent, directional dose equivalent, personal dose equivalent Sievert Sv Catalytic activity Katal kat s1 mol a The SI prefixes (see Sect. 7) may be used with any of the special names and symbols, but when this is done, the resulting unit will no longer be coherent. Radian and steradian are special names for the number 1 that may be used to convey information about the quantity concerned. In practice, the symbols rad and sr are used where appropriate, but the symbol for the derived unit 1 is generally omitted in specifying the values of dimensionless quantities. c Hertz is used only for periodic phenomena, and Becquerel is used only for stochastic processes in activity referred to a radionuclide. d Degree Celsius is the special name for Kelvin, which is used to express Celsius temperatures. Degree Celsius and the Kelvin are equal in size, so that the numerical value of a temperature difference or temperature interval is the same when expressed in either degree Celsius or Kelvin. e In photometry, the name steradian and the symbol sr are usually retained in expression for units. f Activity referred to a radionuclide is sometimes incorrectly called radioactivity. g See http://www.bipm.org/en/CIPM/db/2002/2/ on the use of the sievert. b 4 Quantities and Symbols The following alphabetically listed symbols are generally used in the Heat Atlas. Other more specific notations and symbols, which may differ from the ones listed here are defined within the special sections if needed. 4.1 Quantities Quantity Symbol of the quantity Symbol of the unit 2 Acceleration of gravity g ms Amount of substance N mol 1 Quantity Symbol of the quantity Dynamic viscosity Symbol of the unit Pa s Emissivity e 1 Energy E J Enthalpy H H_ J Enthalpy stream Entropy S J K1 W Gibbs enthalpy G J Heat J Heat flow Q Q_ W Heat flux q_ W m2 Coefficient of thermal expansion b K Coordinate in flow direction x m Heat transfer coefficient a W m2 K1 Coordinate perpendicular to flow direction y m Hydraulic diameter dh = 4 cross-sectional area/circumference dh m Coordinate perpendicular to flow direction z m Individual gas constant R J kg1 K1 Internal energy U J Cross-sectional area A, S m2 Kinematic viscosity n m2 s1 Density r kg m3 Length L, l m Diameter D m Mass kg Diffusion coefficient Dij, dij m2 s1 Mass flow rate M, m _ M kg s1 A1 Symbols and Units Quantity Symbol of the quantity Mass flux _ m Symbol of the unit kg m2 s1 1 Mass fraction of component j in the xj, yj liquid or vapor phase, respectively kg kg Mass loading of component j in the liquid or vapor phase, respectively Xj, Yj kg kg1 Mass transfer coefficient of a component i bi m s1 Molar density n e h mol m3 J mol1 K1 Molar flow es N_ mol s Molar flux n_ mol m2 s1 Molar Gibbs enthalpy e g J mol1 Molar heat capacity at constant pressure or volume respectively ecp , ecv J mol1 K1 Molar enthalpy Molar entropy Molar internal energy Molar mass e u e M ej Molar loading of component j in the Xej , Y liquid or vapor phase, respectively Molar volume e v J mol1 1 J mol1 A m A, S m2 Surface, phase interphase Cross-sectional area 1 m2 s1 D M Diameter dh m Hydraulic diameter dh = 4 cross-sectional area/circumference E J Energy G J Gibbs enthalpy g J kg1 Specific Gibbs enthalpy e g J mol1 Molar Gibbs enthalpy g m s2 Acceleration of gravity H H_ J Enthalpy W Enthalpy stream h e h J kg1 Specific enthalpy ms 1 Specific enthalpy h J kg1 Specific entropy s J kg1 K1 Specific Gibbs enthalpy g J kg1 Specific heat capacity at constant pressure or volume, respectively c p , cv J kg1 K1 1 Specific internal energy u J kg Specific volume v m3 kg1 Surface, phase interphase A m2 Universal gas constant Quantity Dij M 1 Nm K 1 l Wm k 2 p e R Unit 2 J mol1 K1 Molar heat capacity at constant pressure or volume respectively r Total pressure Symbol of the quantity ecp , ecv m mol Radius t Symbols 1 W m2 K4 Time 4.2 Specific heat capacity at constant pressure or volume respectively 3 C T m J Radiation coefficient Radiation coefficient Thermodynamic temperature s W J kg1 K1 Pa; bar Thermal diffusivity Wall thickness Work cp, cv mol mol W Thermal conductivity m3 Velocity of sound pj y V W m2 K4 P Temperature difference (or centigrade temperature) Volume ms Power s 1 C Partial pressure of component j Surface tension c a W m2 K1 k Voidage, gas volume fraction m3 s1 1 Overall heat transfer coefficient Overall mass transfer coefficient m s1 Volumetric flow rate c V_ Velocity of sound kg kmol1 mol mol1 0 Symbol of the unit Latin letters Mole fraction of component j in the e xj , e yj liquid or vapor phase, respectively k Symbol of the quantity Quantity 1 K 1 m s K s Pa; bar J mol 1 K 1 Diffusion coefficient J mol1 2 Molar enthalpy K 1 Overall heat transfer coefficient k Wm k0 m s1 Overall mass transfer coefficient W _ W J Work W Power L, l m Length M e M kg Mass kg kmol1 Molar mass _ M kg s1 Mass flow rate 2 1 _ m kg m N N_ mol Amount of substance mol s1 Molar flow n mol m3 Molar density s Mass flux Vapor quality (ratio of vapor mass flow/total mass flow) x_ Vapor pressure of component j p0j Pa; bar n_ mol m2 s1 Molar flux Velocity in x-direction u m s1 p Pa; bar Total pressure pj Pa; bar Partial pressure of component j p0j Pa; bar Vapor pressure of component j 1 1 Velocity in y-direction v ms Velocity in z-direction w m s1 5 6 A1 Symbols and Units Symbol of the quantity Unit Quantity Symbol of the quantity Unit 2 1 Quantity Q Q_ J Heat k m s Thermal diffusivity W Heat flow l W m1K1 Thermal conductivity q_ W m2 Heat flux n m2 s1 Kinematic viscosity 1 1 3 R e R J kg Individual gas constant r kg m Density J mol1 K1 Universal gas constant s N m1 Surface tension r m c 1 Voidage, gas volume fraction K Radius 1 Entropy S JK s J kg1 K1 1 1 Specific entropy es J mol s m Wall thickness T K Thermodynamic temperature t s U J K Molar entropy Time Internal energy 1 Specific internal energy Subscripts to denote Phase F Fluid phase G Gas phase L Liquid phase S Solid phase u J kg e u J mol1 Molar internal energy u m s1 Velocity in x-direction V V_ m3 Volume I Initial value m s Volumetric flow rate t Instantaneous value v M3 kg1 Specific volume F Final value 1 3 1 Time e v m mol Molar volume v m s1 Velocity in y-direction w m s1 Velocity in z-direction o Outside Xj, Yj kg kg1 Mass loading in the liquid or vapor phase out At the exit in At the inlet i Inside loc Local value s At the surface w At the wall ej , Yej X xj, yj 3 mol mol1 kg kg1 Molar mass loading in the liquid or vapor phase of component j, respectively Mass fraction in the liquid or vapor phase of component j, respectively 1 e yj xj , e mol mol Mole fraction in the liquid or vapor phase x_ 1 Vapor quality (ratio of vapor mass flow/total mass flow) x m Coordinate in flow direction y m Coordinate perpendicular to flow direction z m Coordinate perpendicular to flow direction Greek letters Unit Quantity a W m2 K1 Heat transfer coefficient bi m s1 Mass transfer coefficient of a component i b K1 Coefficient of thermal expansion e State c At the critical point p At constant pressure r Relative (related to the corresponding value at the critical point) v At constant volume ´, ´´, (Superscripts) at the phase boundaries Process Symbol of the quantity dij Position 2 1 m s 1 lam In laminar flow turb In turbulent flow rev Reversible Others Diffusion coefficient tot Total Emissivity LM Logarithmic mean Mean Pa s Dynamic viscosity m y K Temperature difference (or centigrade temperature) G0 Total mass flow as gas L0 Total mass flow as liquid A1 Symbols and Units 5 Non-SI Units Accepted for Use with the SI, and Units Based on Fundamental Constants Quantity Symbol of the quantity Name of the unit Symbol of the unit Time t Minute min 1 min = 60 s Houra h 1 h = 60 min = 3,600 s day d 1 d = 24 h = 86,400 s 1 = (p/180) rad Plane angle a, b, g,. . . Degree b,c ‘ 1‘ = (1/60) = (p/10,800) rad d ‘‘ 1‘‘ = (1/60)‘ = (p/648,000) rad e ha 1 ha = 1 hm2 = 104 m2 L, l 1 L = 1 l = 1 dm3 = 103 cm3 = 103 m3 t 1 t = 103 kg Minute Second Area A, S Volume Hectare V Mass Liter M, m Ton Value in SI unit f g a The symbol of this unit is included in ‘‘Resolution 7’’ of the 9th CGPM (1948). ISO 31 recommends that the degree be divided decimally rather than using minute and second. For navigation and surveying, however, minute has the advantage that one minute of latitude on the surface of the Earth corresponds (approximately) to one nautical mile. c Gon (or grad(e), where grad is an alternative name for the gon) is an alternative unit of plane angle to the degree, defined as (p/200) rad. Thus, there are 100 gon in a right angle. The potential value of gon in navigation is that because the distance from the pole to the equator of the Earth is approximately 10,000 km, 1 km on the surface of the Earth subtends an angle of one centigon at the center of the Earth. However, gon is rarely used. d For applications in astronomy, small angles are measured in arcseconds (i.e., seconds of plane angle), denoted as ‘‘milliarcseconds, microarcseconds, and picoarcseconds, denoted as mas, μas, and pas,’’ respectively, where arcsecond is an alternative name for second of plane angle. e The unit hectare and its symbol ha were adopted by the CIPM in 1879 (PV, 1879, 41). Hectare is used to express land area. f Liter and the symbol lower case l were adopted by the CIPM in 1879 (PV, 1879, 41). The alternative symbol, capital L, was adopted by the 16th CPGM (1979, ‘‘Resolution 6’’) in order to avoid the risk of confusion between the letter l (el) and the numeral 1 (one). g Ton and its symbol t were adopted by the CIPM in 1879 (PV, 1879, 41). In English-speaking countries, this unit is usually called ‘‘metric ton.’’ b 6 Other Non-SI Units Not Recommended for Use Values in boldface are exact Energy (includes work) Calorie (15 C), 1 cal15 Acceleration Foot per second squared, 1 ft/s2 Inch per second squared, 1 in/s2 = 3.048 · 101 = 2.54 · 10 2 m/s2 m/s 2 = 4.185 80 J Calorie (20 C), 1 cal20 = 4.181 90 J Electronvolt, 1 eV = 1.602 177 · 1019 J Erg, 1 erg = 1.0 · 107 J Energy divided by area time Angle 1 Mil = 5.625 · 10 1 Revolution1 = 6.283 185 2 Erg per square centimeter second, 1 erg/(cm2 · s) = 1.0 · 103 W/m2 rad Flow, see mass divided by time, or see volume divided by time Area and second moment of area Force Square foot, 1 ft2 = 9.290 304 · 102 m2 Square inch, 1 in2 = 6.451 6 · 104 m2 Square mile, 1 mi2 = 2.589 988 · 104 m2 Dyne, 1 dyn = 1.0 · 105 N Kilogram-force, 1 kgf = 9.806 65 N Force divided by area, see pressure Capacity, see volume Force divided by length Density, see mass divided by volume Pound-force per foot, 1 lbf/ft = 1.459 390 · 101 N/m = 3.725 895 · 104 J/m3 Electricity and magnetism Biot, 1 Bi Franklin, 1 Fr Gamma, 1 g = 1.0 · 101 A 10 = 3.335 641 · 10 = 1.0 · 10 9 C T Heat, available energy British thermal unitIT per cubic foot, 1 BtuIT/ft3 7 8 A1 Symbols and Units British thermal unitth per cubic foot, 1 Btuth/ft3 = 3.723 403 · 104 J/m3 Heat, coefficient of heat transfer British thermal unitth per second square foot degree Fahrenheit, 1 Btuth/(s · ft2 · F) = 2.042 808 · 104 W/(m2 · K) = 4.184 · 104 J/m2 = 6.973 333 · 102 W/m2 Calorieth per square centimeter, 1 calth/cm2 Heat, density of heat flow rate Heat, fuel consumption Gallon (US) per horsepower hour, 1 gal/(hp · h) Degree Fahrenheit second per British thermal unitIT, 1 F · s/BtuIT = 5.265 651 · 104 K/W Degree Fahrenheit second per British thermal unitth 1 F · s/Btuth = 5.269 175 · 104 K/W Heat, thermal resistivity Heat, density of heat Calorieth per square centimeter minute, 1 calth/(cm2 · min) Heat, thermal resistance = 1.141 089 · 109 m3/J Heat, heat capacity and entropy Degree Fahrenheit hour square foot per British thermal unitIT inch [ F · h · ft2/(BtuIT · in)] = 6.933 472 m · K/W Length Angström, 1 Å = 1.0 · 1010 m Micron, 1 mm = 1.0 · 106 m Mil (0.001 in), 1 mil = 2.54 · 105 m 3 Mile, 1 mi = 1.609 344 · 10 Yard, 1 yd = 9.144 · 101 m m Light British thermal unitIT per degree Fahrenheit, 1 BtuIT/ F 3 = 1.899 101 · 10 J/K Candela per square inch, 1 cd/in2 = 1.550 003 · 103 cd/m2 British thermal unitth per degree Fahrenheit, 1 Btuth/ F = 1.897 830 · 103 J/K Lumen per square foot, 1 lm/ft2 = 1.076 391 · 101 lx Grain, 1 gr = 6.479 891 · 105 kg Ounce (avoirdupois), 1 oz = 2.834 952 · 102 kg Mass and moment of inertia Heat, heat flow rate Calorieth per minute, 1 calth/min = 6.973 333 · 10 2 W = 4.186 8 · 103 Calorieth per gram kelvin, 1 calth/(g · K) = 4.184 · 103 = 3.110 348 · 10 J/(kg · K) Pound (avoirdupois) (*1), 1 lb = 4.535 924 · 101 kg = 3.732 417 · 101 kg J/(kg · K) Pound (troy or apothecary), 1 lb Ton, assay, 1 AT = 2.916 667 · 102 kg Ton, metric, 1 t Heat, thermal conductivity Calorieth per centimeter second degree Celsius, 1 calth/(cm · s · C) = 4.184 · 102 W/(m · K) 3 = 1.0 · 10 kg Mass density see mass divided by volume Mass divided by area Heat, thermal diffusivity Square foot per hour, 1 ft2/h kg Ounce (troy or apothecary), 1 oz Heat, specific heat capacity and specific entropy CalorieIT per gram kelvin, 1 calIT/(g · K) 2 = 2.580 64 · 105 m2/s Heat, thermal insulance Clo, 1 clo = 1.55 · 101 m2 · K/W Degree Fahrenheit hour square foot per British thermal unitIT, 1 F · h · ft2/BtuIT = 1.761 102 · 101 m2 · K/W Degree Fahrenheit hour square foot per British thermal unitth, 1 F · h · ft2/Btuth = 1.762 280 · 101 Ounce (avoirdupois) per square foot, 1 oz/ft2 = 3.051 517 · 101 kg/m2 Ounce (avoirdupois) per square inch, 1 oz/in2 = 4.394 185 · 101 kg/m2 Pound per square foot, 1 lb/ft2 = 4.882 428 kg/m2 Mass divided by capacity see mass divided by volume Mass divided by length m2 · K/W Denier, 1 denier = 1.111 111 · 107 kg/m Mass divided by time (includes flow) Pound per hour, 1 lb/h = 1.259 979 · 104 kg/s A1 Symbols and Units Mass divided by volume (includes mass density and mass concentration) 2 3 Grain per gallon (U.S.), 1 gr/gal = 1.711 806 · 10 kg/m Pound per cubic foot, 1 lb/ft3 = 1.601 846 · 101 kg/m3 Temperature Degree Celsius, 1 C T/K = t/ C + 273.15 K Degree centigrade , 1 degree centigrade t/ C t/deg. cent. C Degree Fahrenheit, 1 F t/ C = (t/ F 32)/1.8 C (*5) Moment of force or torque Dyne centimeter, 1 dyn · cm = 1.0 · 107 N·m Kilogram-force meter, 1 kgf · m = 9.806 65 N·m Moment of force or torque divided by length 1 Pound-force foot per inch, 1 lbf · ft/in = 5.337 866 · 10 Pound-force inch per inch, 1 lbf · in/in = 4.448 222 N · m/m = 9.869 233 · 10-13 m2 Degree Rankine, 1 R T/K = (T/ R)/1.8 = 1.0 · 107 W Foot pound-force per hour, 1 ft · lbf/h = 3.766 161 · 104 W Horsepower (metric), 1 hp = 7.354 988 · 102 W Horsepower (U.K.), 1 hp = 7.457 0 · 102 W Horsepower (electric), 1 hp = 7.460 43 · 102 W Horsepower (boiler), 1 hp = 9.809 50 · 103 W Temperature Interval Degree Celsius, 1 C = 1.0 K Degree centigrade(*5), 1 degree centigrade = 1.0 C Degree Fahrenheit, 1 F = 5.555 556 · 101 C 1 Degree Fahrenheit, 1 F = 5.555 556 · 10 Degree Rankine, 1 R = 5.555 556 · 101 K K Day, 1 d = 8.64 · 104 s Year (365 days), 1 year = 3.153 6 · 107 s Torque, see moment of force Atmosphere, standard, 1 atm (*3) , Bar, 1 bar = 8.466 667 · 105 m/s Mile per hour, 1 mi/h = 4.470 4 · 101 m/s Viscosity, dynamic Centipoise, 1 cP = 1.0 · 103 Pa · s Poise, 1 P = 1.0 · 101 Pa · s Viscosity, kinematic Stokes, 1 St = 1.013 25 · 10 5 = 9.806 65 · 10 4 = 1.0 · 105 Pa Pa Pa 2 Millimeter of mercury, conventional (*4), 1 mmHg = 1.333 224 · 10 Pa Millimeter of water, conventional (*4), 1 mmH2O = 9.806 65 Pa Pound-force per square inch (psi), lbf/in2), 1 psi = 6.894 757 · 103 Pa Torr, 1 Torr = 1.333 224 · 102 Pa Radiology Curie, 1 Ci Foot per hour, 1 ft/h Centistokes, 1 cSt Pressure or stress (force divided by area) = 3.7 · 1010 2 Rad (absorbed dose), 1 rad = 1.0 · 10 Rem, 1 rem = 1.0 · 102 = 2.58 · 10 4 Bq Gy Sv C/kg = 1.0 · 106 = 1.0 · 10 m2/s 4 m2/s 2 = 9.290 304 · 10 m2/s Cubic foot, 1 ft3 = 2.831 685 · 102 m3 Liter (*6), 1 L = 1.0 · 103 m3 Square foot per second, 1 ft2/s Volume (includes capacity) Gallon (US), 1 gal = 3.785 412 · 10 3 m3 Volume divided by time Cubic foot per minute, 1 ft3/min = 4.719 474 · 104 m3/s Cubic foot per minute, 1 ft3/min = 4.719 474 · 101 L/s Cubic inch per minute, in3/min = 2.731 177 · 107 m3/s Cubic yard per minute, 1 yd3/min = 1.274 258 · 102 m3/s Gallon (U.S.) per minute (gpm), 1 gal/min = 6.309 020 · 105 m3/s Speed see velocity Stress see pressure K Velocity (includes speed) Erg per second, 1 erg/s Roentgen, 1 R T/K = t/ F + 459.67)/1.8 K Time Power Atmosphere, technical 1 at Degree Fahrenheit, 1 F N · m/m Permeability Darcy (*2), 1 darcy Work see energy 9 10 A1 Symbols and Units (*1) The exact conversion factor is 4.535 923 700 · 101. All units that contain pound refer to the avoirdupois pound. (*2) Darcy is a unit for expressing the permeability of porous solids, not area. (*3) One technical atmosphere equals one kilogram-force per square centimeter (1 at = 1 kgf/cm2). (*4) Conversion factors for mercury manometer pressure units are calculated using the standard value for the acceleration of gravity and the density of mercury at the stated temperature. Additional digits are not justified because the definitions of the units do not take into account the compressibility of mercury or the change in density caused by the revised practical temperature scale, ITS-90. Similar comments also apply to water manometer pressure units. (*5) The centigrade temperature scale is obsolete; the degree centigrade is only approximately equal to degree Celsius (*6) In 1964, the General Conference on Weights and Measures reestablished the name ‘‘liter or litre’’ as a special name for the cubic decimeter. Between 1901 and 1964, liter was slightly larger (1.000 028 dm3); when one uses highaccuracy volume data of that time, this fact must be kept in mind. 7 18 Decimal multipliers and parts of units can be described by means of prefixes that are written before the names of the units. Prefix Abbreviation 24 10 Yotta Y 1021 Zetta Z Prefix Abbreviation 10 Exa E 1015 Peta P 12 10 Tera T 109 Giga G 106 Mega M 10 Kilo k 102 Hecto h 101 Deca da 10 Deci d 102 Centi c 10 Milli m 106 Micro μ 109 Nano n 10 Pico p 1015 Femto f 1018 Atto a 1021 Zepto z 1024 Yocto y 3 1 3 12 8 SI Prefixes Factor Factor 1. 2. 3. Bibliography SI Brochure, 8th ed. The International Committee for Weights and Measures, 2006 http://www.bipm.org/ http://www.bipm.org/en/si/si_brochure/ Part B Fundamentals of Heat Transfer B1 Fundamentals of Heat Transfer B1 Fundamentals of Heat Transfer Peter Stephan Technische Universität Darmstadt, Darmstadt, Germany 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 Heat Transfer Modes and Basic Principles of Their Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Heat Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Convective Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Thermal Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1 2.2 2.3 3 3.1 3.1.1 3.1.2 3.2 3.2.1 3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.3.5 1 Heat Conduction and Overall Heat Resistances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 One-Dimensional, Steady State Heat Conduction Through a Wall. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Conduction Through a Plane Wall . . . . . . . . . . . . . . . . . . . . 20 Conduction Through a Tube Wall . . . . . . . . . . . . . . . . . . . . . 21 Heat Transmission, Overall Heat Resistances, and Overall Heat Transfer Coefficients . . . . . . . . . . . . . . . . . . . . . 21 Heat Transmission Through a Tube Wall. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Transient Heat Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Semi-Infinite Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Finite Heat Transfer at the Surface. . . . . . . . . . . . . . . . . . . . . 23 Two Semi-Infinite Bodies in Thermal Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Temperature Equalization in Simple Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Plane Plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Introduction The term heat is defined by the first law of thermodynamics as the energy that is transported across the boundary of a thermodynamic system due to a temperature difference between the system and its surroundings. The first law of thermodynamics in a general form can be written as follows: DE ¼ W þ Q þ EM : ð1Þ The right hand side of this equation summarizes the three different forms of energy that can be transported across the system boundary: heat Q, work W, and energy EM that is tied to a mass transport. As a result of such energy transfer across the system boundary the energy inside the system changes by DE, written on the left hand side of the equation. The transport process related to the transfer of heat is called heat transfer. Applying the second law of thermodynamics, one can derive that heat is always transferred in the direction of decreasing temperature. But thermodynamics does not tell us how the amount of heat transferred depends on this driving temperature difference or temperature gradient. Nor does it tell us how it depends on the geometry of a heat exchanger, or on material or VDI-GVC (ed.), VDI Heat Atlas, DOI 10.1007/978-3-540-77877-6_3, # Springer-Verlag Berlin Heidelberg 2010 3.3.6 Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3.7 Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.1.6 4.1.7 Convective Heat Transfer and Nusselt Numbers . . . . . 24 Single Phase Forced Convection . . . . . . . . . . . . . . . . . . . . . . . 25 Laminar Flow Along a Flat Plate. . . . . . . . . . . . . . . . . . . . . . . 25 Turbulent Flow Along a Flat Plate . . . . . . . . . . . . . . . . . . . . . 25 Flow Through Pipes in General. . . . . . . . . . . . . . . . . . . . . . . . 25 Laminar Flow Through Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Turbulent Flow Through Pipes . . . . . . . . . . . . . . . . . . . . . . . . 26 Single Pipe Placed Transversely in a Flow . . . . . . . . . . . . . 26 Row of Pipes Placed Transversely in a Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.1.8 Pipe Bundle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2 Single Phase Natural Convection . . . . . . . . . . . . . . . . . . . . . . 27 4.3 Heat Transfer in Condensation and Boiling . . . . . . . . . . . 27 4.3.1 Condensation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3.2 Boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5 5.1 5.2 5.3 Thermal Radiation and Radiative Heat Exchange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Emission, Absorption, and Transmission . . . . . . . . . . . . . . 28 Heat Exchange Between Two Bodies. . . . . . . . . . . . . . . . . . . 28 Gas Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 6 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 process properties, including the duration of the process. Before these dependencies can be described in detail some general relations and definitions must be given. The heat transferred per unit of time is referred to as the heat flow rate Q_ (SI-unit W), dQ : Q_ ¼ dt ð2Þ The heat flux q_ (SI-unit W/m2) is defined by q_ ¼ dQ_ dA ð3Þ and describes the heat transferred per unit of time and per unit area perpendicular to the heat flow. Generally, three modes of heat transfer are distinguished: ● Conduction, ● Convection, and ● Radiation. The detailed description of calculation procedures for heat transfer related to all these modes in general and for many specific technical applications is subject of the VDI Heat Atlas 18 B1 Fundamentals of Heat Transfer (Parts E–N). Additionally, fundamental heat exchanger design and construction methods as well as information on material properties are presented (Parts C, D, and O). In the following Chapters of Part B, the fundamentals of the three heat transfer modes and primary rules of calculation procedures are presented and applied in an exemplary manner to some basic configurations. For further details, the reader is referred to the specific parts of the VDI Heat Atlas. 2 Heat Transfer Modes and Basic Principles of Their Description 2.1 Heat Conduction Conduction is the transfer of energy due to molecular interactions between neighbouring molecules caused by their random motion. Thus, heat conduction can take place in solids, liquids, or gases, but it does not require any macroscopic motion or flow of the substance. With increasing temperature the random motion of molecules is intensified, and with this the kinetic energy on the molecular level. Collisions between neighboring molecules cause a transfer of energy from those with higher kinetic energy to those with lower kinetic energy. In metals, the energy transported by free electrons additionally contributes to heat conduction. Fortunately, we do not need to look closely into the details and statistics of these molecular processes to derive calculation procedures for heat conduction. It is sufficient to know a single material property together with the local driving temperature gradient. Considering a temperature gradient @T =@x in direction of a coordinate x, the heat flux q_ depends only on the single material property called thermal conductivity l. The relation q_ ¼ l @T @x ð4Þ is well-known as Fourier’s law, named after Jean Baptiste Joseph Fourier, who expressed this relation first in 1822 [1]. The minus sign results from the fact that positive heat transfer is directed toward decreasing temperature. For isotropic materials, i.e., materials with equal thermal conductivities in any direction, Fourier’s law can be written in vector form as ~ q_ ¼ l grad T : ð5Þ The thermal conductivity l [SI-unit W/(K m)] is typically highest for solids, followed by liquids and gases. For gases under normal conditions l is approximately in the range 0:015 W=ðK mÞ lgas 0:15 W=ðK mÞ with, e.g., hydrogen at the upper end and carbon dioxide at the lower end of the range. The thermal conductivity of air at atmospheric conditions is, e.g., lair 0:0246 W=ðK mÞ. For liquids (except liquid metals) under normal conditions l is approximately in the range 0:1 W=ðK mÞ lliquid 0:65 W=ðK mÞ with, e.g., water at the upper end and carbon dioxide or some organic liquids at the lower end of the range. The thermal conductivity of liquid water at atmospheric conditions is, e.g., lwater;liq: 0:6 W=ðK mÞ. For solids under normal conditions l is approximately in the range 1 W=ðK mÞ lsolid 450 W=ðK mÞ with, e.g., metallic materials such as silver and copper at the upper end and nonmetallic materials such as coal, glass, or ice at the lower end of the range. The thermal conductivity of ice (solid water) at 0 C is, e.g., lwater;ice 2:2 W=ðK mÞ, values for some metallic materials are lcopper 395 W=ðK mÞ, laluminum 220 W=ðK mÞ, or lst:steel;18Cr8Ni 21 W=ðK mÞ. Further data and details such as dependency on temperature or pressure can be found in Part D. 2.2 Convective Heat Transfer Convection refers to the heat transport mode in a macroscopically flowing fluid. It is a superposition of conductive heat transport in the fluid and the energy transport due to the macroscopic movement of the fluid, which includes the transport of enthalpy and kinetic energy. Thus, convective heat flux depends not only on material properties, but also on process properties, such as, e. g., fluid velocity. For the design of technical devices the descriptions of convective heat transfer from a moving bulk fluid to the solid fluid boundary (wall) or vice versa are of special interest. A situation with a bulk fluid temperature TF , a bulk fluid velocity wF parallel to the wall, and a wall temperature TW , will result in a velocity and a temperature profile in the fluid near the wall as shown in Fig. 1 where y is the direction normal to the wall. The near wall region with high velocity gradients and high temperature gradients are known as velocity boundary layer and temperature boundary layer. The underlying boundary layer theory was formulated first by Prandtl [2]. The convective heat transport normal to the wall in this boundary layer is directed towards the lower temperature, thus for TF > TW the wall is heated by the fluid, for TF < TW the wall is cooled by the fluid. The heat flux q_ depends on the temperature difference but also on the temperature and velocity profiles in the boundary layer, which can be very complex and even nonstationary, e.g., for turbulent boundary layer flows. However, the simple relation ð6Þ q_ ¼ aðTW TF Þ allows to calculate the heat flux. Herein, a is the heat transfer coefficient [SI-unit W=ðm2 KÞ]. This quantity depends on the relevant fluid and process properties as well as geometrical configurations of the wall or surface roughness, etc. The thickness of the thermal boundary layer dT can be approximated as the thickness of a fictitious nonmoving fluid layer adjacent to the wall that results in the same heat flux as the convective one given by Eq. (6). Figure 2 demonstrates this relationship. The temperature profile caused by convective heat transfer is approximated by a linear temperature drop TW TF in the fictitious nonmoving fluid layer and a constant Fundamentals of Heat Transfer B1 B1. Fig. 1. Boundary layers (left: velocity, right: temperature). general it is determined experimentally and correlations for many technical configurations were derived from such experiments. The basis for the description of the heat transfer coefficient is the use of similarity methods. These descriptions allow the considerable reduction of the number of influencing parameters and for the expression of the general heat transfer laws for geometrically similar bodies and different substances. For this purpose a dimensionless heat transfer coefficient, called Nusselt number named after Wilhelm Nusselt, who first formulated dimensionless numbers in this context [3], is defined by Nu ¼ B1. Fig. 2. Thickness dTl/a of the thermal boundary layer. fluid temperature TF outside. As the fluid is definitely at rest at the wall surface (y ¼ 0) due to the nonslip condition Fourier’s law for conduction [Eq. (4)] delivers the relation between heat flux and temperature gradient at the wall surface: @T ð7Þ q_ ¼ l : @y y¼0 Comparing Eqs. (6) and (7) the thickness of the fictitious nonmoving fluid layer adjacent to the wall follows as l=a, where l is the thermal conductivity of the fluid. With this the heat transfer coefficient can also be interpreted as @T @y y¼0 a ¼ l ð8Þ TW TF and the thermal boundary layer thickness can be approximated by dT l = a. Based on this theoretical approach the heat transfer coefficient a can be determined for some special cases. However, in aL ; l ð9Þ where L is a characteristic length of the system and l the thermal conductivity of the fluid. To derive correlations for the Nusselt number two situations have to be distinguished: forced convection and natural convection. In forced convection, the fluid motion is caused by outer forces, e.g., by the pressure increase in a pump. In natural convection, the fluid motion is caused by density differences in the fluid and the corresponding buoyancy effects in a gravitational field. These density differences usually arise due to temperature differences, rarely due to pressure differences. In mixtures, density differences are also caused by concentration differences. The flow characteristics in forced convection are generally described by the Reynolds number Re ¼ wL ; n ð10Þ where w is the bulk fluid velocity and n the kinematic viscosity of the fluid. The flow characteristics in natural convection are generally described by the Grashof number Gr ¼ L3 g b DT ; n2 ð11Þ where g is the gravitational acceleration, b the thermal volume expansion coefficient at a reference temperature [typically, ðTW þ TF Þ=2], and DT ¼ TW TF the difference between wall and bulk fluid temperature. 19 20 B1 Fundamentals of Heat Transfer Further some fluid properties can be summarized in the dimensionless form of a Prandtl number n Pr ¼ ; a ð12Þ where a ¼ l=ðr cp Þ is the thermal diffusivity, r the density, and cp the constant pressure specific heat. Based on these dimensionless numbers the heat transfer coefficient a can be expressed by correlations in the following form: Nu ¼ f1 ðRe; PrÞ ð13Þ for forced convection and Nu ¼ f2 ðGr; PrÞ ð14Þ for natural convection. Typical values of a for different situations are: 2 2–25 W/m K For free convection in gases 10–1,000 W/m2K For free convection in liquids 2 25–250 W/m K For forced convection in gases 50–20,000 W/m2K For forced convection in liquids 2,500–100,000 W/m2K For boiling and condensing fluids 2.3 Thermal Radiation The energy emitted by any matter to its surroundings in the form of electromagnetic waves is called radiation. Unlike conduction or convection the energy transport from a location A to a location B by radiation is not bounded to any interlinking transport medium because electromagnetic waves can travel through a vacuum. Every matter or body emits radiation corresponding to its surface temperature (To be more precise one should write ‘‘Every matter or body with T > 0 K emits . . .,’’ but as known from thermodynamics other bodies do not exist.). The maximum radiation possible for a given temperature is emitted by a black body. A black body can be experimentally approximated by a blackened surface (e.g., with soot) or by a hollow space, whose walls have the same temperature everywhere, that has a small opening to let radiation out. The total radiation emitted by a black body per unit area is e_ b ¼ s T ; 4 ð15Þ where e_ b is the energy emitted per unit surface area of the black radiator (SI-unit W/m2), simply called the emission, and s ¼ 5:67 108 W=ðm2 K4 Þ is the radiation coefficient, also called the Stefan–Boltzmann constant. The above relation is called the Stefan–Boltzmann law. It was found 1879 by Josef Stefan as a result of many experiments and later in 1884 derived theoretically by his scholar Ludwig Boltzmann [4]. The emission e_ b is an energy flux and thus the related heat flux emitted by a black body follows as q_ b ¼ e_ b ¼ dQ_ b =dA: ð16Þ The radiation emitted by real surfaces is less than the radiation emitted by a black body at the same temperature. The reduced radiative energy or heat flux of a real body e_ compared to a black body is expressed by e_ ¼ e e_ b ¼ e s T 4 ; ð17Þ where e is the emissivity of the real surface with 0 e 1. The emissivity is generally a function of the surface material. It can also be a function of the surface morphology, its temperature, the direction of the radiation, and the wave length of the radiation. However, many surfaces can be treated in good approximation as grey bodies, which are defined by e ¼ const. Typical values for the emissivity are: e 0:96 for dead oxidized steel, e 0:3 for polished steel, e 0:04 for polished aluminium. Further values are given in Part K. 3 Heat Conduction and Overall Heat Resistances 3.1 One-Dimensional, Steady State Heat Conduction Through a Wall The heat conduction through a wall under steady state conditions can be analyzed on the basis of Fourier’s law [see Eqs. (4) or (5)]. For simple geometries, such as a plane wall or a tube wall, and one-dimensional heat transfer analytical solutions can be derived. 3.1.1 Conduction Through a Plane Wall If different temperatures T1 and T2 are prescribed on two surfaces of a plane wall with the thickness d, according to Fourier’s law the heat T1 T 2 t ð18Þ Q ¼ lA d flows through the area A in the time t. The heat flow rate follows as T1 T 2 Q_ ¼ lA d ð19Þ T1 T2 : d ð20Þ and the heat flux as q_ ¼ l Similar to electric conduction, where a current I flows only when a voltage U exists to overcome the resistance Rel, heat flows only when a temperature difference DT ¼ T1 T2 exists: lA Q_ ¼ DT : d ð21Þ Ohm’s law for an electrical current flow says I = U/Rel. Analogous to the electrical resistance Rel one can define a thermal resistance or heat resistance, which is defined by R¼ DT Q_ ð22Þ Fundamentals of Heat Transfer B1 in general (SI-unit K/W). In the case considered above, conduction through the plane wall, the conductive heat resistance follows as Rcond ¼ 3.1.2 d : lA ð23Þ Conduction Through a Tube Wall According to Fourier’s law, the heat flow rate through a cylindrical area of radius r and length L is dT : Q_ ¼ l2prL dr ð24Þ Under steady state conditions, the heat flow rate is the same for all radii and thus Q_ ¼ const. It is therefore possible to separate the variables T and r and to integrate from the inner surface of the cylinder, r ¼ ri with T ¼ Ti , to an arbitrary location r with temperature T. The temperature profile in a tube wall of thickness r ri becomes Ti T ¼ r Q_ ln : l2pL ri transfer processes and the heat conduction process are connected in series. Thus, analogous to electrical resistances, one can add the individual thermal resistances and thereby write an equation for an overall heat resistance as R¼ ð25Þ With temperature To at the outer surface at radius ro , the heat flow rate through a tube of thickness ro ri and length L becomes Ti To : Q_ ¼ l 2p L lnðro =ri Þ B1. Fig. 3. Heat transmission through a plane wall. ð26Þ ð27Þ Ao Ai lnðAo =Ai Þ, where d ¼ ro ri and Am ¼ if Ao ¼ 2pro L is the outer and Ai ¼ 2pri L is the inner surface of the tube. Am is the logarithmic mean between outer and inner tube surface. With this the thermal resistance of the tube can be derived as Rcond ¼ d=ðlAm Þ or Rcond ¼ 3.2 lnðro =ri Þ : l 2pL ð28Þ Heat Transmission, Overall Heat Resistances, and Overall Heat Transfer Coefficients Heat transmission through a plane wall If heat is transferred from a fluid at bulk temperature TF1 to a wall by convection, conducted through the wall to the other side, and then transferred to a second fluid at bulk temperature TF2 , this process is called heat transmission through a wall. The related temperature profile for the case of a plane wall is plotted in Fig. 3. In case of one-dimensional heat transfer perpendicular to the wall, as assumed above in Sect. 3.1, the two convective heat ð29Þ with the two convective heat resistances defined by Rconv ¼ 1 : aA ð30Þ The heat flow passing through the plane wall then can be written as In order to get formal agreement with Eq. (19), it is also possible to write Ti T o Q_ ¼ lAm d 1 d 1 þ þ ai A lA ao A TF1 TF2 Q_ ¼ R ð31Þ Q_ ¼ k A ðTF1 TF2 Þ ð32Þ or with the quantity k called the overall heat transfer coefficient or heat transmission coefficient [SI-unit W/(m2K)]. It follows 1 : ð33Þ R¼ kA If the wall consists of several homogeneous layers with thicknesses d1, d2, . . . and thermal conductivities l1, l2, . . ., Eq. (29) holds likewise with the overall heat resistance X dj 1 1 1 þ þ : ð34Þ R¼ ¼ l A A k A ai A a j o j Of course this analogy to electrical resistances is not restricted to serial circuits but hold also for parallel circuits. In case of parallel heat conduction resistances under the assumption of one-dimensional heat transfer, e.g., the overall heat conduction resistance yields 1 1 1 ¼ P dj : ð35Þ ¼ P R R j j j lj Aj Example: The wall of a cold store consists of a 5 cm thick internal concrete layer [l = 1 W/(K m)], a 10 cm thick cork stone insolation [l = 0.04 W/(K m)], and a 50 cm thick external brick wall. The 21 22 B1 Fundamentals of Heat Transfer inner heat transfer coefficient is ai ¼ 7 W=ðm2 KÞ and the outer one ao ¼ 20 W=ðm2 KÞ. What is the heat flow rate through 1 m2 of the wall if the temperatures inside and outside are –5 C and 25 C, respectively? According to Eq. (34) the overall heat resistance is 1 1 0:05 0:1 0:5 1 ¼ þ þ þ þ K=W ¼ 3:41K=W kA 7 1 1 1 0:04 1 0:75 1 20 1 1 ð5 25Þ W, Q_ ¼ 8:8 W. The heat flow is Q_ ¼ 3:41 3.2.1 Heat Transmission Through a Tube Wall For one-dimensional heat transmission through tubes, Eqs. (31) and (32) again hold, where the heat resistance is the sum of the individual resistances R¼ 1 1 d 1 þ þ ; ¼ kA ai Ai lAm ao Ao ð36Þ i with the outer and inner where d ¼ ro ri and Am ¼ lnAðAo A o =Ai Þ tube surfaces Ao and Ai , respectively. It becomes obvious that the overall heat transfer coefficient k must be related to a single surface A. This is usually the outer tube surface A = Ao, which is often easier to determine. If the tube consists of several homogeneous layers with thicknesses d1, d2, . . . and thermal conductivities l1, l2, . . . Eq. (34) holds likewise with the overall heat resistance X dj 1 1 1 þ þ : ð37Þ ¼ R¼ l A Ao k A ai Ai a j mj o j With the mean logarithmic areas Amj ¼ Aoj Aij = ln Aoj =Aij . 3.3 Transient Heat Conduction During transient heat conduction, the temperatures vary with respect to time. Assuming constant thermal conductivity (isotropy) Fourier’s heat conduction equation follows as @T ¼ a r2 T þ q_ s @t ð38Þ with the volumetric heat source term q_ s (SI-unit W/m3) and the quantity a which is a material property and defined as thermal diffusivity a ¼ l=ðrc Þ (SI-unit m2/s). The Laplace operator yields r2 T ¼ @2T @2T @2T þ þ 2 @x 2 @y 2 @z For plane walls with heat flow in the direction of the x-axis and no heat source, Eq. (38) reduces to @T @2T : ¼a @t @x 2 ð39Þ Thus, in a plane wall with prescribed surface temperatures, the temperature profile is no longer linear as the heat transfer into the wall differs from the heat transfer out. The difference between heat transfer in and out increases (or decreases) the internal energy of the wall and thus, its temperature as a function of time. For the solution of Fourier’s equation, it is suitable to introduce – as in other heat transfer problems – dimensionless quantities, which reduce the number of variables. Equation (39) is considered in order to demonstrate the basic procedure. The dimensionless temperature is set to Y ¼ ðT Tc Þ=ðT0 Tc Þ, where Tc is a characteristic constant temperature and T0 the initial temperature. If the cooling of a plate with an initial temperature T0 in a cold environment is considered, Tc could be, for example, the ambient temperature Tenv. All lengths are related to a characteristic length X, e.g., half of the plate thickness. Furthermore, it is suitable to introduce the dimensionless time, which is called Fourier number, as Fo ¼ at=X 2 . The solution of the heat conduction equation then has the dimensionless form Y ¼ f ðx=X; FoÞ: ð40Þ In many problems, the heat conducted internally to the surface of a solid body is transferred by convection to the surrounding fluid of temperature Tenv. The energy balance then holds at the surface (index w = wall) @T ¼ a ðTw Tenv Þ ð41Þ l @x w or 1 @Y aX ¼ ; Yw @x w l ð42Þ and where x ¼ x=X, Y ¼ ðT Tenv Þ=ðT0 Tenv Þ Yw ¼ ðTw Tenv Þ=ðT0 Tenv Þ. The solution is also a function of the dimensionless quantity aX=l, which is defined as the Biot number Bi, where the thermal conductivity l of the solid body is assumed to be constant, and a is the heat transfer coefficient between the body and surrounding fluid. Solutions of Eq. (39) considering the Biot number have the form Y ¼ f ðx=X; Fo; BiÞ: ð43Þ for Cartesian coordinates; r2 T ¼ 1 @ @T 1 @2T @2T r þ 2 2þ 2 r @r @r r @’ @z for cylindrical coordinates; and 1 @ 1 @2T 2 2 @T r T¼ 2 r þ 2 r @r @r r sin2 Y @’2 1 @ @T þ 2 sin Y r sin Y @Y @Y for polar coordinates: 3.3.1 Semi-Infinite Body Temperature changes may also take place in a region that is thin in comparison to the overall dimensions of the body. Such a body is called semi-infinite. In this case, a semi-infinite plane wall (Fig. 4) with a constant initial temperature T0 is considered. At time t = 0, the surface temperature of the wall is reduced to T(x = 0) = Tenv and then remains constant. The temperature Fundamentals of Heat Transfer B1 B1. Fig. 5. Temperature profile in a semi-infinite body. B1. Fig. 4. Semi-infinite body. profiles normal to the surface at different times t1, t2. . . . are given by: T Tenv x pﬃﬃﬃﬃﬃﬃ ¼f ð44Þ T0 Tenv 2 at pﬃﬃﬃﬃﬃﬃ with the Gaussian error function f x= 2 a t , see Fig. 5. The heat flux at the surface results from the differentiation q_ ¼ lð@T =@x Þx¼0 which yields b q_ ¼ pﬃﬃﬃﬃﬃﬃ ðTenv T0 Þ: pt ð45Þ pﬃﬃﬃﬃﬃﬃﬃﬃ The heat penetration coefficient b ¼ lrc [SI-unit W s1/2/ (m2K)], is a measure for the heat transfer that has penetrated into the body at a given time if the surface temperature was suddenly changed by the amount Tenv – T0 as compared to the initial temperature T0. Some typical values for b are: approximately 36,000 W s1/2/(m2K) for copper, 1,600 W s1/2/(m2K) for concrete, 1,400 W s1/2/(m2K) for water, or 6 W s1/2/(m2K) for gases. For details see Part D. Example: A sudden change in weather causes the temperature at the earth’s surface to drop from +5 to –5 C. How much does the temperature decrease at a depth of 1 m after 20 days? The thermal diffusivity of the soil is a ¼ 6:94 107 m=s. According to Eq. (44), the decrease is: ! T ð5Þ 1 ¼ f ð0:456Þ ¼f 5 ð5Þ 2ð6:94 107 20 24 3;600Þ1=2 B1. Fig. 6. Contact temperature Tm between two semi-infinite bodies. b q_ ¼ pﬃﬃﬃﬃﬃﬃ ðTenv T0 Þ FðzÞ; pt ð46Þ where Fðz Þ ¼ 1 1 13 1 3 . . . ð2n 3Þ þ þ ð1Þn1 2n1 z 2n2 2z 2 22 z 4 pﬃﬃﬃﬃﬃﬃ and z ¼ a a t =l. Figure 5 gives f ð0:456Þ ¼ 0:48, thus, T = –0.2 C. 3.3.2 Finite Heat Transfer at the Surface Let us assume, heat transfer is by convection from the surface of a body to the fluidic environment. At the surface, the relation q_ ¼ lð@T =@x Þ ¼ aðTw Tenv Þ holds, with the ambient temperature Tenv and the time dependent variable wall temperature Tw ¼ T ðx ¼ 0Þ. In this case, Eqs. (44) and (45) no longer hold. Instead, the heat flux is given by 3.3.3 Two Semi-Infinite Bodies in Thermal Contact Two semi-infinite bodies of different, but initially constant, temperatures T1 and T2 with the thermal properties l1, a1 and l2, a2 are suddenly brought into contact at time t = 0 (Fig. 6). After a very short time at both sides of the contact area, a temperature Tm is present and remains constant. This temperature is given by: 23 24 B1 Fundamentals of Heat Transfer Tm T 1 b2 ¼ : T2 T1 b1 þ b2 ð47Þ The contact temperature Tm is closer to the temperature of the body with the higher heat penetration coefficient b. One of the values b can be determined by measuring Tm, if the other value is known. 3.3.4 Temperature Equalization in Simple Bodies A simple body such as a plate, a cylinder, or a sphere may have a uniform temperature T0 at time t = 0. Afterwards, however, it is cooled or heated due to heat transfer between the body and a surrounding fluid of temperature Tenv given by the boundary condition lð@T =@nÞw ¼ aðTw Tenv Þ, where n is the coordinate perpendicular to the body surface. 3.3.5 3.3.6 Cylinder The radial coordinate r replaces coordinate x in Fig. 7, and the radius of the cylinder is R. Again, the temperature profile is described by an infinite series, which can be approximated for Fourier numbers at=R2 0:21 by r T Tenv at ¼ C exp d2 2 I0 d ð49Þ T0 Tenv R R with less than 1% error. The term I0 is a Bessel function of zeroth order. Its values are presented in tables in many textbooks for mathematics, e.g., in [5]. The constants C and d depend, according to Table 2, on the Biot number. When r = R, the surface temperature at the cylinder results from Eq. (49), and for r = 0 the temperature in the center of the cylinder. The heat transfer rate results from Q_ ¼ lAð@T =@r Þr¼R , where the first derivative of the Bessel function I00 ¼ I1 appears. The Bessel function of first order I1 is also given in [5]. Plane Plate The temperature profile shown in Fig. 7 is described by an infinite series. However, for Fourier numbers (or dimensionless times) at=X 2 0:24, the following relation provides a good approximation x T Tenv at ¼ C exp d2 2 cos d ð48Þ T0 Tenv X X with less than a 1% error in temperature. The constants C and d depend, according to Table 1, on the Biot number Bi ¼ aX=l. Where x = X, Eq. (48) leads to the surface temperature Tw at the wall, and x = 0 leads to the temperature in the center of the wall. The heat transfer rate follows from Q_ ¼ lAð@T =@x Þx¼X . 3.3.7 Sphere The cooling or heating of a sphere of radius R is also described by an infinite series. For Fourier numbers a t=R 2 0:18, temperature profile can be approximated by: sin d Rr T Tenv 2 at ¼ C exp d 2 ð50Þ d Rr T0 Tenv R with less than 2% error. The constants C and d depend, according to Table 3, on the Biot number. 4 Convective Heat Transfer and Nusselt Numbers The desired convective heat transfer coefficient a in q_ ¼ aDT is obtained from the Nusselt number [Eq. (9)] by a ¼ Nul=L with Eq. (13) Nu ¼ f 1 ðRe; PrÞ for forced convection and Eq. (14) Nu ¼ f 2 ðGr; PrÞ for natural convection. As stated above in Sect. 2.2, the heat transfer coefficient a and also the functions f1 and f2 can be determined theoretically only for special cases. In general, they must be determined through experimentation and depend on the shape of the cooling or heating areas (even, vaulted, smooth, rough, or finned), the flow structure, and usually to a minor extent, on the direction of the heat transfer (heating or cooling). B1. Fig. 7. Cooling of a plane plate. B1. Table 1. Constants C and d in Eq. (48) Bi 1 10 5 2 1 0.5 0.2 0.1 0.01 C 1.2732 1.2620 1.2402 1.1784 1.1191 1.0701 1.0311 1.0161 1.0017 d 1.5708 1.4289 1.3138 1.0769 0.8603 0.6533 0.4328 0.3111 0.0998 Fundamentals of Heat Transfer B1 B1. Table 2. Constants C and d in Eq. (49) Bi 1 10 5 2 1 0.5 0.2 0.1 0.01 C 1.6020 1.5678 1.5029 1.3386 1.2068 1.1141 1.0482 1.0245 1.0025 d 2.4048 2.1795 1.9898 1.5994 1.2558 0.9408 0.6170 0.4417 0.1412 B1. Table 3. Constants C and d in Eq. (50) Bi 1 10 5 2 1 0.5 0.2 0.1 0.01 C 2.0000 1.9294 1.7870 1.4793 1.2732 1.1441 1.0592 1.0298 1.0030 d 3.1416 2.8363 2.5704 2.0288 1.5708 1.1656 0.7593 0.5423 0.1730 In the following some frequently encountered configurations are presented in an exemplary manner. Further details, configurations and related Nusselt correlations including references are given in Parts F–J. by q_ ¼ aDTm, with the mean logarithmic temperature difference described by 4.1 Single Phase Forced Convection where Tw is the wall temperature, Tin is the temperature at the inlet, and Tout is the temperature at the outlet cross section. 4.1.1 Laminar Flow Along a Flat Plate According to Pohlhausen, for the mean Nusselt number of a plate of length L, the following relation holds Nu ¼ 0:664 Re1=2 Pr1=3 ; ð51Þ where Nu ¼ aL=l, Re ¼ wL=n < 105 , and 0:6 Pr 2;000. The material properties must be evaluated at the mean fluid temperature Tm ¼ ðTw T1 Þ=2, where Tw is the wall temperature and T1 the free-stream temperature far beyond the wall surface. 4.1.2 Turbulent Flow Along a Flat Plate 0:037 Re0:8 Pr ; 1 þ 2:443 Re0:1 Pr2=3 1 ð52Þ where Nu ¼ aL=l, Re ¼ wL=n, 5 105 < Re < 107 and 0:6 Pr 2; 000. The material properties must be evaluated at the mean fluid temperature Tm ¼ ðTw þ T1 Þ=2. Tw is the wall temperature and T1, the free-stream temperature far beyond the wall surface. 4.1.3 4.1.4 Flow Through Pipes in General Below a Reynolds number of Re = 2,300 (Re ¼ wd=n, where w is the mean cross-sectional velocity and d is the pipe diameter), the flow is laminar, while above Re = 104, the flow is turbulent. In the range 2,300 < Re < 104, whether the flow is laminar or turbulent depends on the roughness of the pipe, the means of inflow, and the shape of the pipe in the inflow section. The mean heat transfer coefficient a over the pipe length L is defined ðTw Tin Þ ðTw Tout Þ ; Tin ln TTwwT out ð53Þ Laminar Flow Through Pipes A flow is termed hydrodynamically developed if the velocity profile no longer changes in flow direction. In a laminar flow of a highly viscous fluid, the velocity profile adopts the shape of a Poiseuillean parabola after only a short distance from the inlet. The mean Nusselt number at constant wall temperature can be calculated exactly via an infinite series (Graetz solution), which, however, converges poorly. According to Baehr and Stephan [4], as an approximate solution for the hydrodynamically developed laminar flow, the following equation holds Nu0 ¼ From about Re ¼ 5 105 the boundary layer becomes turbulent. The mean Nusselt number of a plate of length L in this case is Nu ¼ DTm ¼ 3:657 0:0499 þ tanh X; X tanhð2:264X 1=3 þ 1:7X 2=3 Þ ð54Þ where Nu0 ¼ a0 d=l, X ¼ L=ðd Re PrÞ, Re ¼ wd=n, and Pr ¼ n=a. This equation is valid for laminar flow (Re 2; 300) in the entire range 0 X 1 and the maximum deviation from the exact values of the Nusselt number is 1%. The fluid properties must be evaluated at the mean fluid temperature Tm ¼ ðTw þ TB Þ=2 where TB ¼ ðTin þ Tout Þ=2. If a fluid enters a pipe at an approximately constant velocity, the velocity profile changes along the flow path until it reaches the Poiseuillean parabola after a distance Lentry described by the equation Lentry =ðd ReÞ ¼ 5:75 102 . According to [4], for this case, that of a hydrodynamically developed laminar flow, the following equation holds for the range 0:1 Pr 1 Nu 1 ; ¼ Nu0 tanh 2:43 Pr1=6 X 6 ð55Þ where Nu ¼ ad=l and the quantities are defined as above. The error is less than 5% for 1 Pr 1 but is up to 10% for 0:1 Pr 1. The fluid properties must be evaluated at the where mean fluid temperature Tm ¼ ðTw þ TB Þ=2 TB ¼ ðTin þ Tout Þ=2. 25 26 B1 4.1.5 Fundamentals of Heat Transfer Turbulent Flow Through Pipes For a hydrodynamically developed flow (L=d 60) the following equation holds in the range 104 Re 105 and 0:5 Pr 100, Nu ¼ 0:024 Re0:8 Pr1=3 : ð56Þ The fluid properties have to be evaluated at the mean fluid temperature Tm ¼ ðTw þ TB Þ=2 where TB ¼ ðTin þ Tout Þ=2. For hydrodynamically undeveloped flow and for developed flow, Petukhov’s equation (modified by Gnielinski) holds in the range 104 Re 106 and 0:6 Pr 1;000, " 2=3 # Re Pr z=8 d pﬃﬃﬃﬃﬃﬃﬃ 2=3 1 þ Nu ¼ ; L 1 þ 12:7 z=8 Pr 1 ð57Þ where the friction factor z ¼ ð0:78 ln Re 1:5Þ2, Nu ¼ ad=l, and Re ¼ wd=n. The fluid properties must be evaluated at the mean temperature Tm ¼ ðTw þ TB Þ=2. Under otherwise similar conditions, the heat transfer coefficients are larger in pipe bends than in straight pipes with the same cross section. For a pipe bend with a bend diameter D, he following equation holds, according to Hausen, for turbulent flow a ¼ astraight 1 þ 21 Re0:14 ðd=DÞ : B1. Fig. 8. A row of pipes placed transversely in a flow. B1. Fig. 9. Arrangement of pipes in pipe bundles: (a) in straight lines and (b) staggered. ð58Þ 4.1.8 4.1.6 Single Pipe Placed Transversely in a Flow The heat transfer coefficient for a pipe placed transversely in a flow can be determined from Gnielinski’s equation 1=2 ; Nu ¼ 0:3 þ Nu2lam þ Nu2turb ð59Þ where the Nusselt number Nulam of the laminar plate flow is described according to Eq. (51), Nuturb of the turbulent plate flow is described according to Eq. (52), and Nu ¼ aL=l, 1 < Re ¼ wL=n < 107 , and 0:6 < Pr < 1;000. For length L, the overflowed length L ¼ dp=2 must be inserted. The fluid properties must be evaluated at the mean temperature Tm ¼ ðTin þ T out Þ=2. This equation holds for mean turbulence intensities of 6–10%, which can be expected in technical applications. Pipe Bundle If the pipes are placed in straight lines (Fig. 9a), the axes of all pipes are consecutively in the flow direction. If the arrangement is staggered (Fig. 9b), the axes of a pipe row are shifted in comparison to the axes of the row in front. The heat transfer depends additionally on the crosswise and longwise division of the pipes, a ¼ s1 =d and b ¼ s2 =d. The determination of the heat transfer coefficient starts with the calculation of the Nusselt number for a single pipe placed transversely in the flow, according to Eq. (59), in which the Reynolds number contains the mean velocity wm in the pipe bundle: Re ¼ wm L=n, where wm ¼ w=c, w is the far field velocity of the pipe row, c is the void space fraction c ¼ 1 p=ð4aÞ for b > 1, and c ¼ 1 p=ð4abÞ for b < 1. The characteristic length is L ¼ dp=2. The Nusselt number determined in this way must be multiplied with an arrangement factor fA. This leads to the Nusselt number NuB ¼ aB L=l of the bundle: NuB ¼ fA Nu: 4.1.7 Row of Pipes Placed Transversely in a Flow Mean heat transfer coefficients for a single row of pipes placed transversely in a flow (Fig. 8) can also be determined using Eq. (59). Now, however, the Reynolds number must be calculated with the mean velocity wm in the pipe row placed transversely in the flow. The Reynolds number is described by the equation: Re ¼ wm L=n where wm ¼ wc, w is the far field velocity, and c ¼ 1 p=ð4aÞ is the void space fraction, where a ¼ s1 =d (Fig. 8). ð60Þ For a straight arrangement fA ¼ 1 þ 0:7 b=a 0:3 c 3=2 ðb=a þ 0:7Þ2 ð61Þ and for a staggered arrangement fA ¼ 1 þ 2=ð3bÞ: ð62Þ The heat flux is q_ ¼ aDTm with DTm according to Eq. (53). Equations (61) and (62) hold for pipe bundles consisting of 10 or more pipe rows. For heat exchangers with fewer pipe rows, the heat transfer coefficient (Eq. 60) must be multiplied by a factor ð1 þ ðn 1ÞfA =nÞ, where n is the number of pipe rows. B1 Fundamentals of Heat Transfer 4.2 Single Phase Natural Convection The heat transfer coefficient for natural convection at a vertical wall can be calculated with the equation of Churchill and Chu 0 12 B 0:825 þ 0:387 Ra C Nu ¼ @h i 8=27 A ; 9=16 1 þ ð0:492= PrÞ 1=6 ð63Þ a ¼ 0:943 in which the mean Nusselt number Nu ¼ aL=l is formed with the wall height L, and the Rayleigh number is defined as Ra ¼ Gr Pr; ð64Þ where the Grashof number is defined by Gr ¼ such as the application of dewetting agents are necessary. Dropwise condensation therefore appears rather seldom in technical applications. Calculation methods are presented in Part J3. If the condensate flows as a laminar film on a vertical wall of height L, the mean heat transfer coefficient a is according to Nusselt’s film condensation theory [4] gL3 r1 rw : n2 rw gL bðTw T1 Þ; n2 1=6 B 0:60 þ 0:387 Ra C Nu ¼ @h i 8=27 A : 9=16 1 þ ð0:559= PrÞ ð65Þ Nu ¼ 0:766 ðRa f2 Þ1=5 if Ra f2 < 7 104 ð66Þ Nu ¼ 0:15 ðRa f2 Þ1=3 if Ra f2 > 7 104 ; ð67Þ and h i20=11 f2 ¼ 1 þ ð0:322= PrÞ11=20 ; where Nu ¼ aL=l, if L is the shorter side of the rectangle. 4.3 Heat Transfer in Condensation and Boiling 4.3.1 Condensation rl ðrl rv Þ g Dhv l3l 1 l ðTs Tw Þ d If the temperature of a wall surface is lower than the saturation temperature of adjacent vapor, the vapor is condensed at the wall surface. Depending on the wetting characteristics, the condensate forms drops or a continuous liquid film. The heat transfer coefficients are usually larger for dropwise condensation than for film condensation. However, in order to maintain dropwise condensation for a certain amount of time, particular measures ; ð68Þ 1=4 : ð69Þ The equations require that no noticeable shear stress is exerted by the vapor on the condensate film. At Reynolds number Red ¼ w m d=n (where wm is the velocity of the condensate, d the film thickness, and n the kinematic viscosity) between 75 and 1,200 the transition to turbulent flow in the condensate film gradually takes place. In the transition range 1=3 ; ð70Þ a ¼ 0:22 ll n2l =g whereas for turbulent film flow (Red > 1,200), the following relation according to Grigull holds a ¼ 0:003 The same definitions used in Eq. (65) hold over the range of validity is 0 < Pr < 1 and 105 Ra 1012 , and the characteristic length is the diameter d. For horizontal rectangular plates, the following holds for 0 < Pr < 1: where a ¼ 0:728 3 where the volume expansion coefficient is denoted by b, where b ¼ 1=Tw holds for ideal gases. Equation (63) holds in the range 0 < Pr < 1 and 0 < Ra < 1012 . The fluid properties must be evaluated at the mean temperature Tm ¼ ðTw T1 Þ=2. A similar equation holds according to Churchill and Chu also for natural convection in a horizontal cylinder 0 12 1=4 where g is the gravitational acceleration, r the densities of the liquid (index l) and the vapor (index v) phase, respectively, Dhv the latent heat of vaporization, l the dynamic viscosity of the liquid, ll its thermal conductivity, and Ts and Tw the saturation temperature and the wall temperature, respectively. For condensation on horizontal single pipes with an outer diameter d, the following relation holds: If natural convection is caused solely by temperature differences, the Grashof number can be written according to Eq. (11) as Gr ¼ rl ðrl rv Þ g Dhv l3l 1 4 l ðTs Tw Þ L l3l g ðTs Tw Þ L rl n3l Dhv 1=2 : ð71Þ Equations (70) and (71) are valid also for vertical pipes and plates but not for horizontal pipes. 4.3.2 Boiling If a liquid in a container is heated, evaporation starts after the saturation temperature Ts is exceeded. For small excess wall temperatures Tw – Ts the liquid evaporates only on its free surface (silent boiling). Heat is transported by conduction and the buoyancy flow from the heating surface to the free surface of the liquid. For higher, excess wall temperatures vapor bubbles are formed at the heating surface (nucleate boiling) and rise. They increase the movement of the liquid and thus the heat transfer. With increasing excess wall temperature, the bubbles merge more and more into a continuous vapor film, whereby the heat transfer is decreased (transition boiling). Figure 10 shows the different heat transfer ranges for such pool boiling situations. The heat transfer coefficient a is defined as _ ðTw Ts Þ a ¼ q= ð72Þ where the heat flux is q_ in W/m2. Industrial evaporators work in the range of silent boiling or, more often, in the nucleate boiling range. In the silent boiling range the laws for heat transfer in natural convection hold (see Sect. 4.2. and Part F). 27 28 B1 Fundamentals of Heat Transfer e_ ¼ e e_ b ¼ e s T 4 : In limited temperature ranges, many engineering surfaces (with the exception of shiny metal) can be interpreted as grey radiators. The energy radiated by them is distributed over the wave lengths in the same way as it is for black radiators. However, it is reduced by a factor e < 1. Strictly speaking, e ¼ eðT Þ holds true for grey radiators. For small temperature ranges, however, it is admissible to assume e as constant. Assuming a body emits the energy flow per unit area e_ , and this energy flux strikes another body, this second body absorbs the energy flow or rather the heat flow dQ_ a ¼ a dQ_ ¼ a e_ dA: B1. Fig. 10. Boiling ranges for water of 1 bar. A – natural convection (silent boiling), B – nucleate boiling, C – transition boiling, D – film boiling. In the nucleate boiling region, the general relation a ¼ c q_ n F ðpÞ with 0.5 < n < 0.8 holds. For water at boiling pressures between 0.5 and 20 bar, according to Fritz, the following relation holds: a ¼ 1:95 q_ 0:72 p0:24 Properties of the liquid and vapor are taken at saturation conditions. Nu ¼ ad=ll is formed with the detachment diameter of the vapor bubbles d ¼ 0:851b0 ½2s=g ðrl rv Þ 1=2 , where the contact angle is b0 ¼ 45 for water, 1 for low boiling and 35 for other liquids. The equations above are not valid for boiling in forced flow. Detailed calculation procedures for pool boiling are given in > Chap. H2. If boiling occurs in a forced flow, e.g. in a pipe heated externally, both, boiling heat transfer and forced convective heat transfer are driving the transport process. Flow boiling calculation procedures are presented in > Chap. H3. 5 5.1 The absorptivity a defined by this equation depends on the temperature T of the origin of the incident radiation and on the temperature T 0 of the receiving surface. For black bodies, this value is a = 1, as all radiation striking the surface is absorbed. For surfaces which are not black, this value is a < 1. For grey radiators, the absorptivity is a = e. According to Kirchhoff ’s law, the emissivity is equal to the absorptivity, e = a, for each surface which is in thermal equilibrium with its environment so that the temperature of the surface does not change in time. The remaining fractions of dQ_ are reflected at the surface, _ or transmitted through the body, dQ_ d ¼ d dQ. _ It _ dQr ¼ r dQ, follows r þ d þ a ¼ 1: ð73Þ with a in W/(m2K), q_ in W/m2, and p in bar. According to Stephan and Preußer, for arbitrary liquids the following relation is valid for nucleate boiling close to ambient pressure q_ d 0:674 rv 0:156 Nu ¼0:0871 rl l l Ts ð74Þ 2 0:350 2 0:371 Dhv d al rl 0:162 Pr : l al2 sd Thermal Radiation and Radiative Heat Exchange Emission, Absorption, and Transmission As stated in Sect. 2.3. real bodies emit less than black radiators, where the energy emitted from real surfaces is, according to Eq. (17), ð75Þ ð76Þ A body that reflects radiation completely (r = 1, d = a = 0) is called an ideal mirror, a body that absorbs radiation completely (a = 1, r = d = 0) is called a black body. A body is called diathermal (d = 1, r = a = 0) if radiation passes completely through. Examples for this are gases such as O2, N2, and others. 5.2 Heat Exchange Between Two Bodies If two bodies emit radiation to each other the heat transfer between the bodies is equal to the net result of the radiation balance. Assuming, e.g., two parallel black surfaces of temperatures T1 and T2, and area A, which is very large in comparison to their distance, the net heat flow rate ð77Þ Q_ 12 ¼ s A T14 T24 is transferred by radiation. Between two such grey surfaces with the emissivities e1 and e2 , the heat flow rate is Q_ 12 ¼ C12 A T14 T24 ð78Þ with the radiation exchange number s : C12 ¼ 1 1 þ e1 e2 1 ð79Þ Between an internal pipe with the outer surface A1 and an external pipe with the inner surface A2, which are both grey radiators with emissivities e1 and e2 , a heat flow rate is given according to Eq. (78), however, with: s C12 ¼ : ð80Þ A1 1 1 þ 1 A2 e2 e1 Fundamentals of Heat Transfer If A1 << A2, e.g., for a pipe in a large room, the equation holds that C12 = se1. For a number of more complex geometrical configurations with two bodies, specific radiation exchange numbers are given in > Chap. K1. More general relationships for the radiative heat transfer between two grey surfaces, which are arbitrarily arranged in space, make use of the definition of so-called view factors ’ that depend on the geometric arrangement of the surfaces. A view factor ’ij is defined as the fraction of the radiative energy leaving body i that strikes body j. Details for such arrangements as well as for enclosed spaces with multiple surfaces involved in radiative heat exchange are given in > Chap. K2. 5.3 Gas Radiation Most gases are transparent to thermal radiation and neither emit nor absorb radiation. Exceptions are some gases such as B1 carbon dioxide, carbon monoxide, hydrocarbons, water vapor, sulfur dioxide, ammonia, hydrochloric acid, and alcohols. They emit and absorb radiation only in certain wave length regions. Emissivity and absorptivity of these gases depend not only on temperature, but also on the geometric shape of the gas body. Details are given in > Chap. K3. 6 1. 2. 3. 4. 5. Bibliography Fourier JBJ (1822) Théorie Analytique de la Chaleur, see reprint (2009): Cambridge University Press, 1st edn Prandtl L (1904) Über Flüssigkeitsbewegungen bei sehr kleiner Reibung. Internationaler Mathematischer Kongress, Heidelberg; see also: Oertel H, Bolle M, Efling D (2004): Prandtl’s Essentials of Fluid Mechanics, Springer Nusselt W (1915) Das Grundgesetz des Wärmeübergangs. GesundheitsIngenieur 38, pp. 477–482 Baehr HD, Stephan K (2006) Heat and mass transfer, 2nd edn. Springer Bronstein IN, Semendjajew KA, Musiol G, Muehlig H (2007) Handbook of mathematics, 5th edn. Springer 29 A2 Dimensionless Numbers A2 Dimensionless Numbers Holger Martin Karlsruher Institut für Technologie (KIT), Karlsruhe, Germany 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Dimensionless Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1 Introduction Dimensionless Numbers Notation Name Definition Ar Archimedes number gl Dr/(rn2) Bi Biot number aal/li Fo Fourier number kt/l2 Fr Froude number w2/(gl) Ga Galilei number g l3/n2 3 3 2 Gr Grashof number gbDT l /n Gz Graetz number l2/(k tr) Hg Hagen number (Dp/DL) l3/(rn2) Ka Kapitza number g4/(rs3) Le Lewis number k/dij al/l Nu Nusselt number Pe Péclet number w l/k Pr Prandtl number n/k Ra Rayleigh number gbDT l3/(nk) Re Reynolds number rwl/ Sh Sherwood number b l/dij Sc Schmidt number n/dij St Stanton number a/(rcpw) We Weber number w2lr/s 3 Examples of Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 The diameter of the particles, drops, or bubbles is usually chosen as the characteristic length l. The equations in the VDI-Heat Atlas are often given in dimensionless forms. The dimensionless numbers used in these equations are presented below in tabular form with notation, name, and definition, and by a numerical example for each of these numbers. 2 3 Examples of Usage The Archimedes number, Ar, is often used in equations describing the motion of particles (solid particles, drops, or bubbles) in gases or liquids (as in > Chaps. L3.2 and > M5). Usually, it appears in these equations together with the Reynolds number, Re. The number Ar/Re2 can be interpreted as the ratio of weight minus buoyancy and the inertial force: Ar=Re2 ¼ ðDr=rÞ=Fr ¼ gl 3 Dr=ðrw 2 l 2 Þ VDI-GVC (ed.), VDI Heat Atlas, DOI 10.1007/978-3-540-77877-6_2, # Springer-Verlag Berlin Heidelberg 2010 Example Quartz sand, with an average size d = 500 mm and a solid density rS = 2,610 kg/m3, is to be fluidized in air at a pressure of p = 1 bar und T = 300 K. With the gas density r = 0.6072 kg/m3 and the kinematic viscosity of n = 48.09 · 106 m2/s (> Chap. D2) from the definition of Ar, with l = 500 · 106 m, r = 0.6072 kg/m3, n = 48.09 · 106 m2/s, and Dr = (2,6100.6) kg/m3 = 2,609 kg/m3, the result is Ar = 2,278. The Biot number, Bi, may be seen as a ratio of two heat transfer resistances in series: (l/li)/(1/aa). It is often very useful in calculations of transient heating or cooling processes of solid bodies in liquid, or gas flows (> Chap. E2). Example Spherical PVC particles with a heat conductivity li = 0.15 W/m K and a radius of R = 2 cm shall be cooled in an airstream. The heat transfer coefficient (surface-to-ambient air) was determined to be aa = 60 W/m2 K. With l = R = 2 · 102 m, the Biot number becomes Bi = 8.00, which means that the internal conductive resistance is eight times the outer heat transfer resistance in this case. The transient conduction inside the particles is rate-controlling. The Fourier number, Fo, as a dimensionless time is commonly used in transient conduction problems (see Sect. B and > Chap. E2). Example A steel ball with the thermal diffusivity k = 7.0 · 106 m2/s and the radius R = 1 cm is cooled in water for 1 min. Using t = 1 min = 60 s and l = R = 102 m, the Fourier number turns out to be Fo = 4.2. The Froude number, Fr, which can be seen as a ratio of inertial force and gravity, appears in problems of forced motion when gravity has some additional influence, for example, with free liquid (or granular solid) surfaces and in other multiphase flow problems. Example A water–steam mixture flows through a horizontal tube of internal diameter di = 25 mm with an average liquid-phase velocity of wL = 5 m/s. With the characteristic length l = di = 25 · 103 m, the Froude number for the liquid phase is Fr = 102. 12 A2 Dimensionless Numbers The Galilei number, Ga, may be written in terms of the Reynolds and Froude numbers: Ga = Re2/Fr. It is also a factor in Ar and Gr: Ar = Ga Dr/r; Gr = Ga b DT Example In the example for the Archimedes number, Ga = 0.5302 und Dr/r = 4,297. The Grashof number, Gr, is formed similarly to the Archimedes number, Ar. The term Dr/r, being the relative difference of densities of two different phases, such as solid– gas, for Ar, is replaced by the term b DT in the Grashof number (where b is the thermal expansion coefficient, and DT a characteristic spatial temperature difference). It is a relative difference of densities within one phase only (liquid or gaseous), which occurs because of a spatial temperature difference DT. For an ideal gas, b = 1/T. The Grashof number is important in describing heat transfer in natural convection flow problems (Sects. B and F). Example A flat, vertically mounted heater of a height l = 60 cm in a room at a temperature T1 = 20 C has a surface temperature of Ts = 60 C. At a reference temperature of Tm = (Ts + T1)/2 = 40 C, the relevant physical properties, b, the thermal expansion coefficient, and n, the kinematic viscosity are found to be b40 C ¼ 1 313:15 K ¼ 3:1 103 K1 ; n40 C = 16.92 · 106 m2/s, and the Grashof number becomes Gr = 9.47·108. The Graetz number, Gz, is the reciprocal of a Fourier number, Fo. It is mainly used in calculations for steady flow, in which the time tr (the residence time of the fluid in a heated or cooled portion of a channel) is usually expressed via the length L and the mean flow velocity w. The characteristic length l in this case is the diameter, d, of the flow channel: Gz ¼ d 2 ðktr Þ ¼ wd 2 ðkLÞ ¼ Ped d=L ¼ Red Pr d=L Example Waster at an average temperature of 30 C flows with a velocity of w = 1.5 m/s through a tube with the internal diameter of di = 18 mm. The tube is heated over a length of L = 3.0 m. With k30 C = 0.148 · 106 m2/s, tr = L/w = 2 s and l = di = 18 · 103 m the result is Gz = 1,095. The Hagen number, Hg, though not as widely used in the relevant literature so far, has proven to be a very useful generalization of the two similarly built Archimedes and Grashof numbers. It works for both the forced convection and the natural convection flow problems. It can be seen as a dimensionless pressure gradient, (Dp/DL)/(rn2/l3). In case of natural convection flows, Dp/DL is the static pressure gradient g Dr or g r b DT in a gravity field, and the Hagen number becomes an Archimedes number or a Grashof number. The linear HagenPoiseuille law of fully developed forced laminar tube flow (Re 2,300) simply reads as Hg = 32 Re, if the internal tube diameter is used as the characteristic length l. Example In a tube of the internal diameter d = 0.022 m a pressure drop of Dp = 103 Pa was measured over the length of DL = 10 m. Water at 20 C is flowing inside: r = 998.21 kg/m3, n = 1.004 · 106 m2/s. With the internal diameter, d, as the characteristic length, l, a Hagen number of Hg = 1 058 227 is obtained. With such a high value of Hg, a turbulent tube flow can be expected, because the critical Hagen number for the transition of laminar to turbulent flow is Hgcrit = 73,600 (Hg = 32 · Re, corresponding to a critical Reynolds number of Recrit = 2,300). The Kapitza number, Ka, contains only the physical properties, viscosity, density, and surface tension, apart from the acceleration of gravity, g. It plays a certain role in liquid film flows, as for example in film condensation. Ka can be written in terms of Weber, Froude, and Reynolds numbers, We, Fr, and Re, respectively as: Ka = We3/(Fr Re4). Example With the data for water at 20 C and 1 bar from > Chap. D2, the result is Ka = 2.57·1011. The Lewis number, Le, is the ratio of two physical properties, that is the quotient of thermal diffusivity and the (mass) diffusion coefficient. It occurs in problems of coupled heat and mass transfer, as for example, in drying or in evaporative cooling. The Lewis number can also be written in terms of Prandtl and Schmidt numbers: Le = Sc/Pr. Example For the evaporation of water in (dry) air at a total pressure of p = 1 bar and a temperature of T = 273.15 K with a diffusivity of dwater–air = 22.6 · 106 m2/s and a thermal diffusivity of k = 19.1 · 106 m2/s, a Lewis number of Le = 0.845. The Nusselt number, Nu, is a dimensionless heat transfer coefficient. For steady-state conduction through a stagnant plane layer of thickness l and conductivity l the heat transfer _ coefficient, defined as a = q/DT, is simply a = l/l. The Nusselt number al/l, in this case, by definition, has a value of Nu = 1. As the characteristic length l, the internal diameter of a flow channel (as in > Chap. G1), the length (in flow direction) of a plate in parallel flow (in > Chap. G4), or the quantity (n2/g)1/3, having the dimension of a length can be chosen (see Sect. B and > Chap. J1). In any case, the definition of a, the choice of the characteristic length l, and the reference temperature for the physical properties must be specified. Example For a cylinder with an outer diameter of d = 25 mm in a crossflow of air, from > Chap. G6, a Nusselt number Nul = 126.3 has been calculated. The reference temperature turns out to be Tm = 100 C, so that l = 31.81 · 103 W/m K. The characteristic length for (long) cylinders in crossflow, following 3 > Chap. G6, is l = (p/2) d = 39.27 · 10 m. So, to get the heat transfer coefficient, a = (l/l) ·Nul = 102.3 W/(m2 K) needs to be calculated. The Péclet number, Pe, can be written as the product of Re and Pr: Pe = Re Pr. It does not contain the viscosity, as this property is found in Pr in the numerator, and in Re in the denominator. The Péclet number is found in forced convection flow problems with heat transfer (see also the numbers Gz, Re, and Pr). It can be seen as a ratio of convective Dimensionless Numbers enthalpy transport (with the flow) to heat transfer (by conduction) to the fluid. Example At a Reynolds number of Re = 1,400, the Péclet number for air at 0 C (Pr = 0.7) has a value of Pe = 1,400 · 0.7 = 980; for water at 0 C (Pr = 13.0) one gets Pe = 1,400 · 13.0 = 18,200. The Prandtl number, Pr, like Le and Sc, is a ratio of physical properties; with n = /r und k = l/(rcp) it can also be written in the form Pr = cp/l. Example Liquid benzene at 50 C has the physical properties = 43.6·105 Pas, cp = 1.821·103 J/kg K, and l = 0.134 W/(m K). One obtains a Prandtl number of Pr = 5.93. The product Gr Pr is also known as the Rayleigh number, Ra. The Reynolds number, Re, can be seen as a ratio of inertial forces to frictional forces. The numerical value of Re is the crucial criterium to decide whether a flow remains in a stable laminar mode, or it may undergo a transition to turbulent flow: For the fluid flow in a circular tube, the critical Reynolds number is Recr = 2,300. For Re < Recr the flow is laminar, for Re > Recr it may become turbulent. The characteristic length l in this case is usually taken as the inner diameter of the tube (> Chap. G1). For parallel flow over a flat plate (see > Chap. G4), the characteristic length l is the length x in flow direction, measured from the leading edge. The critical Reynolds number for this flow is about Rex,crit = 5·105. In liquid film flow, the stability does not depend on Re alone, but also from a number that contains the surface tension, such as Ka or We. Example _ = 8,000 kg/h passes a tube with Water, at a mass flow rate of M the internal diameter di = 52 mm. The temperature is 10 C, so that the density is r = 999.8 kg/m3. The flow velocity is _ rd 2 p 4 ¼ 1:05 m s; l ¼ di ¼ 52 103 m; w¼ M v ¼ 1:300 106 m2 s; Re ¼ 41 900: A2 The Sherwood number, Sh – corresponding to the Nusselt number – is formed as a dimensionless mass transfer coefficient. The equations in the form Nu = Nu (Re, Pr, . . .) used to calculate the heat transfer coefficient a can also be applied to predict the mass transfer coefficient b: Just replace Nu by Sh and Pr by Sc (this is called the ‘‘analogy between heat and mass transfer’’). Example The diffusivity of steam (subscript ‘‘1’’) in air (subscript ‘‘2’’) at 1 bar and 25 C is d12 = 26.5·106 m2/s. With n = 15.6 · 106 m2/s one arrives at a Schmidt number of Sc = 0.589. Using this value, in place of Pr, in Eq. (5) of > Chap. G4 with Re1 = 104, one gets (in place of Nu) the value Shl = 73.8. The mass transfer coefficient b is obtained from this with l = 10 cm (the flow velocity of air ought to be w = 1.56 m/s to make Re1 = 104) as b = (d12/l)·Shl = 19.6 mm/s. The Schmidt number, Sc, is the mass transfer analog of the Prandtl number, Pr. For its use and calculation see the example at the Sherwood number, Sh. The Schmidt number can also be obtained from Sc = Le Pr. The ratio Nu/Pe = a/(rcpw) is also known as the Stanton number, St. The Weber number, We, as the Kapitza number, Ka, contains the surface tension s. So it plays a role for flow problems with free surfaces, for drop formation, and for the atomization of liquids. It can be expressed in terms of Ka, Fr, and Re: We = (Ka Fr Re4)1/3. Example A drop of water with a diameter of d = 5 mm is falling in stagnant air (20 C, 1 bar) with a velocity of w = 11 m/s. The Weber number, with rG = 1.188 kg/m3, the characteristic length l = d = 5 · 103 m, and with s20 C = 72.78 · 103 N/m, is We = 9.88. 13 Part C Fundamentals of Heat Exchanger Design C1 Thermal Design of Heat Exchangers C1 Thermal Design of Heat Exchangers Wilfried Roetzel 1 . Bernhard Spang 2 1 2 Helmut-Schmidt-Universität, Universität der Bundeswehr Hamburg, Hamburg, Germany BUCO Wärmeaustauscher International GmbH, Geesthacht, Germany 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2 Nomenclature, Definitions and Basic Equations . . . . . 33 3 3.1 3.2 3.3 3.4 Design Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Cell Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Mean Temperature Difference Concept . . . . . . . . . . . . . . . . 35 Key to the Design Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 General Approximation Equation for the Estimation of F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4 Analytical Design Formulae for Common Flow Arrangements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Stirred Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Countercurrent and Cocurrent Flow . . . . . . . . . . . . . . . . . . . 38 Multipass Shell-and-Tube Heat Exchangers . . . . . . . . . . . . 38 Cross-flow Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1 4.2 4.3 4.4 1 Introduction Plate Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Spiral Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Plug-in Double-Pipe Heat Exchangers . . . . . . . . . . . . . . . . . 44 5 5.1 5.2 5.3 Heat Exchanger Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Coupled Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Two Heat Exchangers Coupled by a Circulating Thermal Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Phase Change with Superheating and Subcooling . . . . . 47 6 6.1 6.2 Examples of Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Rating of Existing Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Design and Dimensioning of Heat Exchangers . . . . . . . . 49 7 Additional Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 8 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Q_ ¼ kAD#m Widely different tasks are involved in designing heat exchangers. They range from thermal rating or dimensioning through mechanical analysis and costing, to the optimization of heat exchangers and systems. This chapter is restricted to steady state thermal design of heat exchangers in which two fluids are separated by fixed walls [1]. 2 4.5 4.6 4.7 Nomenclature, Definitions, and Basic Equations A schematic diagram of a heat exchanger showing the main parameters is presented in Fig. 1. The local heat flux q_ at the heat transfer surface can be expressed in terms of the local temperature difference ð#1 #2 Þ between the two fluids and the local overall heat transfer coefficient kloc, i.e., q_ ¼ kloc ð#1 #2 Þ ð1Þ The total heat flow rate Q_ is obtained by integrating the local heat flux over the entire area of the heat transfer surface, i.e., ð _ ð2Þ Q_ ¼ qdA A With the introduction of a mean overall heat transfer coefficient k and a mean temperature difference D#m Eqs. (1) and (2) can be replaced by VDI-GVC (ed.), VDI Heat Atlas, DOI 10.1007/978-3-540-77877-6_4, # Springer-Verlag Berlin Heidelberg 2010 ð3Þ One of these two mean values must be defined separately. The following definition of the mean temperature difference is chosen: ð 1 ð#1 #2 Þ dA ð4Þ D#m ¼ A A in which ð#1 #2 Þ is the hypothetical local temperature difference if the heat capacities and the mean value k are constant. The mean value k is then defined by Eq. (3). Its determination is dealt with in > Chap. C2. In the special case of constant local overall heat transfer coefficient kloc and of constant heat capacities over the entire heat transfer surface area, it is k = kloc. Both the heat flow rate Q_ and the mean temperature difference are considered to be positive if heat is transferred from fluid 1 to fluid 2, i.e., if #01 > #02 . The mean temperature difference depends on the flow arrangement of the heat exchanger and on the degree and direction of mixing within the two fluid streams. Its (implicit or explicit) determination allows for a simple method of calculating the heat flow rate transferred over a given area or the area required to transfer a given heat flow rate. Using the energy balance equations for the two fluids in the heat exchanger, the heat flow rate transferred in steady state operation can be expressed in terms of the changes in enthalpy within the two streams. Thus, _ 2 h20 h200 _ 1 h10 h100 ¼ M Q_ ¼ M ð5Þ 34 C1 Thermal Design of Heat Exchangers (d) Heat capacity rate ratios R1 ¼ R2 ¼ C1. Fig. 1. Schematic diagram of a heat exchanger. _ 1; M _ 2 = mass flow rates M _ 1; W _ 2 = heat capacity rates W h1 ; h2 = specific enthalpies #1 ; #2 = temperatures _1 W _2 W _2 1 W ¼ _ R W1 1 ð13Þ ð14Þ where 0 Ri 1 (i = 1,2). The following relationships between the dimensionless numbers can be derived from Eq. (7): In Eq. (5), heat flow to the surroundings, kinetic and potential energies, and all energy transferred into the system from the outside (e.g., energy dissipated by an agitator) are ignored. It is valid for temperature changes in single-phase systems, changes in phase, and chemical reactions. In single-phase systems, the change in enthalpy can be expressed as a change in temperature _: by introducing the heat capacity rate W 0 _ h h00 M _ i cpm;i ði ¼ 1; 2Þ _ i ¼ i 0 i 00 i ¼ M ð6Þ W #i #i If the enthalpy is independent of pressure (e.g., as in an ideal gas) or if the pressure drop in flow direction can be neglected (isobaric change of state), cpm,i is the mean specific heat capacity at constant pressure between the inlet and the outlet temperatures. If a phase change occurs in a system that consists of only one pure substance (and the pressure remains constant), the heat capacity flow rate becomes infinite. Equations (3), (5), and (6) can then be combined to _ 1 #01 #001 ¼ W _ 2 #002 #02 ð7Þ Q_ ¼ kAD#m ¼ W The following dimensionless numbers are useful in the design of heat exchangers. They are obtained by dividing Eq. (7) by the absolutely largest temperature difference #01 #02 in the heat _ 2. _ 1 or W exchanger and by the heat capacity flow rate W P1 NTU1 1 ¼ ¼ ¼ R2 P2 NTU2 R1 P1 P2 ¼ Y¼ NTU1 NTU2 3 ð15Þ ð16Þ Design Concepts There are many methods for designing heat exchangers. They differ from one another in their field of application, physical and mathematical complexity, and accuracy. The most accurate but also most involved are the numerical finite difference or step-by-step methods. At the outset, not only the temperature field but also the flow field may be unknown. In this case, the equation of continuity and the momentum balance equations as well as the energy balance equation have to be solved numerically. The results depend greatly on the quality of the equations and mathematical models adopted for the calculation (turbulence models, equations for the flow resistance of fittings, etc.). In view of the tremendous expenditure and the uncertainty involved, the use of such methods in the design of heat exchangers is only rarely justified. Those methods are not discussed in this chapter. A much easier method has been developed by Gaddis and Schlünder [2, 3] for rating baffled shell-and-tube heat exchangers. (a) Dimensionless mean temperature difference Y¼ D#m #01 #02 ð8Þ where 0 Y 1. (b) Dimensionless temperature changes in the two streams 1 and 2 P1 ¼ P2 ¼ #01 #001 #01 #02 #002 #02 #01 #02 ð9Þ ð10Þ where 0 Pi 1 (i = 1,2). (c) Number of transfer units in streams 1 and 2 kA _1 W kA NTU2 ¼ _2 W NTU1 ¼ where 0 NTUi 1 (i = 1,2). ð11Þ ð12Þ 3.1 Cell Method The method consists of subdividing the heat transfer area into a finite number of area elements over which the two fluid streams or their branches successively flow in the same or in a different sequence. By this, the entire heat exchanger is represented by a system of interconnected but nonoverlapping modules or cells with individual flow arrangements. If the inlet temperatures for any one cell are given and the corresponding value of kA is known, the outlet temperatures can be determined from the equations for the appropriate flow arrangement (see Sect. 4). If the two streams pass through all the cells in series or in parallel, two equations can be derived for the relationship between the inlet and outlet temperatures of both streams in each cell. The temperature of each stream at the inlet to the respective first cell is known. If there are n cells, a total of 2n equations can be drawn up to determine the 2n unknown outlet temperatures for both streams. The system of equations can then be solved to yield all unknown temperatures including the outlet temperatures of the complete heat exchanger. Thermal Design of Heat Exchangers By means of the intermediate temperatures between the cells, individual values of the thermophysical properties and hence for the heat transfer coefficients in each cell may be determined, making the cell method more sophisticated. Differences in the correlations for the heat transfer coefficients, the heat transfer areas, and the flow arrangement in each cell can thus be embraced. To illustrate this method, an example is given. Consider a shell-and-tube heat exchanger with n tube-side and one shellside passes and with z baffles on the shell side. In the model shown in Fig. 2, it is n = 2 and z = 2. For simplification, it is assumed that each cell has the same number of transfer units (NTU). Let the number of transfer units in the entire heat exchanger be NTU1tot and NTU2tot = R1NTU1tot. Then, the following applies for the individual cells: NTUi ¼ NTUi;tot i ¼ 1; 2 nðz þ 1Þ ð17Þ The dimensionless temperature changes P1 and P2 in the cells can then be obtained from the individual flow arrangement (e.g., cross-flow with lateral mixing on the shell-side and no mixing on the tube-side, see Sect. 4) and from NTU1 and R1 = NTU2/NTU1. The dimensionless temperatures for the streams are T1 ¼ #1 #02 #2 #02 0 0 and T2 ¼ 0 #1 #2 #1 #02 ð18Þ Hence the following applies for the cell j in Fig. 3: 00 00 ð1 P1 ÞT1p T1j00 þ P1 T2q ¼0 ð19Þ 00 00 P2 T1p T2j00 þ ð1 P2 ÞT2q ¼0 ð20Þ and If the entire flow arrangement is fixed, cell j can be uniquely tied in with the adjacent cells p and q. If j is the cell in which the streams 1 and/or 2 enter into the complete heat exchanger, it is 00 00 T1p ¼ 1 and T2q ¼0 described below can be applied. It is also recommended for studying effects for which no allowance can be made in the analytical solutions, e.g., small number of baffles in shell-andtube heat exchangers (see Sect. 4.3). It is to observe that the results obtained from the cell method are of no higher accuracy than the heat transfer coefficients used, even if the exchanger is subdivided into a large number of cells. An example is presented in Sect. 6.1 to illustrate the application of the cell method in rating an existing heat exchanger. 3.2 Mean Temperature Difference Concept Usually, simple mathematical methods based on the mean temperature difference concept for the complete heat exchanger yield results with sufficient accuracy for the design. The charts and equations involved are easy to use. The equations are derived by integrating the local energy balances as given by Eqs. (1)–(4) for a given flow arrangement. The flow arrangements are characterized by idealizing assumptions concerning the flow direction and the degree of lateral and axial mixing. The real flow pattern can greatly deviate from the ideal flow, as occurs, e.g., in baffled shell-and-tube heat exchangers. Nevertheless, the design equations derived for the ideal flow arrangements are usually sufficiently accurate. Only under extreme conditions, such as high NTUs or small number of baffles, more complex calculation models, such as the cell method [2, 3] (Sect. 3.1) or the axial dispersion model [4, 5] are recommended. In addition to the idealizations of the flow arrangements, the following simplifying assumptions are made. – The heat exchanger is operated in steady state. – The only parameter that changes the enthalpy of the streams is the heat flux that is transferred, that is, heat losses to the surroundings and kinetic and potential energies are ignored. ð21Þ If Eqs. (19) and (20) are written for all n(z + 1) cells, a system of linear equations is obtained for the 2n(z + 1) unknown cell outlet temperatures which can be solved by known methods. If stream 1 leaves the entire heat exchanger from cell m, the relevant dimensionless temperature change is given by 00 P1tot ¼ 1 T1m ð22Þ The cell method can be recommended for the thermal design of flow arrangements for which none of the analytical solutions C1. Fig. 2. Shell-and-tube heat exchanger with one shell-side and two tube-side passes and two shell-side baffles; longitudinal section and cell model. C1 C1. Fig. 3. Cell j in the heat exchanger. 35 36 C1 Thermal Design of Heat Exchangers – If no phase change occurs, the specific heat capacities, and thus their rates, are constant. Allowance for the change in heat capacity with temperature is discussed in > Chap. C2. – If a change in phase does occur, the local heat capacity flow rate is assumed to be constant as well, which implies a linear relationship between enthalpy flow rate and temperature. The analysis of heat exchangers in which superheating or subcooling occurs as well as a change in phase is explained in Sect. 5.3. – The effects of conduction and mixing in the direction of flow are ignored, except in the case of a stirred tank (Sect. 4.1). Another assumption that must be made in determining the temperature fields in the equipment is that the overall heat transfer coefficient is constant. It is unnecessary for the calculation of outlet temperatures if the mean coefficient as defined by Eqs. (3) and (4) is taken (> Chap. C2). Equations for common flow arrangements are presented in Sect. 4. Since the dimensionless temperature change P1 is expressed as a function of NTU1 and R1, the equations can be applied directly to the rating of existing heat exchangers. Only in some cases these equations can be solved for NTU1. Hence heat exchanger design usually involves iterative solution of the equation P1 = f (NTU1, R1). If the flow arrangement is symmetric, the subscript 1 of P, NTU, and R may be replaced by the subscript 2. In the equations for these flow arrangements, the subscript attached to the dimensionless numbers is i, where i = 1 or i = 2. Most of the 31 design charts presented in Figs. 15–45 were plotted from the equations listed in the tables of Sect. 4. A few were plotted from the results of analytical or numerical methods due to the lack of closed-form solutions; the same assumptions as those listed above were made in their determination. 3.3 Key to the Design Charts The design charts can be explained with Fig. 4 [6]. The flow arrangements involved, together with the geometrically defined streams 1 and 2, are sketched alongside the respective charts. The coordinate axes represent the dimensionless temperature changes P1 and P2 of the two streams. If the flow arrangements are symmetric, the charts will also be symmetrical about the P1 = P2 axis. In this case, P1 and P2 can be interchanged, as is indicated in the diagrams by the subscripts 1,2 and 2,1, the first or second digit of which is respectively valid for the particular case in question. The scale at the top of each chart represents the heat capacity rate ratio R1 (0 R1 1); and that on the right-hand margin, the heat capacity rate ratio R2 = 1/R1 (0 R2 1). The straight line connecting the scale on the margin to the origin is the geometric location of the respective heat capacity rate ratio marked on the scale. Two different sets of curves are plotted in the charts. The full-line curves apply for NTU1 = const. above the diagonal, and for NTU2 = const. below the diagonal. As is evident from Eq. (15), the curves intersect on the diagonal at NTU1 = NTU2. C1. Fig. 4. Schematic diagram of the design charts. The only curve with a smooth transition at the diagonal is that for the limiting curve NTU = 1, which is valid for infinitely large heat transfer areas. Temperature changes beyond this curve are usually impossible. Only a few special flow arrangements, e.g., the mixed–mixed cross-flow (Fig. 32), can attain higher temperature changes with two finite values of NTU. In these cases, the locus of the maximum possible dimensionless temperature changes has been designated as Pmax and included in the chart. No operating points are possible above the limiting curve NTU = 1 or the Pmax curve. The limiting curve NTU = 1 for some flow arrangements, e.g., pure countercurrent flow (Fig. 17), coincides with the right-hand and upper margins, i.e., P1 = 1 and P2 = 1. The second set of curves, which are shown as dashed lines in the charts, are those for constant values of the correction factor F for the logarithmic mean temperature difference. The factor F is defined by F¼ Y NTUiC ¼ ði ¼ 1; 2Þ NTUi YC ð23Þ where YC is the dimensionless temperature difference and NTUC is the number of transfer units in a pure countercurrent heat exchanger in which the dimensionless temperature changes P1 and P2 are the same as that attained for Y and NTUi in the flow arrangement investigated. If flow is purely countercurrent, the relationship F = 1 applies over the entire range of the chart. For all other flow arrangements, the limiting curve NTU = 1 coincides with the F = 0 curve. 3.4 General Approximation Equation for the Estimation of F For flow arrangements in which axial mixing or dispersion does not occur, the following generally valid approximation equation with individual empirical coefficients for each flow arrangement C1 Thermal Design of Heat Exchangers can be recommended for the estimation of the logarithmic mean temperature difference correction factor [7]: 1 F¼ c 1 þ aR1db NTUb1 ð24Þ The coefficients a, b, c, d were determined through least square fits for numerous flow arrangements [7], based on the data calculated for the design charts. The values of a, b, c, d are given in Table 1. For symmetric flow arrangements, d = ½. Coefficients for additional flow arrangements can be found in the works by B. Spang and W. Roetzel [7]. With the correction factor F, the dimensionless temperature changes can be calculated using the known formula for counterflow. C1. Table 1. Values of the coefficients a, b, c, and d for Eq. (24) Flow arrangement a b c d Pure cocurrent flow 0.671 2.11 0.534 0.500 Shell-and-tube heat exchanger with one shell-side and two tube-side passes; e = 1/2 0.317 2.09 0.543 0.500 Shell-and-tube heat exchanger with one shell-side and four tube-side passes 0.274 2.08 0.624 0.508 Shell-and-tube heat exchanger with one shell-side and six tube-side passes 0.262 2.07 0.650 0.509 Shell-and-tube heat exchanger with one shell-side and eight tube-side passes 0.258 2.07 0.661 0.509 Shell-and-tube heat exchanger with one shell-side and three tube-side passes, two of it in countercurrent flow; e = 1/3 0.431 2.33 0.371 0.450 Shell-and-tube heat exchanger with one shell-side and two countercurrent tube-side passes 0.168 2.18 0.490 0.395 Shell-and-tube heat exchanger; divided flow with one shell-side and one tube-side pass 0.272 1.86 0.529 0.329 Shell-and-tube heat exchanger; divided flow with one shell-side and two tube-side passes 0.230 2.03 0.733 0.531 Shell-and-tube heat exchanger; split flow with longitudinal baffle and two shell-side and two tube-side passes 0.0763 2.05 0.536 0.344 Shell-and-tube heat exchanger; double split flow with two longitudinal baffles and two shell-side passes on each side; two tube-side passes 0.0749 2.00 0.544 0.337 Pure cross-flow 0.433 1.60 0.267 0.500 Cross-flow with one tube row; laterally mixed on one side 0.234 1.91 0.597 0.668 Cross-flow, laterally mixed on both sides 0.251 2.06 0.677 0.500 Cross-flow with two tube rows and one pass 0.158 1.53 0.705 0.617 Cross-flow with three tube rows and one pass 0.150 1.38 0.722 0.596 Cross-flow with four tube rows and one pass 0.167 1.34 0.648 0.583 Cross-flow with five tube rows and one pass 0.195 1.35 0.560 0.569 Cross-flow with six tube rows and one pass 0.226 1.37 0.486 0.559 Cross-flow with ten tube rows and one pass 0.333 1.50 0.338 0.535 Counterdirected countercurrent cross-flow with two tube rows and two passes 0.0737 1.97 0.553 0.640 Counterdirected countercurrent cross-flow with three tube rows and three passes 0.0332 2.01 0.540 0.640 Counterdirected countercurrent cross-flow with four tube rows and four passes 0.0188 2.01 0.540 0.650 Counterdirected countercurrent cross-flow with six tube rows and six passes 0.00820 2.03 0.537 0.659 Counterdirected countercurrent cross-flow with four tube rows and two passes 0.0649 1.63 0.625 0.608 Codirected countercurrent cross-flow with two tube rows and two passes 0.0537 1.88 0.621 0.651 Codirected countercurrent cross-flow with three tube rows and three passes 0.0227 1.88 0.632 0.657 Counterdirected countercurrent cross-flow with two passes; stream 2 unmixed, stream 1 mixed only between passes 0.149 1.76 0.264 0.497 Counterdirected countercurrent cross-flow with three passes; stream 2 unmixed, stream 1 mixed only between passes 0.0711 1.85 0.253 0.422 Counterdirected countercurrent cross-flow with four passes; stream 2 unmixed, stream 1 mixed only between passes 0.0419 1.89 0.246 0.399 Plate heat exchanger with one pass for stream 1 and two passes for stream 2 0.272 1.86 0.529 0.322 Plate heat exchanger with one pass for stream 1 and three passes for stream 2, two of them in countercurrent flow 0.211 1.85 0.582 0.292 Plate heat exchanger with one pass for stream 1 and four passes for stream 2 0.244 1.90 0.577 0.323 Plate heat exchanger with two passes for stream 1 and four passes for stream 2 in overall countercurrent flow arrangement 0.0748 1.87 0.525 0.317 37 38 C1 Thermal Design of Heat Exchangers For Ri 6¼ 1 Pi ¼ 1 exp½ðRi 1ÞNTUi F 1 Ri exp½ðRi 1ÞNTUi F ð25Þ and for Ri = 1, NTU1 = NTU2 = NTU P1 ¼ P2 ¼ NTUF 1 þ NTUF ð26Þ For the m,2m shell-and-tube heat exchanger with m 2 (Figs. 28 and 29), the correction factor could also be calculated using the formula for m = 1 (1,2-shell-and-tube heat exchanger). One has to merely divide the total NTU by m: NTUi ; Ri ð27Þ Fm;2m ¼ F1;2 m The presented coefficients are valid for 1 F 0.25 and 0 Ri 1. The maximum relative error in F falls below 5% and in P below 3%. In the generally recommended range 1 F 0.7 below 1% and 2%, respectively. The general approximation Eqs. (24–27) are mainly suitable for rating purposes. For the design from given temperature changes iterations are required: first the required NTU1C for pure countercurrent flow is calculated, then the required NTU1 = NTU1C/F can be introduced in the approximation Eqs. (24–27) with a guessed value of F, yielding an improved value of F, etc. 4 Analytical Design Formulae for Common Flow Arrangements 4.1 Stirred Tank The end points described by Eq. (29) apply to all the flow arrangements that are dealt with below, because all of them are analyzed under the idealized assumption that mixing and heat conduction do not occur in the direction of flow. Mixing in the flow direction reduces the performance of a heat exchanger. Hence, if it is anticipated, the heat exchanger concerned should be designed as a stirred tank in order to obtain results on the safe side. Schematic flow diagrams and design charts for the two types of stirred tanks are presented in Figs. 15 and 16, and the design formulae are summarized in Table 2. 4.2 Countercurrent and Cocurrent Flow The best-known flow arrangements are those for countercurrent and cocurrent flow. Both are symmetrical. If the NTU is given, countercurrent flow reaches the highest values of P; and if P is given the smallest required NTUs. The thermal efficiency of cocurrent flow is very poor, only the two types of stirred tanks have a lower efficiency. The mean temperature difference, as defined by Eq. (4), is both in cocurrent and countercurrent flow the logarithmic mean of the local temperature differences D#a and D#b at both ends of the heat exchanger, i.e., D#m ¼ D#a D#b D#a ln D# b ð30Þ In the limiting case of D#a ! D#b, which arises for R1 ! 1 in countercurrent flow and for NTU ! 0 in cocurrent flow, the logarithmic approaches the arithmetic mean: 1 D#m ¼ ðD#a þ D#b Þ 2 The stirred tank is the only heat exchanger in which mixing and heat conduction are assumed to take place in the direction of flow. In one-sided tanks (Fig. 16), stream 2 is completely mixed in both the flow and transverse directions, but stream 1 is mixed only in the transverse direction. In two-sided tanks (Fig. 15), both streams are completely mixed in all directions. The flow arrangement is symmetric in two-sided tanks, but not in one-sided. The NTUj = const. curves for the stream j that is completely mixed in the flow direction merge into the coordinate axis at points given by NTUj Pj ¼ ð28Þ 1 þ NTUj The curves for the stream i that is not mixed in the flow direction merge into the coordinate axis at points given by Pi ¼ 1 eNTUi ð29Þ ð31Þ The equations in dimensionless notation that correspond to Eqs. (30) and (31) are listed in Table 3, and the charts for the two flow arrangements are shown in Figs. 17 and 18. 4.3 Multipass Shell-and-Tube Heat Exchangers For asymmetric flow arrangements, subscript 1 is allotted to the shell-side stream and subscript 2 to the tube-side stream. The simplest case with one shell-side and one tube-side pass and a sufficiently large number of baffles on the shell side, or none at all, is the countercurrent or cocurrent flow according to Sect. 4.2. Charts for multipass flow arrangements are shown in Figs. 19–29. That for the shell-and-tube heat exchanger with one shell-side and five tube-side passes (1,5-HEX, cf. Fig. 23) C1. Table 2. Equations for stirred tanks Flow arrangement Two-sided stirred tank; i = 1, 2 One-sided stirred tank, stream 2 mixed P = f(NTU, R) NTU = f(P, R) NTUi 1 þ NTUi ð1 þ Ri Þ 1 1 ¼ R1 þ P1 1 eNTU1 Pi 1 Pi ð1 þ Ri Þ P1 NTU1 ¼ ln 1 1 R1 P1 Pi ¼ NTUi ¼ Limiting curve Pi1 ¼ 1 1 þ Ri P11 ¼ 1 1 þ R1 Thermal Design of Heat Exchangers C1 C1. Table 3. Equations for countercurrent and cocurrent flow Flow arrangement Pure counter current flow i = 1, 2 Pure cocurrent flow i = 1, 2 P = f(NTU, R) NTU = f(P, R) Q = f(P1, P2) Limiting curve 1; Ri 1 Pi1 ¼ 1 Ri ; Ri > 1 1 1 Ri Pi P1 P2 1 exp½ðRi 1ÞNTUi ln Y ¼ 1P2 for Ri 6¼ 1 NTUi ¼ 1 Pi 1 Ri 1Ri exp½ðRi 1ÞNTUi ln 1P1 P NTU Y ¼ 1 P NTU ¼ for Ri 6¼ 1 Pi ¼ 1P 1 þ NTU 1 1 exp½NTUi ð1 þ Ri Þ ln½1 Pi ð1 þ Ri Þ ðP1 þ P2 Þ Pi1 ¼ Pi ¼ NTUi ¼ Y¼ 1 þ Ri 1 þ Ri 1 þ Ri ln½1 ðP1 þ P2 Þ Pi ¼ was obtained by an analytical design method [8, 9]; and that in Fig. 27 for double split flow by a closed-form equation [10]. The equations for the other flow arrangements are listed in Table 4. The NTU-ratio e that occurs in the equations for the 1,2and 1,3-HEX is defined by e¼ ðkAÞcocurr:pass ðkAÞtot ð32Þ The ratio e allows for differences in the heat transfer area and in the heat transfer coefficient for the various passes (with the restriction that the product kA is the same in each of the two counterflow passes in the 1,3-HEX). The heat transfer coefficient on the tube side depends on temperature. In the 1,2-HEX, this can be allowed for by determining separate heat transfer coefficients for each pass. The reference temperature in this case is the arithmetic mean of the inlet and outlet temperatures in the pass concerned. The intermediate temperature #2z, i.e., at the outlet of the first pass and at the inlet to the second, is required for its determination. Concerning the flow direction in the tube-side passes, two layouts I and II are possible. In layout I, the first pass is countercurrent to the shell-side stream, in layout II cocurrent. The equations for the determination of the temperatures #I2z and #II2z are given in Table 4. The 1,2-HEX can be adopted as an approximate model for a 1,n-HEX with n = 2m tube-side passes (m = 1, 2, 3, . . .) of roughly the same area [8, 9]. The areas of the countercurrent and the cocurrent passes in the 1,2-model must be the same as those in the actual 1,2m-HEX. In the normal case the areas are the same in all the passes and a constant mean heat transfer coefficient can be adopted for the complete heat exchanger. Under these circumstances, a ratio of e = ½ can be taken for the 1,2-HEX, and of e = 1/3 for the 1,3-HEX. The charts in Figs. 19 and 21 are also calculated with these values. The flow arrangement obtained with one shell-side pass and an infinite number of equal tube-side passes (1,n-HEX with n ! 1) corresponds to that of mixed–mixed cross-flow (cf. Sect. 4.4) [17]. It can also serve as an approximation for a large even number of tube-side passes (1,2m-system with m = 2, 3, . . .). The results from this approximation are more on the safe side than those obtained from the approximation with the equations for the 1,2-system. An upper limit for the error of the approximation can be derived from a comparison with the chart (Fig. 20) or the equation (Table 4) for the 1,4-HEX. Shell-and-tube heat exchangers with an odd number of tube-side passes can be approximately described by the equations for the 1,3-system with two countercurrent passes of the same area if the NTU-ratio e is formed from the sum of the areas of all the cocurrent passes; for instance, e = 3/7 for a total of seven passes of the same area, four of which are countercurrent. As has already been mentioned, the first of a number of tube-side passes may flow countercurrent (layout I) or cocurrent (layout II) to the shell-side stream. If the number is odd, layout I is always the more advantageous, because the countercurrent passes predominate. If there is an even number of tubeside passes of the same area and if the calculation is based on constant values for the heat transfer coefficient, the same results are obtained for both layouts. However, a more accurate calculation with varying heat transfer coefficients reveals that the more favorable layout is that in which the coefficients for the countercurrent passes are higher than those for the cocurrent [8, 9]. Hence, the following rule can be derived for an even number of equal tube-side passes. If a liquid is to be heated in the tubes, the first tube-side pass should be cocurrent to the shell-side stream (layout II); if it is to be cooled, countercurrent (layout I). The opposite applies if a gas flows in the tubes. A number m of identical 1,n-HEXs can be connected in series {m,(mn)-HEXs} in order to achieve higher temperature changes. The equations that apply in this case are those given in Sect. 5.1 for the countercurrent coupling of identical individual heat exchangers. Charts for n = 2 and m = 2 and 4 are shown in Figs. 28 and 29. Also the Eq. (27) can be applied for the m,2m-HEX. Strictly speaking, the equations and charts presented in this section are valid only if there is an infinite number of baffles on the shell side, or none at all. The equations and charts allow a good approximation if the number of baffles is sufficiently large, i.e., at least ten for countercurrent flow and at least five for 1,2HEXs (according to Gardner and Taborek [18]). If the number of baffles is small, allowance must be made for the fact that both streams are in cross-flow between two baffles. This can be done by subdividing the system into cells, as described in Sect. 3.1. The equations to be adopted in the calculations for each cell are those for cross-flow with one tube row (Sect. 4.4) and laterally mixed stream 1 on the shell side (which corresponds to stream 1 on the tube-side as conventionally designated in cross-flow heat exchangers). For a finite number of baffles, there are two layouts A and B with different positions of the inlet and outlet relative to one another (Fig. 5). In both layouts they are adjacent. In layout A they exert a certain cocurrent effect, in layout B a 39 40 C1 Thermal Design of Heat Exchangers C1. Table 4. Equations for shell-and-tube heat exchangers, stream 1 on shell side, stream 2 inside the tubes Flow arrangement One shell-side and two tube-side passes [8, 9] i = 1, 2 1 Pi 1 1 ¼ 2 1 þ Ri þ S coth 2 SNTUi Equation Limiting curve Pi1 ¼ or 2 2Pi ð1 þ Ri Þ NTUi ¼ arcoth S SPi where pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ S ¼ 1 þ R2i þ 2Ri ð2e 1Þ NTU-ratio e from Eq. (32) Temperature W2z of tube-side stream between passes 1 SP1 exp NTU #I2z #02 2 ð1 þ R1 ð2e 1ÞÞ Layout I: 0 0 ¼1 1 #1 #2 2sinh NTU 2 S 1 SP1 exp NTU #II2z #02 2 ð1 þ R1ð2e 1ÞÞ Layout II: 0 0 ¼ 1 P1 1 #1 #2 2sinh NTU 2 S qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ One shell-side 1 þ ðR1 =mÞ2 1 R1 R1 =m and 2m ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ þ 1 eR1 NTU1 1 eR1 NTU1 =m tube-side passes, P1 1 exp NTU1 1 þ ðR1 =mÞ2 m = 1, 2, . . ., 1 0 1 sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 [1, 11] 1@ R1 R1 A 1þ 1þ þ 2 m m S One shell-side S1 e 1 þ eS3 eS2 1 þ S2 eS2 þ eS3 1 eS1 þ . . . P1 ¼ and three tubeS1 ðeS1 þ eS3 ÞðR1 eS2 1Þ þ S2 ðeS2 þ eS3 Þð1R1 eS1 Þ þ . . . side passes, two . . . þ NTU1 ð1 R1 Þ eS2 eS1 1 þ eS3 countercurrent . . . þ NTU1 ð1 R1 ÞðeS2 eS1 Þð1 þ R1 eS3 Þ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ [12] 2 S1=2 ¼ p2 p4 q S3 ¼ 12 R1 NTU1 ð1 eÞ p ¼ NTU1 1 12 R1 ð1 3eÞ q ¼ 12 eð1 eÞNTU21 R1 ð1 R1 Þ NTU-ratio e from Eq. (32) P eð1 eÞ 1þe 2 ¼ NTU 2 1P 1 þ 3e 1 þ 3e for R1 ¼ 1 One shell-side and two tubeside passes, both countercurrent [12] Divided flow with one shellside and one tube-side pass [13] P1 ¼ e0:5NTUð1þ3eÞ 1 þ e0:5NTUð1eÞ þ 1 2=ð2 þ R1 Þ; R1 2 1=R1 ; R1 > 2 1 ð2 R1 Þð2 þ R1 exp½NTU1 ð1 þ R1 =2ÞÞ for R1 6¼ 2 R1 R1 ð2 þ R1 Þð2 R1 exp½NTU1 ð1 R1 =2ÞÞ 1 1 þ expð2NTU1 Þ for R1 ¼ 2 P1 ¼ 2 4ð1 þ NTU1 Þ P1 ¼ 1 ð1 bÞ2 ð1 gÞ P1 ¼ for R1 6¼ 2 R1 R1 2b2 ð1 gÞ 1 exp½NTU1 ð2 þ R1 Þ=4 b¼ 1 þ 2=R1 1 exp½NTU1 ð2 R1 Þ=2 g¼ 2=R1 exp½NTU1 ð2 R1 Þ=2 ð1 þ 2NTU1 ÞeNTU1 eNTU1 P1 ¼ for R1 ¼ 2 2 þ ð3 þ 4NTU1 ÞeNTU1 eNTU1 1; R1 1 ; R1 > 1 1 R1 P11 ¼ for R1 6¼ 2 1 1 1 for R1 ¼ 2 ¼1þ þ P1 NTU1 1 þ expðNTU1 Þ ke0:5 NTU1 ðk1Þ 1 ekNTU1 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 þ ðR1 =mÞ2 1 1 eNTU1 ð0:5R1 1Þ 1 e0:5R1 NTU1 þ 1 ð0:5R1 1Þ eNTU1 ð0:5R1 1Þ þ e0:5R1 NTU1 þ ðR1 e0:5R1 NTU1 þ 1Þ eNTU1 ð0:5R1 1Þ 1 1 1 þ 2R1 R1 =m þ 2 P11 ¼ Divided flow with 1 R1 ekNTU1 þ 1 2ke0:5 NTU1 ð1þkÞ þ 1 one shell-side and P1 ¼ 1 þ 2 þ k ekNTU1 1 k 1 þ ðk þ 1ÞekNTU1 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ two tube-side k ¼ 0:5 R21 þ 4 passes [14] Split flow with longitudinal baffle and two shell- side and two tube-side passes (tube-side outlet and shellside inlet at the same side) [15, 16] 1 P11 ¼ 2 1 þ Ri þ S P11 ¼ 2=ð2 þ R1 Þ; R1 2 1=R1 ; R1 > 2 1 R1 ¼1þ þk 2 P11 ( P11 ¼ ; R1 2 1=R1 ; R1 > 2 2þR1 2þR1 þR21 Thermal Design of Heat Exchangers C1. Fig. 5. Layouts of shell-and-tube heat exchangers with one shell-side and two tube-side passes and with baffles on the shell side. Layout A: the adjacent nozzles for stream 1 and 2 are either both inlets or both outlets. Layout B: one of the adjacent nozzles for stream 1 and 2 is an inlet, the other one is an outlet. countercurrent one. Analysis by the cell method [2, 3] shows that layout B is fundamentally superior to layout A and should therefore be preferred, although the differences are not very pronounced. 4.4 Cross-flow Heat Exchangers If the flow arrangement is asymmetric, subscript 1 is allotted to the stream inside the tubes and subscript 2 to that outside the tubes. In Sect. 4.3, complete lateral mixing in each pass for all shell-and-tube flow arrangements was assumed. In cross-flow heat exchangers, however, even the limiting case of no lateral mixing is of significance. Thus, there are three fundamental cross-flow arrangements, each with one pass on both sides, as indicated below. – Both streams are unmixed in the lateral direction (pure cross-flow or unmixed–unmixed cross-flow; Fig. 30). – Stream 1 (inside the tubes) is laterally mixed, and stream 2 (outside the tubes) is not (cross-flow with one tube row or mixed–unmixed cross-flow; Fig. 31). – Both streams are laterally mixed (mixed–mixed cross-flow; Fig. 32). The analytical solutions for these flow arrangements are given in Table 5. Since the thermal efficiency is reduced by lateral mixing, the calculation for the case of complete mixing yields results on the safe side. The degree of lateral mixing of stream 1 and the thermal efficiency achieved in cross-flow arrangements with n tube rows (n = 2, 3, . . .) in one pass lie between the figures obtained for cross-flow with one tube row and those for pure cross-flow (Figs. 33–35, and the equations in Table 5). In multipass cross-flow heat exchangers, the thermal efficiency depends not only on the degree of lateral mixing in each pass but also on the overall flow arrangement, i.e., on whether the flow is overall countercurrent or cocurrent, and on the degree of mixing between passes. If the outer stream is not laterally mixed, the thermal efficiency also depends on whether the flow on the tube side is in alternate directions in successive passes (counterdirected countercurrent cross-flow) or in the same direction in each pass (codirected countercurrent crossflow). Many flow arrangements are feasible, but only a few are of practical significance. If the two streams are adequately mixed C1 between each pass, the coupling equations given in Sect. 5.1 for overall cocurrent or countercurrent flow should be used. The counterdirected countercurrent cross-flow with stream 2 unmixed is easy to realize in tube bundles of rectangular crosssection. The relevant design charts are shown in Figs. 36–41. Equations are presented in Table 5 for flow arrangements with four or less passes and with stream 1 completely mixed in the lateral direction (one tube row for each pass; Figs. 36–38) and for flow arrangements with two passes and two tube rows in each pass (Fig. 39). Counterdirected cross-flow heat exchangers with four or more passes and one tube row per pass can be designed with the aid of the following approximate equation [24]: 1 pﬃﬃﬃﬃﬃ 3sinh NTU R1 n nNTU pﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃ ð33Þ F¼ 1 NTU1 R1 1 þ 2cosh n R1 where n is the number of passes. The dimensionless temperature change Pi (i = 1, 2) can then be obtained from Eq. (25) or (26). The error in P is at the most 1% for n 4. The charts for flow arrangements in which the number of tube rows in each pass is very large (each pass as in pure crossflow; Figs. 40 and 41) were calculated numerically. For the numerical calculation each pass was subdivided into 40 40 cells. In addition to the given charts and coefficients for Eq. (24), a most powerful approximation [24] can be recommended which is valid for any number of counterdirected pure cross-flow passes. The codirected countercurrent cross-flow arrangement in which the flow is in the same direction in each pass is the more effective one. It is realized in helical coil heat exchangers (Fig. 6), in which each turn corresponds to one pass with one row of tubes. In Table 5 design equations are given for arbitrary values of n. Alternatively, if mixing between passes or counterdirected pass flow is assumed for the design calculation, the exchanger surface will be overestimated and one is on the safe side. Countercurrent cross-flow transforms into pure countercurrent flow as the number of passes increases. However, if the NTU is high, i.e., NTU > 5, the equations for countercurrent flow do not apply unless the number of passes is about 20 or more. 4.5 Plate Heat Exchangers The following is restricted to the thermal analysis of heat exchangers with a large number of plates, i.e., those in which thermal end effects can be ignored (heat is transferred on only one side of the channels at the ends). According to Kandlikar and Shah [25], this end effect can generally be neglected if there are more than 40 plates in the complete heat exchanger. Solutions that have been determined numerically or analytically for equipment with a smaller number of plates and for various flow arrangements can be found in the literature [25, 26]. Plate heat exchangers can be classified regarding the number of passes for the two streams. Subscript 1 is allotted to the stream with the smaller number of passes. Flow arrangements with the same number of passes on each side are symmetrical. Several flow arrangements are feasible with a given number of passes on each side. They are partly identical regarding the 41 42 C1 Thermal Design of Heat Exchangers C1. Table 5. Equations for cross-flow heat exchangers, stream 1 inside tubes Flow arrangement Pure cross-flow [19, 20] i = 1, 2 Cross-flow with one tube row, laterally mixed on one side [21] Cross-flow, laterally mixed on both sides [21] i = 1, 2 Pi ¼ 1 1 X Ri NTUi m¼0 (" 1 eNTUi Equation Limiting curve #" #) m m X X 1; Ri 1 1 1 Pi1 ¼ NTUji 1 eRi NTUi ðRi NTUi Þj 1=Ri ; Ri > 1 j! j! j¼0 j¼0 P1 ¼ 1 exp eR1 NTU1 1 =R1 1 or NTU1 ¼ ln½1 þ R1 lnð1 P1 Þ R1 1 1 Ri 1 ¼ þ Pi 1 eNTUi 1 eRi NTUi NTUi n1 Cross-flow with n X j nB P ¼ 1 e 1 nj anj1 1 tube rows and n j¼0 one passa where n-1 = 0; n0 = 1 1 nR1 B2 þ 2ja þ a nj ja2 nj1 ; j = 0, 1, 2, … njþ1 ¼ jþ1 a ¼ eR1 NTU1 =n ; B ¼ ð1 aÞ=R1 Counterdirected 1 d d ¼ þ 1 e2d=R1 countercurrent 1 P1 2 2 cross-flow where d ¼ 1 eR1 NTU1 =2 with two tube rows and two passes [22] Counterdirected 1 d 2 3d=R1 d d2 d ¼ 1 e þ d 1 1 ed=R1 countercurrent R1 1 P1 2 4 2 cross-flow with where d ¼ 1 eR1 NTU1 =3 three tube rows and three passes [22] Counterdirected 1 d d d2 d 2d d þd 1 ¼ 1 1 þ 1 e2d=R1 countercurrent 1 P1 2 2 4 2 R1 2 cross-flow with d 3 4d=R1 þ 1 e four tube rows 2 and four passes [23] where d ¼ 1 eR1 NTU1 =4 Counterdirected 1 3 2d2 d d2 1 e4d=R1 þ e4d=R1 2R1 d 4 d þ R1 þ d 1 2 þ 8 1 countercurrent ¼ 2 2 1 P1 cross-flow 1 þ Rd1 with four tube where d ¼ 1 eR1 NTU1 =4 rows and two passes [23] n 1 Codirected Y 1 B ¼ e dj countercurrent 1 P1 j¼0 cross-flow with n B 2 tube rows and n where d0 = 1; d1 ¼ e R1 B i X mj amj1 passesa di ¼ d1 ; i = 2, 3, 4,… i1 Q j¼2 dk k¼ijþ1 m-1 = 0; m0 = 1 1 2 R1 B þ 2ja þ a mj ja2 mj1 ; j = 0, 1, 2, … mjþ1 ¼ jþ1 a ¼ eR1 NTU1 =n ; B ¼ ð1 aÞ=R1 a P11 ¼ 1 e1=R1 Pi1 ¼ 1 1 þ Ri P11 ¼ 1 en=R1 P11 ¼ 1 j n1 X 1 j n 1 j! n R 1 j¼0 2 1 þ e2=R1 P11 ¼ 1 4 3 2 R1 e1=R1 þ e3=R1 8 1 2=R1 ¼3þ4 1 þ e4=R1 e 1 P11 R1 1 2 5 4=R1 þ e4=R1 2R1 3 þ R1 þ 8 1 e 1 ¼ 2 1 P11 1 þ R11 n 1 Y 1 ¼ e1=R1 dj1 1 P11 j¼0 where d01= 1; d11 ¼ e1=R1 1=R1 i X 1 di1 ¼ d11 i1 Q j¼2 j!Rj dk1 1 k¼ijþ1 i = 2, 3, 4,. . . These equations have been derived by Th. Bes, Institute of Thermodynamics, Helmut Schmidt University/University of the Federal Armed Forces Hamburg, 1993 Thermal Design of Heat Exchangers thermal performance. A method of determining the thermal efficiency is to break down the flow arrangement into a system of cocurrent and countercurrent units connected in series and parallel and to apply the coupling equations (Sect. 5.1). Design charts showing the most favorable flow configurations in four different arrangements of passes are presented in Figs. 42–45. The equations used for their determination are listed in Table 6. The most advantageous flow arrangement with the same number of passes on both sides is pure countercurrent flow. 4.6 C1 Spiral Heat Exchangers In spiral heat exchangers with a finite number of turns, the two streams flow in countercurrent, but the thermal efficiency is poorer than that in pure countercurrent flow. A schematic diagram of the flow arrangement is shown in Fig. 7. The stream that enters on the inside is allotted the subscript 1. The following approximation equation [28] applies to the logarithmic mean temperature difference correction factor: F¼ 1 1 þ NTU2 ln NTU2 1 þ NTUri 2 ð34Þ kp do H NTU ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ _2 _ 1W W ð35Þ ri þnb where C1. Fig. 6. Schematic diagram of a helical coil heat exchanger with n = 10 turns (or passes). is formed with the geometric mean of both heat capacity flow rates, and with the outside shell surface of diameter do and height H. The number of turns is denoted with n, ri is the radius of the central tube and b the width of the flow channels. The temperature change Pi (i = 1, 2) can be determined from the correction factor F by means of Eqs. (25) or (26) (Sect. 3.4). If n 4 and F > 0.8, the relative error for P is less than 1%. The approximation equation yields symmetrical results, although the flow arrangement is slightly asymmetric. Equations (34) and (35) are valid for a constant overall heat transfer coefficient. In a special method [29] the effect of changing radius of channel curvature on the transfer coefficients can also be taken into account. C1. Table 6. Equations for plate heat exchangers [27]. P1c dimensionless temperature change for pure countercurrent flow (Table 3). P1p dimensionless temperature change for pure cocurrent flow (Table 3) Flow arrangement Equation Limiting curve One pass for stream 1 and two passes for stream 1 1 2=ð2 þ R1 Þ; R1 2 P1c þ P1p R1 P1c P1p P1 ¼ P11 ¼ 2 1=R1 ; R1 > 2 2 2 where P1c ¼ P1c ðNTU1 ; R1 =2Þ and P1p ¼ P1p ðNTU1 ; R1 =2Þ One pass for stream 1 and three passes for 1 1 1 ð9 R1 Þ=ð9 þ 3R1 Þ; R1 3 P1p þ P1c 1 R1 P1p P1 ¼ 2 R1 P1c P11 ¼ 1=R1 ; R1 > 3 stream 2, two in countercurrent 3 3 3 where P1c ¼ P1c ðNTU1 ; R1 =3Þ and P1p ¼ P1p ðNTU1 ; R1 =3Þ One pass for stream 1 and four passes for stream 1 ð4=ð4 þ R1 ÞÞ2 ; R1 4 P1 ¼ d 1 R1 d P11 ¼ 2 4 1=R1 ; R1 > 4 1 1 P1c þ P1p R1 P1c P1p d¼ 2 4 where P1c ¼ P1c ðNTU1 ; R1 =4Þ and P1p ¼ P1p ðNTU1 ; R1 =4Þ Two passes for stream 1 and four passes for dð1 dÞð1 dR1 Þ 4= 4 þ R21 ; R1 2 P1 ¼ d þ P11 ¼ 2 stream 2 in overall counterflow 1=R1 ; R1 > 2 1 d R1 1 1 P1c þ P1p R1 P1c P1p d¼ 2 2 where P1c ¼ P1c ðNTU1 ; R1 =2Þ and P1p ¼ P1p ðNTU1 ; R1 =2Þ 43 44 C1 4.7 Thermal Design of Heat Exchangers Plug-in Double-Pipe Heat Exchangers The dimensionless temperature change P that occurs within a heating or cooling medium that flows in a double-pipe heat exchanger with closed ends (Fig. 8) can be obtained from the following equation [1]: P¼2 1 emNTU 1 þ m þ ðm 1ÞemNTU ð36Þ where #0 #00 ; #0 #s ðkAÞo ; NTU ¼ _ W sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ðkAÞi ; m¼ 1þ4 ðkAÞo P¼ #s is the temperature of the ambient medium to be heated or cooled and is assumed to be constant (complete mixing or phase change), _ is the heat capacity flow rate of the heating or cooling W medium, (kA)o is the product of the overall heat transfer coefficient and the area of the outer pipe, and (kA)i is the corresponding product for the inner pipe. Equation (36) is valid regardless of whether the heating or cooling medium enters the inner or outer pipe. 5 Heat Exchanger Systems 5.1 Coupled Heat Exchangers A number of heat exchangers of the same or different types may be connected together. The temperature changes that can be achieved by the coupled system depend on the nature of the connections, the behavior of the individual units, and the degree of mixing of the streams between the units. It is assumed here that the streams between the individual exchangers are completely mixed and that the heat capacity rates in the entire system are constant. Exchangers can be connected in series with overall cocurrent (Fig. 9) or countercurrent (Fig. 10) flow, and stream 2 can be readily divided into a number of parallel substreams (Fig. 11). The individual flow arrangements are unaffected by the nature of the series or parallel connections, and the equations and design charts in Sect. 4 still apply. C1. Fig. 7. Schematic diagram of a spiral heat exchanger with n = 3 turns in the double spiral. C1. Fig. 9. Schematic diagram of three heat exchangers in series connection with overall cocurrent flow. C1. Fig. 8. Inserted double-pipe heat exchanger for heating or cooling a medium at a constant temperature. C1. Fig. 10. Schematic diagram of three heat exchangers in series connection with overall countercurrent flow. Thermal Design of Heat Exchangers C1 exchangers will partially or totally reduce the overall temperature changes P1tot and P2tot. This effect is particularly pronounced for two exchangers with crossing temperatures. If, for example, for n = 2 identical exchangers R1 = 1 and P1 = 1 (counterflow, NTU1 = NTU2 = 1), the total temperature change P1tot = 0, according to Eq. (42). Similar effects may also occur in single heat exchangers, e.g., in multipass shell-and-tube exchangers (Fig. 5, layout A) or in the mixed–mixed cross-flow. (b) Series connection with overall countercurrent flow C1. Fig. 11. Schematic diagram of three heat exchangers in parallel connection, stream 2 divided into three substreams. The number of transfer units NTU1tot and the heat transfer area Atot in a coupled system are the sums of the corresponding values NTU1i and Ai for the individual exchangers, regardless of the type of connection. Thus, NTU1tot ¼ n X NTU1i ð37Þ i¼1 In principle, series connections with overall countercurrent flow are more effective than those in cocurrent flow [30]. The equation that applies in this case is n Y 1 P1tot 1 P1i ¼ ð43Þ for R1 6¼ 1 1 R1 P1tot i¼1 1 R1 P1i or 1 R1tot ¼ n X 1 R i¼1 1i ð39Þ If R1a = R1b = . . . = R1, 1 R1tot n ¼ R1 Ftot NTU1tot ¼ Ftot ð38Þ If the exchangers are connected in series (Figs. 9 and 10), the heat capacity rate ratios R1 and R2 in each of them are equal and identical to the corresponding ratios for the entire system. If they are connected in parallel (Fig. 11), the following applies: ð40Þ The relationship between the dimensionless temperature change in each of the exchangers P1i and that in the entire system P1tot differs for the types of connection. ½1 P1i ð1 þ R1 Þ n X Fi NTUi ð45Þ i¼1 In this particular case, Ftot = Fi = F, where Fi is the correction factor for the individual exchanger and Ftot is the value for the whole system. (c) Stream 2 split up into parallel substreams The equation that applies in this case is [31] n Y ð1 P1i Þ ð48Þ i ¼1 ð41Þ i¼1 Groups of exchangers within a system may be considered as single units. The total effect is independent of the sequence in which the individual elements are connected. In the special case that the dimensionless temperature change is the same in each exchanger, i.e., P1a = P1b = . . . = P1, Eq. (41) can be simplified to give 1 P1tot ð1 þ R1 Þ ¼ ½1 P1 ð1 þ R1 Þn NTU1i ¼ In the special case of equal dimensionless temperature changes, i.e., Pi = P, Eqs. (43) and (44) become 1 P1tot 1 P1 n ¼ for R1 6¼ 1 ð46Þ 1 R1 P1tot 1 R1 P1 Ptot nP ¼ ð47Þ for R1 ¼ 1 and 1 Ptot 1 P 1 P1tot ¼ The following equation applies [30]: 1 P1tot ð1 þ R1 Þ ¼ n X i¼1 (a) Series connection with overall cocurrent flow n Y ð44Þ for R1 = 1 (Pi = P1i = P2i and Ptot = P1tot = P2tot). From Eq. (43) one can derive for the correction factor If NTU1a = NTU1b = . . . = NTU1, NTU1tot ¼ nNTU1 n X Ptot Pi ¼ 1 Ptot 1 Pi i¼1 For the special case in which the dimensionless temperature change is the same in each exchanger, i.e., P1i = P1, Eq. (48) can be simplified to give 1 P1tot ¼ ð1 P1 Þn ð49Þ Many types of connections other than those dealt with above are feasible. They are described and discussed in detail in > Chap. C5. In the cell method, as described in Sect. 2, a single exchanger is regarded as a system of individual elements. ð42Þ It could be closely approximated if, for example, the individual exchangers are all identical. A possible adverse effect of the series connection in overall cocurrent flow should be mentioned: If in the first exchanger the temperatures cross, i.e., if P11(1 + R1) > 1, the following 5.2 Two Heat Exchangers Coupled by a Circulating Thermal Fluid For heat transfer between two gases, space considerations or safety aspects sometimes require systems that consist of two 45 46 C1 Thermal Design of Heat Exchangers 1 k1 k2 ¼ þ _ _2 _ Ws;opt W1 W ð51Þ with k1 ¼ ðkAÞ1 ðkAÞ2 and k2 ¼ ðkAÞ1 þðkAÞ2 ðkAÞ1 þðkAÞ2 ð52Þ Under this optimum condition, the exchanger system can be regarded as one single counterflow heat exchanger with the effective overall heat transfer resistance C1. Fig. 12. Schematic diagram of a system of two heat exchangers coupled by a circulating stream. single heat exchangers coupled by a circulating thermal fluid. Such a system is shown in Fig. 12. The following equations apply to the individual exchangers. When the subscripts consist of two digits, the first refers to the fluid, and the second to the exchanger. Heat exchanger 1 Heat exchanger 2 NTU11 ¼ ðkAÞ1 _1 W R11 ¼ P11 ¼ NTU22 ¼ _1 W _s W #01 #001 #01 #0s1 ðkAÞ2 _2 W R22 ¼ _2 W _s W P22 ¼ #002 #02 #0s2 #02 R1tot ¼ #01 #001 #01 #02 ð54Þ #00s1 ¼ #0s2 ¼ k1 #01 þ k2 #002 #0s1 ¼ #00s2 ¼ k1 #001 þ k2 #02 ðkAÞeff ¼ _1 W The first step in rating a system is to determine the dimensionless temperature changes P11(NTU11; R11) and P22(NTU22; R22) for the individual exchangers and their flow arrangements using the equations and design charts in Sect. 4. The dimensionless temperature change within the whole system can then be determined from the following equation [1, 32]: 1 1 1 ¼ þ R1tot R11 P1tot P11 P22 sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ k2 F2 p1 ; k2 ¼ 1 k1 k1 F1 p2 _ s;opt from Eq. (51). Then, the and the optimum flow rate W unknown inlet and outlet temperatures of the circulating flow stream can be determined from _1 1 W ¼ _ R W2 2tot NTU1tot ð53Þ The required value of (kA)eff is determined from the given data _ 1; W _ 2 ) in the known manner for the hypothetical single (P1tot,W counterflow heat exchanger. The individual values of the real counterflow exchangers (kA)1 and (kA)2 have to be designed such that Eq. (53) is fulfilled. For individual flow arrangements other than counterflow one can, as an approximation, simply replace in Eqs. (52) and (53) (kA)1 and (kA)2 by (kA)1F1 and (kA)2F2, respectively. Many designs are possible which fulfill Eq. (53). The economically optimal values of both heat transfer surface areas A1 and A2 depend on the ratio of the prices per unit area p1/p2 as well as the ratios of both the overall heat transfer coefficients k1/k2 and the correction factors F1/F2 [33]. The optimum surfaces can be estimated as follows [33]. With guessed values of the above-mentioned ratios one can first calculate optimal values of k1 and k2 according to 1 ¼1þ k1 The following apply to the entire system. P1tot ¼ 1 1 1 ¼ þ ðkAÞeff ðkAÞ1 ðkAÞ2 ð50Þ Concerning the total temperature change P1tot, there exists an optimum value of the circulating heat capacity flow rate _ s;opt [1] if the overall heat transfer coefficients do not W depend on the circulating flow rate. For two counterflow heat exchangers [33] ð55Þ Using the charts or equations for the individual flow arrangements one can determine for both exchangers the required values of (kA)1 and (kA)2 as well as F1 and F2. The heat transfer calculations yield k1 and k2, and the guessed values in Eq. (54) can be improved. This way the required heat transfer surfaces A1 and A2 can iteratively be determined. A detailed investigation of the thermal behavior of such systems was carried out by NaRanong [34, 35]. In his work, various individual flow arrangements are considered and the effect of transfer coefficients varying with the circulating flow rate are taken into account. Not only the steady state but also the transient behaviour is investigated. The coupled system can also be regarded as a heat exchanger network (see > Chap. C5). Thermal Design of Heat Exchangers 5.3 Phase Change with Superheating and Subcooling Normally, heat exchangers in which superheated vapor is cooled and completely condensed and the condensate is subcooled are also regarded as coupled systems. The same applies to the reverse case of evaporation. The three unit operations are designed as if they were to take place in separate exchangers and the individual areas are added together to obtain the area of the entire system. In Fig. 13, the average temperatures over the cross-sections have been plotted against the heat flow rate Q_ transferred from the vapor in the heat exchanger (on the assumption of constant specific heat capacities and constant pressure during condensation). Since it is unknown how the entire heat transfer area has to be divided over the three unit operations, assumptions must be made on the flow arrangement in the desuperheating section a and the subcooling section c. These assumptions must be checked in the light of the results obtained, and the calculation must then be repeated when necessary. If the inlet and outlet temperatures for the complete heat exchanger and the boiling point #bp are known, the temperatures #2ab and #2bc can be derived from the energy balances for the desuperheating and subcooling sections. The dimensionless temperature changes P1j and P2j (j = a, b, c) can thus be determined for the three parts of the exchanger. The values obtained for P1j and P2j can then be taken to calculate the number of transfer units NTU2j (j = a, b, c) for the flow arrangements in each part. The method to be adopted is that described in Sect. 4. Regardless of the flow arrangement, Eq. (29) with i = 2 always applies for the condensation section b. The mean overall heat transfer coefficient in the condensation section can be calculated by the three-point method described in > Chap. C2, Sect. 6. The single-phase coefficients at the ends ab and bc may be used for this purpose. The values for (kA)j and Aj (j = a, b, c) can be obtained directly from NTU2j , and the partial areas can be added to the total area. This simple mathematical treatment actually applies only to evaporation and condensation in the tubes of a countercurrent C1 heat exchanger. In other cases, the results must be regarded merely as a rough guide. More accurate results can be obtained only by step-by-step numerical calculations [36]. 6 Examples of Application The two principal aims in heat exchanger design are – Rating existing designs – Designing or dimensioning heat exchangers from scratch Each aim requires different means of applying the equations and charts given above. This is demonstrated with some characteristic examples. 6.1 Rating of Existing Designs For this problem the design of the heat exchanger, the mass flow _ 2 ), and the _ 1 and W rates (and hence the heat capacity rates W inlet temperatures #01 and #02 are known. The aim is to determine the outlet temperatures #001 and #002 and the transferred heat _ The product (kA) can be obtained from the design flow rate Q. data, the mass flow rates, and by means of estimated reference temperatures for the thermophysical properties (> Chap. C2). The estimated values of the reference temperatures must be checked with the results and the calculation must be repeated with improved estimates if necessary. Example 1 Ambient air (volumetric flow rate at the inlet 2 m3/s, inlet temperature #02 = 20 C, pressure 1 bar) shall be heated in an existing heat exchanger using hot water (mass flow rate 1 kg/s, inlet temperature #0 1= 120 C, pressure 10 bar). The heat exchanger consists of a rectangular tube bundle with 120 finned tubes (material aluminium) in staggered arrangement. The tubes are arranged in six tube rows and six counterdirected passes. The air on the outside flows perpendicular to the tubes, the water inside the tubes. The dimensions of the finned tubes are as follows: Outside tube diameter = 16 mm Inside tube diameter = 12 mm Tube length = 1 m Circular fins with outside diameter = 42 mm Fin pitch = 400 fins/m Fin thickness = 0.4 mm Tube pitch in the bundle = 45 mm The outlet temperatures and the thermal performance shall be calculated. Additional heat transfer resistances due to fouling are to be neglected. Solution C1. Fig. 13. Temperature as a function of the heat transferred in a countercurrent condenser with vapor desuperheating and condensate subcooling. In this case, the usual mean value of the overall heat transfer coefficient shall approximately be used: k ~k (cf. > Chap. C2). In Example 2 of > Chap. C2, it is shown that in this case the 47 48 C1 Thermal Design of Heat Exchangers usual mean value is a very good approximation for the true mean overall heat transfer coefficient. The reference temperatures (arithmetic mean of inlet and outlet temperatures) must be estimated: tube side #1 = 100 C, on the outside #2 = 60 C. At these reference temperatures the properties of water and air, respectively, are determined (> Chap. D2). For the tube-side heat transfer, the correlations from > Chap. G1 yield Re1 = 1.88·104 and a1 = 4,625 W/m2 K, where the correction for temperature-dependent properties has been neglected. For the outside heat transfer, the correlations from > Chap. M1 yield Re2 = 3.78·103 and a2 = 48.7 W/m2 K. Following > Chap. C2 it is k·A = 4,495 W/K. With the heat capacity flow rates _ 2 = 2,404 W/K _ 1 = 4,220 W/K and W W the dimensionless parameters NTU2 and R2 can be determined: NTU2 = 1.87 (NTU1 = 1.06) R2 = 0.57 (R1 = 1.76). From the chart Fig. 38, for counterdirected countercurrent cross-flow with six tube rows and six passes one obtains P1 = 0.42 (P2 = 0.74). The outlet temperatures can then be calculated from Eqs. (9) and (10): #001 = 78 C and #002 = 94 C. From Eq. (7) the transferred heat flow rate is Q_ = 177 kW. Solution The heat exchanger is considered to be a system of four single and identical units (Fig. 14). It is assumed that stream 2 (inside the tubes) is not laterally mixed in the individual units and that stream 1 (on the shell side) is completely laterally mixed. Thus the flow arrangement selected for each unit is mixed–unmixed cross-flow or crossflow with one tube row (Fig. 31, equation in Table 5). For the whole exchanger, Eqs. (11) and (12) yield NTU1tot ¼ NTU2tot ¼ 1:357ðR1 ¼ R2 ¼ 1Þ: For the individual cells, Eq. (17) yields 1 NTU1;2 ¼ NTU1;2tot ¼ 0:3392 4 The equation for cross-flow with one tube row or mixed– unmixed cross-flow, stream 1 mixed (Table 5) yields P1 ¼P2 ¼ 0:25 Dimensionless temperatures according to Eq. (18) are introduced to simplify the further calculations. At the inlet T10 ¼ 1 and T20 ¼ 0. The unknown outlet temperatures in the individual units are designated as T1a, T1b, T1c, and T1d = 1 P1tot as well as T2a, T2b, T2c, and T2d = P2tot (see Fig. 14). If the dimensionless temperature changes in each unit are expressed as defined in Eqs. (9) and (10), eight equations are obtained for these eight unknown temperatures. Following stream 2 through the units, one gets T2a 0 T2b T2a ; P2b ¼ ; T1c T2a T1b 0 T2c T2b T2d T2c ; P2d ¼ : P2c ¼ 1 T2b T1a T2c P2a ¼ Note From the chart Fig. 38, one can see that in this case the correction factor F exceeds 0.99. Generally, for small NTU-values the flow arrangement has little impact on the thermal performance. The equations for pure countercurrent flow (or the chart Fig. 17) yield nearly the same results. However, there is no general limit where the impact of the flow arrangement can be neglected (see for example the flow arrangement ‘‘two-sided stirred tank’’ in Fig. 15 with the NTU-values and heat capacity rate ratios of this example). It is recommended to use always the equations or the chart for the flow arrangement under consideration because this requires no significant additional work. Example 2 In this example, the cell method (Sect. 3.1) is applied. The design data of a shell-and-tube heat exchanger are given. The flow arrangement consists of two tube-side and one shell-side pass with one shell-side baffle. Heat transfer: k·A = 4,749 W/K _ 1 = 3,500 W/K, #01 = 100 C Stream 1 on the shell side: W _ 2 = 3,500 W/K, #02 = 20 C Stream 2 inside the tubes: W 00 The outlet temperatures #1 and #002 shall be determined. The (unrealistic) assumption of only one shell-side baffle has been made in order to facilitate the calculation required to follow this numerical example. C1. Fig. 14. System of four coupled heat exchangers as a model for a shell-and-tube design with two tube-side passes and one shell-side pass with one shell-side baffle in layout A (Example 2). Thermal Design of Heat Exchangers C1 C1. Fig. 15. Two-sided stirred tank. C1. Table 7. Results for the calculation of the dimensionless outlet temperatures of the individual units with P1 = P2 = 0.25 T2a 0.167 T2b T2c T2d T1c T1b T1a T1d 0.333 0.5 0.5 0.833 0.667 0.5 0.5 With identical individual units it is P2a = P2b = P2c = P2d = P2. Following stream 1 through the units yields P1c ¼ P1a ¼ 1 T1c T1c T1b ; P1b ¼ ; 1 T2b T1c T2a T1b T1a T1a T1d ; P1d ¼ : T1b 0 T1a T2c In this case, too, P1a = P1b = P1c = P1d = P1. This system of linear equations can be solved iteratively by known numerical methods. The results are listed in Table 7. The dimensionless temperature changes for the complete heat exchanger are obtained from the dimensionless outlet temperatures T1d and T2d, i.e., P1tot ¼P2tot ¼ 0:5 and the real outlet temperatures from Eqs. (9) and (10), i.e., #001 ¼ #002 ¼ 60 C 6.2 Design and Dimensioning of Heat Exchangers In this case a heat exchanger has to be designed to solve a given heat transfer problem. Designing and dimensioning of a heat exchanger is much more difficult than rating an existing exchanger and requires a lot of experience. The procedure depends on the problem to be solved, and in particular, on the specified heat transfer conditions. Example 3 The following heat capacity flow rates and inlet temperatures are given: _ 2 ¼ 7; 000 W=K; _ 1 ¼ 8;500 W=K; W W 0 #1 ¼ 300 C; #02 ¼ 100 C: For stream 1 an outlet temperature of #001 = 160 C is prescribed. The outlet temperature for stream 2 follows from the energy balance for the complete exchanger according to Eq. (7) as #002 = 270 C. A shell-and-tube heat exchanger with several shell-side passes and two tube-side passes per shell-side pass shall be used. How many shell-side passes and which heat transfer area are required? Solution The flow arrangement corresponds to the coupling of several identical shell-and-tube heat exchangers, each with one 49 50 C1 Thermal Design of Heat Exchangers C1. Fig. 16. One-sided stirred tank. C1. Fig. 17. Pure countercurrent flow. shell-side and two tube-side passes in overall countercurrent flow. The dimensionless temperature changes for the complete heat exchanger are P1tot ¼ 300 160 270 100 ¼ 0:7 and P2tot ¼ ¼ 0:85: 300 100 300 100 The heat capacity rate ratio is R1 ¼ 8;500 ¼ 1:214 ðR2 ¼ 0:8235Þ: 7;000 From Eq. (46) for the countercurrent series connection of identical individual exchangers together with the equation Thermal Design of Heat Exchangers C1 C1. Fig. 18. Pure cocurrent flow. C1. Fig. 19. Shell-and-tube heat exchanger with one shell-side and two tube-side passes; e = 1/2. for the shell-and-tube exchanger with one shell-side and two tube-side passes (Table 4) it can be calculated that at least three shell-side passes for the complete exchanger are necessary to reach the required thermal performance. For three shell-side passes the logarithmic mean temperature difference correction factor F is marginally smaller than 0.7. A rule of thumb in heat exchanger design says that the correction factor should be F > 0.7 0.8 (see also [37]). For smaller 51 52 C1 Thermal Design of Heat Exchangers C1. Fig. 20. Shell-and-tube heat exchanger with one shell-side and four tube-side passes. C1. Fig. 21. Shell-and-tube heat exchanger with one shell-side and three tube-side passes, two of it in countercurrent flow; e = 1/3. values of F the operating point falls within a range where small changes in P cause pronounced changes in F, with the result that the thermal performance is very sensitive to fluctuations. Therefore, in practice at least four shell-side passes are necessary to reach the required temperature changes. For four shell-side passes it is P1 = 0.426, NTU1 = 0.95 and NTU1tot = 4·0.95 = 3.8. As the design details are not yet fixed, resort must be taken to typical values of the overall heat transfer coefficient (> Chap. C3) for estimating the heat transfer area. With Thermal Design of Heat Exchangers C1 C1. Fig. 22. Shell-and-tube heat exchanger with one shell-side and two countercurrent tube-side passes. C1. Fig. 23. Shell-and-tube heat exchanger with one shell-side and five tube-side passes, three of it in countercurrent flow. k = 500 W/m2 K (liquid inside and outside the tubes) the required total area is ðAtot Þreq ¼ _2 R1 NTU1tot W k 65 m2 After the design details have been fixed, the overall heat transfer coefficient can be determined and it can be checked by rating (Sect. 6.1), whether the required thermal performance is actually attained. 53 54 C1 Thermal Design of Heat Exchangers C1. Fig. 24. Shell-and-tube heat exchanger; divided flow with one shell-side and one tube-side pass. C1. Fig. 25. Shell-and-tube heat exchanger; divided flow with one shell-side and two tube-side passes. In this case the NTU-value of the individual exchanger could be calculated from an explicit equation NTU = f (P, R). For most flow arrangements this is not possible, and the equation P = f (NTU, R) must be solved iteratively for NTU if P and R are given. Example 4 For air-cooled cross-flow heat exchangers usually the inlet and outlet temperature and the heat capacity rate of the process stream 1 are given, whereas for the air (stream 2) only the Thermal Design of Heat Exchangers C1 C1. Fig. 26. Shell-and-tube heat exchanger; split flow with longitudinal baffle and two shell-side and two tube-side passes. C1. Fig. 27. Shell-and-tube heat exchanger; double split flow with two longitudinal baffles and two shell-side passes on each side; two tubeside passes. inlet temperature is known. However, empirical values for preferred approach velocities w2 in certain finned tube bundles are also known. With these values the overall heat transfer coefficient and the number of transfer units NTU2 can be estimated. For this purpose, only the ratio of total heat transfer area A and the cross-sectional area f for the air flow has to be known, but not their individual values, as shown by the following relationship: 55 56 C1 Thermal Design of Heat Exchangers C1. Fig. 28. Shell-and-tube heat exchanger with two shell-side and four tube-side passes. C1. Fig. 29. Shell-and-tube heat exchanger with four shell-side and eight tube-side passes. Thermal Design of Heat Exchangers C1. Fig. 30. Pure cross-flow. C1. Fig. 31. Cross-flow with one tube row; laterally mixed on one side. C1 57 58 C1 Thermal Design of Heat Exchangers C1. Fig. 32. Cross-flow, laterally mixed on both sides. C1. Fig. 33. Cross-flow with two tube rows and one pass. NTU2 ¼ kA w2 f r2 cp2 ð56Þ One can also introduce the overall heat transfer coefficient relating to the cross-sectional area f kf ¼ ðkAÞreq f ð57Þ which subsequently allows the immediate calculation of the required cross-sectional area Thermal Design of Heat Exchangers C1 C1. Fig. 34. Cross-flow with three tube rows and one pass. C1. Fig. 35. Cross-flow with ten tube rows and one pass. freq ¼ ðkAÞreq kf ð58Þ In the following the flow arrangement and the heat transfer data from Example 1 are taken. Thus, the flow arrangement is a counterdirected countercurrent cross-flow with six tube rows and six passes and the design data of the finned tube bundle from Example 1 except for the tube length. The process stream _ 1 = 4,220 W/K) is to be cooled from #01 = 120 C to (water, W 59 60 C1 Thermal Design of Heat Exchangers C1. Fig. 36. Counterdirected countercurrent cross-flow with two tube rows and two passes. C1. Fig. 37. Counterdirected countercurrent cross-flow with three tube rows and three passes. Thermal Design of Heat Exchangers C1. Fig. 38. Counterdirected countercurrent cross-flow with six tube rows and six passes. C1. Fig. 39. Counterdirected countercurrent cross-flow with four tube rows and two passes. C1 61 62 C1 Thermal Design of Heat Exchangers C1. Fig. 40. Counterdirected countercurrent cross-flow with two passes; stream 2 unmixed, stream 1 mixed only between passes. C1. Fig. 41. Counterdirected countercurrent cross-flow with three passes; stream 2 unmixed, stream 1 mixed only between passes. Thermal Design of Heat Exchangers C1. Fig. 42. Plate heat exchanger with one pass for stream 1 and two passes for stream 2. C1. Fig. 43. Plate heat exchanger with one pass for stream 1 and three passes for stream 2, two of it in countercurrent flow. C1 63 64 C1 Thermal Design of Heat Exchangers C1. Fig. 44. Plate heat exchanger with one pass for stream 1 and four passes for stream 2. C1. Fig. 45. Plate heat exchanger with two passes for stream 1 and four passes for stream 2 in overall countercurrent flow arrangement. Thermal Design of Heat Exchangers #001 = 70 C. The inlet temperature of the air is #02 = 20 C. The required cross-sectional area of the tube bundle and the tube length shall be calculated. C1 Superscripts 0 At the inlet 00 At the outlet * Hypothetical value Solution The ratio of the heat transfer area A and the cross-sectional area f follows from the design data of the finned tube bundle: A ¼ 132: f In > Chap. C3 typical values of the overall heat transfer coefficient (related to the outside surface area) for gas heaters with finned tubes of 12–50 W/m2 K are given. With k = 20 W/m2 K kf ¼ 2; 640 W=m2 K: The air approach velocities are usually in the range of 2–5 m/s. With w2 = 2 m/s Eq. (56) yields NTU2 = 1.25. From Eq. (9) it follows P1 = 0.5 From the chart in Fig. 38 it is P2 = 0.57 and R2 = 0.88. It follows NTU1 ¼ R2 NTU2 ¼ 1:10 and ðkAÞreq ¼ 4; 640 W=K Equation (58) yields freq = 1.76 m2. With the design data of the tube bundle the required tube length is 1.96 m 2 m. 7 Additional Symbols Symbol Description Unit F Logarithmic mean temperature difference correction factor (Eq. 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Na Ranong Ch (2001) Stationäres und instationäres Verhalten von zwei gekoppelten Wärmeübertragern mit umlaufenden Fluidstrom. Ph.D. thesis, Department of Mechanical Engineering, University of the Federal Armed Forces Hamburg, Hamburg 35. Na Ranong Ch, Roetzel W (2002) Steady-state and transient behaviour of two heat exchangers coupled by a circulating flowstream. Int J Therm Sci 41:1029–1043 36. Butterworth D (1975) A calculation method for shell and tube heat exchangers in which the overall coefficient varies along the length. NEL Report No. 590, pp. 56–71, National Engineering Laboratory East Kilbride, Glasgow 37. Taborek J (1979) Evolution of heat exchanger design techniques. Heat Transfer Eng 1(1):15–29 C2 Overall Heat Transfer C2 Overall Heat Transfer Wilfried Roetzel1 . Bernhard Spang2 1 2 Helmut-Schmidt-Universität, Universität der Bundeswehr Hamburg, Hamburg, Germany BUCO Wärmeaustauscher International GmbH, Geesthacht, Germany 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2 Local and Mean Heat Transfer Coefficient . . . . . . . . . 67 3 Local Overall Heat Transfer Coefficient . . . . . . . . . . . . 67 4 Mean Overall Heat Transfer Coefficient . . . . . . . . . . . . 68 5 5.1 5.2 Allowance for the Flow Length Effect . . . . . . . . . . . . . . . 68 Flow Length Effect on One Side Only . . . . . . . . . . . . . . . . 69 Laminar Flow in Both Streams . . . . . . . . . . . . . . . . . . . . . . . 69 6 6.1 Allowance for the Temperature Effect. . . . . . . . . . . . . . . 70 Usual Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 1 Multi-Point Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 One Constant Fluid Temperature . . . . . . . . . . . . . . . . . . . . 70 Constant Heat Capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Temperature-Dependent Heat Capacities . . . . . . . . . . . . 70 Averaging the Resistances to Heat Transfer . . . . . . . . . . 72 Other Flow Arrangements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 7 Reduction in Heat Transfer Caused by Protective Layers and Fouling. . . . . . . . . . . . . . . . . . . . . . . 73 8 Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 9 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Introduction In a heat exchanger hot and cold fluids are separated by a wall of one or more layers. The process of steady state heat transport from the hot fluid to the cold fluid through the separating wall is denoted with overall heat transfer and characterized by the overall heat transfer coefficient. This overall coefficient varies together with the two local heat transfer coefficients, and suitable mean values have to be introduced for the thermal design and rating of heat exchangers. 2 6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5 Local and Mean Heat Transfer Coefficient If heat transfer is convective, the local heat transfer coefficient at a surface is directly related to the length of the flow path x, the local temperature of the fluid #, and the temperature of the wall surface #w over which the fluid flows. In other words, it is given by aloc ¼ aloc ðx; #; #w Þ: The direct dependence of heat transfer on the length of the flow path is caused by the development of the velocity and temperature profiles, and is referred to as the flow length effect. The relationship to temperature is brought about by the temperaturedependent properties of the fluid or by radiation, and is referred to as the temperature effect. The mean coefficient of heat transfer at a surface is obtained directly from the correlation for convective heat transfer (cf. Part G). Thus VDI-GVC (ed.), VDI Heat Atlas, DOI 10.1007/978-3-540-77877-6_5, # Springer-Verlag Berlin Heidelberg 2010 1 a ¼ L ðL ð 1 aloc dx ¼ aloc dA A x¼0 ð1Þ A is valid for constant temperatures # and #w (or for constant fluid properties) and is averaged over the length of flow path or area of contact. The average applies only for the length effect and depends on the local temperatures # and #w, i.e., a ¼ að#; #w Þ: 3 Local Overall Heat Transfer Coefficient The local overall heat transfer coefficient is the reciprocal of the total heat transfer resistance, consisting of the two heat transfer resistances at surfaces A1 and A2, and the conductive wall resistance Rw: 1 1 1 ¼ þ Rw þ : kloc A a1;loc A1 a2;loc A2 ð2Þ The left-hand side of Eq. (2) applies to an area A of any given size. The resistance offered by the wall is calculated from its thickness d and the material’s thermal conductivity l, i.e., Rw ¼ d ; lAm ð3Þ where Am is the mean area that governs the thermal conductivity. 68 C2 Overall Heat Transfer For a cylindrical tube of circular cross-section, Am ¼ A1 A2 d1 d2 ¼ pL: A1 d1 ln ln A2 d2 ð4Þ For a spherical shell, pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Am ¼ A1 A2 ¼ d1 d2 p: ð5Þ The local temperatures at the surfaces #w1 and #w2 on which heat is transferred are obtained from the following equation: a1;loc A1 ð#1 #w1 Þ ¼ a2;loc A2 ð#w2 #2 Þ ¼ kloc Að#1 #2 Þ: ð6Þ If the wall consists of n layers, its total resistance to heat transfer is the sum of those offered by the individual layers, i.e., n n X X d Rwj ¼ : ð7Þ Rw ¼ lAm j j¼1 j¼1 The intermediate temperature #z,p behind the pth layer, as counted from the temperature #w1, can be derived from the equation #w1 #z;p n X Rwj ¼ ð#w1 #w2 Þ j¼1 p X Rwj : ð8Þ j¼1 The local overall heat transfer coefficient, as defined by Eq. (2), depends on the temperatures of the two fluids, the two wall surface temperatures, and the lengths of both flow paths, i.e., kloc ¼ kloc ð#1 ; #2 ; #w1 ; #w2 ; x1 ; x2 Þ: 4 Mean Overall Heat Transfer Coefficient The local overall heat transfer coefficient kloc varies with the length of the flow path and the local fluid and wall temperatures over the area available for heat transfer. A mean value k must be found that can be used in the equations and charts given in > Chap. C1. A figure that is frequently taken for this purpose is the value ~k obtained by substituting the mean for the local heat transfer coefficients in Eqs. (2) and (6), i.e., 1 1 1 þ Rw þ : ¼ ~ a1 A1 a2 A2 kA ð9Þ This value depends only on the local fluid and wall temperatures, i.e., remains unchanged over the entire heat transfer area (~# = #1– #2 = const.): ð 1 k ¼ kA ¼ kloc dA: ð10Þ A A In this case, the local overall heat transfer coefficient may be an arbitrary function of location and temperature. In addition, it can be demonstrated that the area-average overall coefficient, as defined by Eq. (10), is the true mean value in cocurrent and countercurrent flow without restrictions if the heat capacity rates are constant. Equation (10) does not apply in most other cases. However, the better the P1,P2-chart in the operating range agrees with that for pure countercurrent or pure cocurrent flow, the less the difference between kA and k, provided the heat capacity rates are constant. The difference is particularly small for arrangements in countercurrent cross-flow and in countercurrent coupling of individual units, because they closely agree with pure countercurrent flow. Likewise, cocurrent cross-flow, cocurrent coupling of individual units, and cross-flow with lateral mixing on both sides agree well with pure cocurrent flow, and again very small differences are obtained. Larger differences may arise in pure cross-flow and in cross-flow equipment with few passes [2]. Reservations must also be made for mixed flow arrangements in which so-called true cocurrent and countercurrent passes occur. Examples are multipass plate (true cocurrent and countercurrent flow) and shell-and-tube heat exchangers. In these cases, the (area-average) overall heat transfer coefficient must be determined separately for each pass in order to ensure accuracy, because the sizes of the countercurrent and cocurrent passes relative to one another, i.e., the NTUs, affect the quality of the flow arrangement. A simplifiation can be made by determining a common mean coefficient for all the cocurrent passes and another one for all the countercurrent passes [3]. If the overall heat transfer coefficient depends on temperature and the flow differs greatly from pure countercurrent or cocurrent flow arrangement, an approximate value for k can be obtained by correcting the reference temperatures in the methods described below [2]. If the specific heat capacity varies with temperature, an apparent mean value must be taken [4] that differs from the mean value k, as determined from Eq. (10), even in pure cocurrent and countercurrent flow. For the determination of the mean value k the temperature and the flow length effect have to be taken into account. This can be done separately as shown in the following. ~k ¼ ~k ð#1 ; #2 ; #w1 ; #w2 Þ: As a rule, iteration must be resorted to for determining either the overall coefficient from Eq. (9) or the wall temperatures, because they are interdependent. Of practical importance are a few cases where the heat transfer coefficient can be calculated without iteration [1]. The mean value ~k determined from Eq. (9) is merely an approximation for the true mean value of the overall heat transfer coefficient k. The true mean value can be derived as follows from Eqs. (1)–(4) in > Chap. C1, but only if the temperature difference 5 Allowance for the Flow Length Effect The frequently adopted mean value ~k that is obtained from Eq. (9) makes only a rough allowance for the flow length effect, because it is determined from heat transfer coefficients that have already been integrated. However, in analogy to Eq. (1), which corresponds to Eq. (10), the values for kloc ought to be integrated over the whole area at constant temperatures (or properties). Overall Heat Transfer Therefore, a distinction is drawn between ~k and a mean value k that makes due allowance for the flow length effect. In common with the usual approximation ~ k, k still depends on the local fluid and wall temperatures, i.e., k ¼ k ð#1 ; #2 ; #w1 ; #w2 Þ: In most cases of practical importance, e.g., turbulent flow on both sides, the flow length effect is so slight that the normal, simplified approach according to Eq. (9) yields sufficient accuracy (~k k [5]). However, if flow is laminar, unacceptable errors on the unsafe side with an uncertainty of more than 10% may occur (~k > k). In such cases, the approximate value must be corrected by a factor V 1, i.e., k ¼ ~kV : ð11Þ Equations for the determination of V in various cases are given below [6, 7]. 5.1 It is assumed that the flow length effect of one stream can be expressed as 1 x 1=p aL;loc ¼ aL 1 ð12Þ p L with integer values p 2. For laminar flow in channels of uniform cross-section p = 3 [5, 6]. The heat transfer coefficient of the other stream does not directly depend on the flow length 0 x/L 1 (no length effect). The correction factor is 2 p 1 p1 p 6 ln 1 þ V ¼ ð1 þ uÞðp 1Þ4 u p uðp 1Þ j 3 p2 u p1 X p 7 þ 5 p 1 j j¼0 ð13Þ aL AL 1. ~kA The coefficient aL is the mean heat transfer coefficient determined from the correlation under consideration and AL is the corresponing surface area. Although Eq. (13) is valid for all integer values p 2 and arbitrary values of u, the numerical evaluation becomes difficult for p > 5 and u > 1. In such cases the following equation is recommended which has been found by a series development: with u ¼ V ¼ ð1 þ uÞðp 1Þ 1 X j¼1 u p1 p j 1 : ð1 p j Þ Equations (13) and (14) can be applied to all flow arrangements in which no axial dispersion takes place. 5.2 Laminar Flow in Both Streams For both laminar streams the flow length effect is expressed by Eq. (12) with p = 3. Regarding the mean value aL for laminar flow (Part G), one should keep in mind that the boundary conditions for heat transfer depend on the flow arrangement. For countercurrent flow and R 1 the boundary condition ‘‘uniform heat flux, q_ = const.’’ is more appropriate than the condition ‘‘uniform wall temperature, #w = const.’’ The reverse is valid for cocurrent flow. Using the abbreviations a1 ¼ aL1 A1 ; a2 ¼ aL2 A2 ð14Þ The equation is valid for u(p–1)/p > 1 and arbitrary values of p. The truncation error of the sum is smaller than the following summand. ð15Þ V is given by the following equations: For countercurrent flow V ¼1þ Flow Length Effect on One Side Only C2 0:65 þ 0:23Rw ða1 þ a2 Þ : 4:1 þ aa12 þ aa21 þ 3Rw ða1 þ a2 Þ þ 2Rw2 a1 a2 ð16Þ For cross-flow V ¼1þ 0:44 þ 0:23Rw ða1 þ a2 Þ : 4:1 þ aa12 þ aa21 þ 3Rw ða1 þ a2 Þ þ 2Rw2 a1 a2 ð17Þ If both fluids are transversally mixed at the inlets to each pass, Eq. (17) is valid for all kinds of cross-flow. For cocurrent flow, with the simplifying abbreviation Z¼ Rw 1 1 þ a1 a2 ð18Þ V is given by [6, 7] 4 8 3 V ¼ ð1 þ Z Þ 1 Z þ Z 2 ln 1 þ 3 9 2Z ð19Þ The correction equations, Eqs. (13)–(19), are valid for laminar flow in channels of constant cross-section. An additional effect of the flow path length that occurs in spiral heat exchangers is that the heat transfer coefficients depend on the radius of curvature of the channel wall, which varies with the length of the flow path. The relationship is linear for an Archimedes’ spiral. The normal methods of calculation with mean heat transfer coefficients allow quite accurately for this effect, because the coefficients on both sides of the curved wall change in the same manner. The allowance for laminar length effects is as discussed above. Other definite relationships between local heat transfer coefficients and the flow length exist for flow channels of changing cross-section, e.g., in conical tubes. In these cases, the mean value k is calculated from Eq. (10) by determining the values of kloc with constant temperature at several points and integrating these values over the surface A. In the case of conical tubes, it is advisable to integrate the product klocd over the length of the channels. 69 70 C2 Overall Heat Transfer 6 Allowance for the Temperature Effect 6.1 Usual Method The simplest method of allowing for the temperature effect is to determine the temperature-dependent mean coefficient k at one reference temperature for each fluid – usually the arithmetic mean of the temperatures at the inlet and outlet, i.e., 1 #i ¼ ð#i 0 þ #i 00 Þ 2 where i = 1, 2. The same simple method is usually adopted for the calculation of pressure drop (cf. > Chap. L1). It can give rise to unacceptable errors if the fluid properties depend strongly on temperature or if heat is transferred by radiation or free convection. If this is the case, a more accurate method of calculating the overall heat transfer coefficients at several points in the heat exchanger is recommended [5, 8]. The pressure drop can also be determined more accurately by a similar procedure [9]. 6.2 n cpi;j 1 1 X aj ¼ k cpmi j¼1 kj with the local values kj #i;j ; #k ; #w;i;j ; #w;k;j ; Rw and cpi;j #i;j , determined for the reference temperatures D#a sj : ð22Þ #i;j ¼ #k þ D#b D#b The coefficients aj and sj are given in Table 1. 6.2.2 In the special case of constant heat capacities, which often can be assumed as an approximation, the mean overall heat transfer coefficient n 1 X 1 aj ¼ k k j j¼1 and the reference temperatures Multi-Point Method 1 1 ð _ _ 1 M 1 cpm1 M 2 cpm2 ln D#b d ðln D#Þ !; ¼ D#b k ln D#a 1 1 ln k D#a _ 1 cp1 M _ 2 cp2 M Constant Heat Capacities #i;j ¼ #i;b þ #i;a #i;b This method applies to cocurrent and countercurrent flow, _ 2 ¼ 1 for any _ 1 ¼ 1 or W including the limiting cases of W given flow arrangement with the exception of the stirred tank. It allows for the temperature dependence of heat transfer coefficients and heat capacities. If the effects of length and temperature are pronounced and occur simultaneously, it is assumed that the local overall heat transfer coefficient kloc can be approximated (in the same way as a heat transfer coefficient) by the product of a pure flow length function and a pure temperature function in the range considered [5]. The desired mean value k can be determined from the equation ð20Þ where the indices ‘‘a’’ and ‘‘b’’ designate the ends of the exchanger. The positive sign is valid for parallel flow and the negative sign for counterflow. The integral is approximated according to Gauss [5, 8] or Simpson [8, 11] using n = 2 or n = 3 (or more) reference points j at which the mean (with respect to laminar length effect) overall heat transfer coefficient kj has to be determined. First two simple special cases are considered. 6.2.3 D#a D#b sj D#a D#b 1 ð24Þ 1 Temperature-Dependent Heat Capacities In the general case of temperature-dependent heat transfer coefficients and heat capacities the integral in Eq. (20) cannot be calculated directly [5, 8]. For the simple integration as in the case of constant heat capacities the hypothetical temperatures have been introduced which are linear functions of the related enthalpies and coincide with the true fluid temperatures at the inlets and outlets of the exchanger [4, 8]. If the heat capacities are constant, the hypothetical temperatures and the true temperatures are identical. The concept of hypothetical temperatures leads to the following equations, in which the hypothetical C2. Table 1. Coefficients for Gauss and Simpson integration with n points n Gauss 2 j 1 2 1 2 One Constant Fluid Temperature The fluid temperature #k remains constant if the heat capacity _ i cpmi =M _ k cpmk ¼ 0 (i = 1, 2; k = 2, 1). The Gauss rate ratio Ri ¼ M or Simpson integration yields ð23Þ for the calculation of kj #1;j ; #2;j ; #w1;j ; #w2;j ; Rw . In the limiting case D#a ¼ D#b which occurs in a balanced counterflow exchanger, the fraction on the right hand side in Eq. (24) turns to the value sj. 3 6.2.1 ð21Þ 3 Simpson 3 1=a 2 3=b sj aj 1 2 1 2 5 18 4 9 5 18 1 6 2 3 1 6 1 2 1 2 1 2 1 2 1 2 1 1 2 0 pﬃﬃﬃ þ 16 3 pﬃﬃﬃ 16 q3ﬃﬃ þ 12 35 12 qﬃﬃ 3 5 Overall Heat Transfer temperatures are eliminated. All temperatures are true fluid temperatures. With the factor D#b D#a sj Cj ¼ D#j D#b it is n 1 X 1 aj C j : ¼ k kj j¼1 ð25Þ The factor Cj represents a correction for variable heat capacities. For the determination of the local temperatures #i;j and their difference D#j ¼ #1;j #2;j the local specific enthalpies hi,j have to be calculated from s j D#a D#b 1 : ð26Þ hi;j ¼ hi;b þ hi;a hi;b D#a D#b 1 The local temperatures #i;j hi;j are then determined from the enthalpies hi,j with the help of equations of state, tables or diagrams. With the temperatures #i;j the local mean coefficient kj #1;j ; #2;j ; #w1;j ; #w2;j ; Rw and D#j can be calculated. If the heat capacities are constant h ¼ cp # þ h0 and Eq. (26) turns to Eq. (24). With the temperatures from Eq. (24) the correction factor in Eq. (25) Cj = 1. So for cpi = const(i = 1, 2) all three methods described in 6.2.1, 6.2.2, and 6.2.3 are identical. For variable heat capacities and one constant fluid temperature the Eqs. (25) and (26) and the Eqs. (21) and (22) do not yield identical results, but their accuracy is about the same. The Eqs. (21) and (22) are more convenient for the special case of one constant fluid temperature. Concerning the appropriate integration method: Basically the Gauss integrations achieve the highest accuracy for a given number of reference points. With two points a polynomial of third degree is exactly integrated, a polynomial of fifth degree requires three points. In normal cases of industrial application the two-point-Gauss method is sufficiently accurate. However, extreme cases may arise in which the three-point-Gauss integration is required [10, 8]. This may occur when high viscous oils are heated up by condensing steam or when a transition takes place between laminar and turbulent flow. However, the main problem in such extreme cases is not the proper integration but the accurate prediction of the local heat transfer coefficients. The Simpson method is nearly as accurate as the two-pointGauss integration, although three reference points are used. The method has been recommended [11] because the Reynolds numbers are frequently determined anyhow at the inlet and outlet in order to check whether or not the flow is turbulent or laminar throughout the exchanger. Another advantage is that at the terminal reference points j = 1 = a and j = 3 = b the reference temperatures are the given inlet and outlet temperatures and the correction factors in Eq. (25) C1 = Ca = C3 = Cb = 1. So, only at the central reference point j = 2 the enthalpies are needed for the determination of the reference temperatures if the heat capacities vary with temperature. C2 If the heat capacities vary, this mean value of k must be regarded as an apparent coefficient that differs from the areaaverage value obtained from Eq. (10) and even from a value that remains unchanged over the heat transfer area, i.e., k ¼ kj . In other words, k 6¼ k. Unsuitable cases may arise if the specific heat capacities depend considerably on temperature or if other pronounced nonlinear relationships exist between enthalpy and temperature, e.g., in the h(#) condensing curve for mixtures. Thus, in countercurrent flow with high values of NTU1 NTU2, the temperature curves for both fluids may theoretically intersect at a point (#1 = #2). This would entail that the process concerned would be impracticable. A case of this nature would occur if the values for D#a and D#b were positive and a temperature difference D#j were negative or zero. Example 1 An example given by Colburn [12] is calculated with the threepoint-Simpson method. _ 1 ¼ 5:4kW=K) is to be cooled down from Aniline (W 0 #1 ¼ 125 C to #001 ¼ 25 C in a countercurrent heat exchanger. _ 2 ¼ 12kW=K) at an inlet temperature The coolant is water (W 0 of #2 ¼ 20 C . From the energy balance it follows #002 ¼ 65 C. The wall resistance is 1.76 10–4 m2 K/W. It can be assumed as a close approximation that the heat capacities in this case (two liquids) are constant. Since flow is turbulent on both sides, there are no length effects to be taken into account. For the data used by Colburn the temperature dependence of the heat transfer coefficients can be expressed by the following numerical equations [12] (converted into SI units): a1 ¼ 829 þ 8:3#1 þ 0:0834#21 ; a2 ¼ 6; 092ð1 þ 0:0127#2 Þ; # in C, a in W/(m2 K). The usual method (calculation of the heat transfer coefficients at the arithmetic mean fluid temperatures #1m = 75 C and #2m = 42.5 C, respectively) yields with A1 = A2 = A the approximate value k = 1,245 W/(m2 K). For the three-point-Simpson method the mean overall heat transfer coefficients ka and kb at both ends (j = 1, 3) must be calculated. They are ka ð#1 ¼ 125 C; #2 ¼ 65 CÞ ¼ 1; 720 W=ðm2 KÞ; kb ð#1 ¼ 25 C; #2 ¼ 20 CÞ ¼ 816 W=ðm2 KÞ: According to Eq. (24) the fluid temperatures at the central reference point j = 2 are #1;2 ¼ 47:4 C and #2;2 ¼ 30:1 C and hence the central mean overall heat transfer coefficient k2 ¼ 996 W= m2 K From Eq. (23) the approximation for the desired mean value is k = 1,030 W/(m2 K). A numerical finite-difference calculation yields the exact value k = 1,034 W/(m2 K). The two-point-Gauss method yields k = 1,037 W/(m2 K) and the three-point-Gauss method the exact value k = 1,034 W/(m2 K). 71 72 C2 6.2.4 Overall Heat Transfer Averaging the Resistances to Heat Transfer Since the resistances to heat transfer in Eqs. (9) and (20) are additive, Eqs. (20)–(25) can also be applied separately to 1/a1, Rw and 1/a2 by substituting a and 1/Rw for k in Eqs. (21), (23), and (25). The triple application then yields the proper (for variable heat capacities) apparent mean values (with respect to temperature effects) of both heat transfer coefficients and the wall resistance. Subsequently the mean value ~k with respect to temperature effects according to Eq. (9) and, if flow is laminar, the desired mean value k ¼ ~kV using the correction equations Eqs. (11)– (19) can be determined. 6.2.5 Other Flow Arrangements Although, strictly speaking, the multi-point method is valid only for pure cocurrent or countercurrent flow, it can be applied as an approximation to other flow arrangements in which the thermal behaviour is similar. Similarity to countercurrent flow can be found in countercurrent spiral heat exchangers, all counter-crossflow configurations, and systems coupled in overall countercurrent flow. For a system of identical heat exchangers, a combined mean overall heat transfer coefficient common to all individual units can be determined analogous to that for a single countercurrent flow exchanger. Thus the total effect is correctly described but intermediate temperatures cannot be correctly calculated with the common mean coefficient. If the arrangement deviates more from pure countercurrent flow, an additional correction to the reference temperatures for calculating the true overall coefficient is recommended [7]. The logarithmic mean temperature difference correction factor F is used to express the degree of deviation from pure countercurrent flow. No correction is needed if F = 1. The correction equations for i = 1, 2 and the reference point j are 1F : ð27Þ #i;j;corr ¼ #i;j þ ð1Þi #1;j #2;j 2=3 1 þ Ri The two corrected reference temperatures are used solely for calculating the true heat transfer coefficients at the reference point. The remaining equations for countercurrent flow are unaffected. If the three-point-Simpson method is used, for simplicity the correction is only applied to the central reference point (j = 2), but has to be weighted with the factor 3/2 in front of (–1)i for compensation [2]. Considerations corresponing to those for countercurrent flow apply to cocurrent spiral exchangers, all cocurrent cross-flow configurations, and systems coupled in overall cocurrent flow. For the purpose of calculating the common mean coefficient k, the cocurrent system can be regarded as one single cocurrent heat exchanger, provided that P1tot + P2tot < 1. A comparison of the P1, P2-charts for other flow arrangements with those for cocurrent or countercurrent flow allows an estimation on whether the flow arrangement concerned conforms more to the one or to the other. For instance, pure crossflow corresponds more to countercurrent flow, mixed-mixed cross-flow more to cocurrent flow. As mentioned above the cocurrent method can only be used as a model for the calculation of the mean overall heat transfer coefficient ~k if P1 + P2 < 1. However, the mixed-mixed crossflow can reach values P1 + P2 > 1. In such cases either the general method, i.e., counterflow with correction Eq. (27) or preferably a special method [8], derived for mixed-mixed crossflow (a(#) and cp(#)), has to be applied. This method [8] is also applicable to multipass shell-and-tube heat exchangers with one shell-side and a high even number of tube-side passes (1,2mHEX; m 2; see > Chap. C1). For other types of multipass 1,n-HEX the most general analytical method [3] can be used, in which for each pass an individual tubeside heat transfer coefficient is calculated, using the arithmetic mean of the terminal pass temperatures as reference temperature. One mean shellside coefficient (for all passes) could be determined as discussed before, e.g., as for the counterflow with correction Eq. (27). For the mixed-unmixed cross-flow (one tube row) a special method (a(#) and cp(#)) can be recommended for the calculation of ~k [8]. Example 2 It shall be checked with the three-point-Simpson method if the usual mean value of the overall heat transfer coefficient used in the calculation of Example 1 in > Chap. C1 is sufficiently accurate. Solution As the flow on both sides is turbulent, only the temperature effect has to be taken into account: k ¼ ~k. The heat capacities of water and air at the present temperatures and pressures are nearly constant, so that Eqs. (23) and (24) can be applied. At first the outlet temperatures have to be estimated. The outlet temperatures calculated in Example 1 of > Chap. C1 are taken. Hence the temperatures at both ends of the heat exchanger are #1;a ¼ #01 ¼ 120 C; #2;a ¼ #002 ¼ 94 C and #1;b ¼ #001 ¼ 78 C; #2;b ¼ #02 ¼ 20 C The fluid temperatures at the point j = 2 follow from Eq. (24) (constant heat capacities) #1,2 = 103 C, #2,2 = 64 C. The correction from Eq. (27) is negligible because the correction factor F is greater than 0.99 (> Chap. C1, Example 1). The fluid property values of water at a pressure of 10 bar and of air at 1 bar can be taken from the tables in > Chap. D2 at the fluid temperatures at both ends and at the central reference point ‘‘2’’. With these property values the tubeside heat transfer coefficients follow from correlations given in > Chap. G1: at point a: a1,a = 4,912 W/(m2 K), at point b: a1,b = 4,129 W/(m2 K), at point ‘‘2’’: a1,2 = 4,668 W/(m2 K). On the shellside it follows from > Chap. M1: at point a: a2,a = 50.3 W/(m2 K), Overall Heat Transfer n X 1 d : ¼ 1 þ k0 A ’ lAm j j¼1 at point b: a2,b = 46.8 W/(m2 K), at point ‘‘2’’: a2,2 = 49.0 W/(m2 K). Equation (9) yields the mean overall heat transfer coefficient k ¼ ~k: at point a: ka A ¼ 4; 679 W=K, at point b: kb A ¼ 4; 253 W=K, at point ‘‘2’’: k2 A ¼ 4; 528 W=K where area A is arbitrary. From Eq. (23) the desired mean value is kA = 4,504 W/K. In this case the usual mean value kA = 4,495 W/K deviates only slightly from the actual mean value. 7 ð29Þ The thermal conductivities of some protective coatings and fouling layers are listed in Table 2. The corresponding figures for materials of construction and insulation are presented in > Chap. D6, and for various forms of fouling in > Chap. C4. 8 Symbols Symbol F Reduction in Heat Transfer Caused by Protective Layers and Fouling Heat transfer surfaces often have to be coated to provide protection against corrosion. Other coats, e.g., oxides, may also be formed if the heat transfer surfaces react with the flowing substance; or deposits that are difficult to remove may accumulate on the heating and cooling surfaces. All these layers impede the heat flow through the wall of an exchanger. Their effect depends on their thickness and thermal conductivity and, in particular, on the heat flow through the wall. While, for example, a lead coating on the heat transfer surface of a gas cooler would have practically no effect on overall heat transfer, the same lead layer may considerably reduce the thermal performance of an evaporator with its usually very high heat flux. The reduction of overall heat transfer can be expressed by a correction factor ’, i.e., k ¼ ’ k0 ; C2 ð28Þ where k0 is the overall heat transfer coefficient if no layers were present and k is the actual heat transfer coefficient. With the thickness dj of layer j and its thermal conductivity lj it is Description Unit logarithmic mean temperature difference correction factor (C1 Eq. (23)) n number of layers or of reference points NTU number of transfer units (C1 Eqs. (11) and (12)) P dimensionless temperature change (C1 Eqs. (9) and (10)) R heat capacity rate ratio (C1 Eqs. (13) and (14)) wall resistance m2 K/W Rw _ W heat capacity flow rate (C1 Eq. (6)) W/K d thickness m # temperature K Subscripts 1, 2 stream 1 or 2 in the heat exchanger or j = 1, 2, 3 for reference points a, b ends of the heat exchanger L on the laminar flow or length effect side w wall z intermediate value Superscripts 0 at the inlet 00 at the outlet 9 Bibliography C2. Table 2. Thermal conductivity in W/m K at room temperature Protective coatings Tin 65 Oppanol (polyisobutylene) 0.2–0.35 Fouling Scale, high-gypsum 0.6–2.3 Lead 35 Scale, high-silicate 0.08–0.18 Glass 0.76–0.84 Acid-resistant bricks 1.2 Soot, dry 0.035–0.07 Vitreous silica 1.34 Coal dust, dry 0.11 Enamel 0.9–1.2 Carbon bricks 1.6–4.7 Ice 1.75–2.3 Rubber 0.15–0.17 Porcelain 1.7–3.5 Slime from cooling water 0.35 Asphalt 0.76 Salting 0.6 Igelit (PVC film) 0.16 Slime from brine 0.46 1. Roetzel W (1977) Iteration-free calculation of heat transfer coefficients in heat exchangers. Chem Eng J 13(3):233–237. 2. Spang B, Roetzel W (1992) Test of a thermal design method considering variable transfer coefficients and heat capacities for cross-flow arrangements. Heat Transfer, 3rd UK Natnl. Conf. Incorp. 1st Europ. Conf. Thermal Sciences, IChemE Symp. Ser. No. 129, Vol. 1, pp. 435442 3. Roetzel W, Spang B (1987) Analytisches Verfahren zur thermischen Berechnung mehrgängiger Rohrbündelwärmeübertrager. Fortschr.-Ber. VDI, Reihe 19, No. 18, VDI-Verlag, Düsseldorf 4. Roetzel W (1988) Analytische Berechnung von Wärmeübertragern mit nachträglicher Berücksichtigung temperaturabhängiger Wärmekapazitäten. Wärme- und Stoffübertragung 23:175–177 5. Roetzel W (1969) Berücksichtigung veränderlicher Wärmeübergangskoeffizienten und Wärmekapazitäten bei der Bemessung von Wärmeaustauschern. Wärme- und Stoffübertragung 2:163–170 6. Peters DL (1970) Heat exchanger design with transfer coefficients varying with temperature or length of flow path. Wärme- und Stoffübertragung 3:222–226 7. Roetzel W (1974) Heat exchanger design with variable transfer coefficients for cross-flow and mixed flow arrangements. Int. J. Heat Mass Transfer 17:1037–1049 73 74 C2 Overall Heat Transfer 8. Roetzel W, Luo X (2008) Mean overall heat transfer coefficient in heat exchangers allowing for temperature dependent fluid properties. Paper RW1 in: Proc. 6th Int. Conf. On Heat Transfer, Fluid Mechanics and Thermodynamics, HEFAT 2008, Pretoria, South Africa, 30 June–2 July 2008, CD ROM, ISBN 978–1–86854–691–6. An extended and revised version is accepted for publication in Heat Transfer Engineering. 9. Roetzel W (1973) Calculation of single phase pressure drop in heat exchangers considering the change of fluid properties along the flow path. Wärmeund Stoffübertragung 6:3–13 10. Shah RK, Sekulic DP (1998) Nonuniform heat transfer coefficients in conventional heat exchanger design theory. ASME J Heat Transfer 119:520–525 11. VDI-Wärmeatlas, 10. Auflage, Springer-Verlag, Berlin Heidelberg, 2006 12. Colburn AP (1933) Mean temperature difference and heat transfer coefficient in liquid heat exchangers. Ind Eng Chem 25:873–877 C3 Typical Values of Overall Heat Transfer Coefficients C3 Typical Values of Overall Heat Transfer Coefficients Wilfried Roetzel 1 . Bernhard Spang2 1 2 1 1 Helmut-Schmidt-Universität, Universität der Bundeswehr Hamburg, Hamburg, Germany BUCO Wärmeaustauscher International GmbH, Geesthacht, Germany Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Introduction The empirical values listed below are intended for the preliminary design of heat exchangers. The lower values apply to comparatively adverse conditions, e.g., low flow velocities, viscous liquids, free convection, and fouling. The higher values are valid for particularly favorable conditions, e.g., high flow Type of exchanger Shell-and-tube heat exchanger velocities, thin fluid layers, optimum mass flow ratios, and clean surfaces. In special cases, values may fall below or exceed the given range. Therefore, the figures must be regarded critically and with the necessary caution. The given k values do not take additional heat conduction resistances of insulation and protective coatings into account. Conditions of heat transfer Gas (1 bar) on tube side and gas (1 bar) on shell side Typical k value (W/m2 K) 5–35 High-pressure gas (200–300 bar) on shell side 150–500 and high-pressure gas (200–300 bar) on tube side Liquid on shell side (tube side) and gas (1 bar) on tube side (shell side) 15–70 High-pressure gas (200–300 bar) on tube side and liquid on shell side 200–400 Liquid on shell and tube sides 150–1,200 Heating steam on shell side and liquid on tube side 300–1,200 See below for use as evaporator or condenser Evaporator Heating steam outside the tubes 1. With natural circulation (a) Viscous liquids 300–900 (b) Low viscosity liquids 600–1,700 2. With forced circulation 900–3,000 Brine-heated ammonia evaporator 200–800 continued VDI-GVC (ed.), VDI Heat Atlas, DOI 10.1007/978-3-540-77877-6_6, # Springer-Verlag Berlin Heidelberg 2010 76 C3 Typical Values of Overall Heat Transfer Coefficients Type of exchanger Condenser Conditions of heat transfer Typical k value (W/m2 K) Cooling water on tube side and organic vapors or 300–1,200 ammonia on shell side Steam-turbine condenser (pure steam; thin brass 1,500–4,000 tubes) k decreases with an increase in the inert gas fraction Waste-heat boiler Hot gas on tube side and boiling water on shell side Gas heater Steam or hot water on (finned) tube side and gas outside finned tubes Double-pipe heat exchanger 15–50 (a) Free convection (heater) 5–12 (b) Forced flow 12–50 Gas (1 bar) on tube side and gas (1 bar) on shell side 10–35 High-pressure gas (200–300 bar) on tube side and gas (1 bar) on shell side 20–60 High-pressure gas (200–300 bar) on tube side 150–500 and high-pressure gas (200–300 bar) on shell side High-pressure gas (200–300 bar) on tube side and liquid on shell side 200–600 Liquid on shell and tube sides 300–1,400 continued C3 Typical Values of Overall Heat Transfer Coefficients Typical k value (W/m2 K) Type of exchanger Conditions of heat transfer Falling-film cooler Cooling water on shell side and gas (1 bar) on tube side 20–60 Cooling water on shell side and high-pressure gas (200–300 bar) on tube side 150–350 Cooling water on shell side and liquid on tube side 300–900 Falling-film condenser, e.g., for refrigerants: cooling water outside and condensing vapor inside tubes 300–1,200 Cooling water or brine outside and gas (1 bar) inside the coils 20–60 Cooling water outside and high-pressure gas (200–300 bar) inside the coils 150–500 Cooling water or brine outside and liquid inside the coils 200–700 Cooling water or brine outside and condensing vapor inside the coils 350–900 Flat channels, gas to water 20–60 Flat channels, liquid to water 350–1,200 Corrugated plates, liquid to liquid 1,000–4,000 Helical coil heat exchanger Plate heat exchanger continued 77 78 C3 Typical Values of Overall Heat Transfer Coefficients Type of exchanger Compartmental heat exchanger Spiral plate heat exchanger Stirred tank Conditions of heat transfer Typical k value (W/m2 K) Gas to gas (1 bar) 10–35 Gas to liquid 20–60 Liquid to liquid 700–2,500 Condensing vapor to liquid 900–3,500 (A) Outer shell Condensing vapor outside and liquid inside the tank 500–1,500 Condensing vapor outside and boiling liquid inside the tank 700–1,700 Cooling water or brine outside and liquid inside the tank 150–350 (B) Inner coil Condensing vapor inside the coils and liquid inside the tank 700–2,500 Condensing vapor inside the coils and boiling liquid inside the tank 1,200–3,500 Cooling water or brine inside the coils and liquid 500–1,200 inside the tank (C) Outer tube welded onto shell Condensing vapor inside the heating channels and liquid inside the tank 500–1,700 Condensing vapor inside the heating channels and boiling liquid inside the tank 700–2,300 Cooling water or brine inside the cooling channels and liquid inside the tank 350–900 C4 Fouling of Heat Exchanger Surfaces C4 Fouling of Heat Exchanger Surfaces Hans Müller-Steinhagen Universität Stuttgart, Stuttgart, Germany 1 1.1 1.2 1.3 1.4 1.5 1.5.1 1.5.2 1.5.3 1.5.4 2 2.1 2.2 2.3 2.4 2.5 2.5.1 2.5.2 2.5.3 2.5.4 2.6 2.6.1 2.6.2 3 3.1 3.2 3.3 3.4 3.4.1 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 The Fouling Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Mechanisms of Heat Exchanger Fouling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Sequential Events of Fouling. . . . . . . . . . . . . . . . . . . . . . . . . . 83 Approximate Influence of Operating Conditions on Fouling in Industrial Heat Exchangers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Costs due to Heat Exchanger Fouling . . . . . . . . . . . . . . . . 85 Capital Expenditure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Fuel Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Maintenance Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Costs due to Production Loss. . . . . . . . . . . . . . . . . . . . . . . . . 86 Consideration of Fouling in the Design of Heat Exchangers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Preliminary Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Selection of Heat Exchanger Type . . . . . . . . . . . . . . . . . . . . 87 Material Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Shell and Tube Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . 87 Other Heat Exchanger Types. . . . . . . . . . . . . . . . . . . . . . . . . . 89 Plate and Frame Heat Exchangers . . . . . . . . . . . . . . . . . . . . 89 Plate-Fin Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Printed Circuit Heat Exchanger . . . . . . . . . . . . . . . . . . . . . . 90 Polymer Compact Heat Exchangers . . . . . . . . . . . . . . . . . . 90 Effect of Fouling on Pressure Drop . . . . . . . . . . . . . . . . . . . 90 Tube-Side Pressure Drop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Shell-Side Pressure Drop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 HTRI Fouling Mitigation by Design Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Crude Oil Best Practice Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Cooling Tower Water Best Practice Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Excess Surface/Coefficient Adjustments . . . . . . . . . . . . . . 92 Design Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Shell-Side Bundle Geometry Exit/Entrance Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Introduction In most industrial processes, heat exchanging fluids contain certain amounts of dissolved or suspended material or provide conditions favorable for the growth of biological organisms. Design and operation of heat exchangers are still to a major extent determined by the process-related formation of deposits VDI-GVC (ed.), VDI Heat Atlas, DOI 10.1007/978-3-540-77877-6_7, # Springer-Verlag Berlin Heidelberg 2010 3.4.2 3.4.3 3.5 3.5.3 3.5.4 3.5.5 Allowable Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Longitudinal Baffles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Example for Fouling Mitigation by Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Original Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Operation History with Original Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Root Cause Analysis of Performance . . . . . . . . . . . . . . . . . 93 New Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Final Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4 4.1 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.3 4.3.1 4.3.2 4.3.3 Online Mitigation Methods . . . . . . . . . . . . . . . . . . . . . . . . . 94 Start-Up Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Chemical Fouling Mitigation Methods . . . . . . . . . . . . . . . 94 Scale Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Particulate Fouling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Chemical Reaction Fouling . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Biofouling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Corrosion Fouling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Gas-Side Fouling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Mechanical Fouling Mitigation Methods . . . . . . . . . . . . . 97 Liquid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Gas Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Other Devices for Fouling Mitigation . . . . . . . . . . . . . . . . 99 5 5.1 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.2 Cleaning of Heat Exchangers. . . . . . . . . . . . . . . . . . . . . . . 100 Chemical Cleaning Methods . . . . . . . . . . . . . . . . . . . . . . . . . 100 The Basic Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Cleaning Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Cleaning Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 OnStream Chemical Cleaning . . . . . . . . . . . . . . . . . . . . . . . 102 Problems Associated with Chemical Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Mechanical Cleaning Methods. . . . . . . . . . . . . . . . . . . . . . . 102 6 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 3.5.1 3.5.2 on the heat transfer surfaces, i.e., fouling. Since the thermal conductivity of such deposits is low, see Table 1, their resistance to heat transfer may well exceed that of the clean fluids, resulting in significantly reduced heat exchanger performance. As a result, substantial safety margins in the design, pretreatment of hot/cold fluids and regular cleaning of equipment may be required. 80 C4 Fouling of Heat Exchanger Surfaces C4. Table 1. Thermal conductivity of various deposits C4. Table 2. Fouling of heat exchangers in various industries [3] Extent of problem Sodium aluminum silicate 0.2–0.4 W/mK Milk components 0.5–0.7 W/mK Industry group Hematite (boiler deposit) 0.6 W/mK Biofilm 0.7 W/mK Food and kindred products Chemical reaction Calcium sulfate (boiler) 0.8–2.2 W/mK Crystallization Major Calcite (boiler deposit) 0.9 W/mK Biological Medium Serpentine (boiler deposit) 1.0 W/mK Particulate Minor/Major Gypsum (boiler deposit) 1.3 W/mK Corrosion Minor Calcium sulfate 2.3 W/mK Magnesium phosphate 2.3 W/mK Calcium phosphate 2.6 W/mK Crystallization Major Calcium carbonate 2.9 W/mK Particulate Minor Magnetite iron oxide 2.9 W/mK Biological Minor Chemical reaction Minor Textile mill products Wood and paper products Chemical and allied industries The Fouling Resistance The possibility of deposition on heat transfer surfaces is generally considered in the design of heat exchangers by using the socalled fouling resistances in the calculation of the overall heat transfer coefficient k. 1 1 A2 1 þ Rf ;1 þ Rwall þ þ Rf ;2 ð1Þ ¼ A1 k a1 a2 In Eq. (1), a, A, and Rf are the heat transfer coefficients, the heat transfer areas and the fouling resistances, respectively, for the two heat exchanging fluids; Rwall is the thermal resistance of the separating wall. It is obvious that the frequently used expression ‘‘fouling factor’’ is incorrect, as the effect of fouling is to create an additional thermal resistance. The fouling resistance reduces the overall heat transfer coefficient k, and hence leads to the reduction of heat duty of an existing heat exchanger or to additional surface requirement in the design of new heat exchangers. In the utility industry, it is common to use the cleanliness factor CF CF ¼ kf kc Major Particulate Biological Surveys [1–3] have indicated that more than 90% of heat exchangers suffer from fouling problems. Table 2 identifies the kind and typical extent of fouling for fluids from various industries [39]. More information about research and industrial fouling problems may be found under www.heatexchanger-fouling.com. 1.1 Type of fouling ð2Þ instead of the fouling resistance Rf, where CF is a function of tube material, flow velocity, and fouling propensity of the cooling water. Typically, cleanliness factors are adding less excess surface and are, hence, more realistic than fouling resistances. However, this purely empirical ratio of overall heat transfer coefficients for fouled and dirty conditions does not provide any access to the understanding of the mechanisms of deposit formation and hence the potential effects of operating conditions. The main source of publicly available fouling resistances are the approximately 100 values suggested by the Tubular Exchanger Manufacturers Association (TEMA) [4], which are reproduced Petroleum refineries Tone, glass, concrete Electricity generation Corrosion Medium Crystallization Medium Particulate Minor/Medium Biological Medium Chemical reaction Minor/Major Corrosion Medium Chemical reaction Major Crystallization Medium Particulate Minor/Medium Biological Medium Corrosion Medium Particulate Minor/Major Biological Major Crystallization Medium Particulate Major Freezing Major Corrosion Minor in Tables 3–5. Although the TEMA tables were originally considered to be only a rough guideline for shell-and-tube heat exchanger design, they are unfortunately often treated as accurate values. This may cause considerable errors because 1. The values were developed in 1949 and were based on hand calculation procedures for heat exchanger design in use at the time. Even though calculation methods have evolved, the values presented by TEMA have not been altered since its publication. 2. Fouling resistances are included for a number of fluids that are known not to foul, such as refrigerants, demineralized water, liquefied natural gas (LNG) and non-polymerizing (diolefin-free) condensing gases, or any other streams which do not foul within the operating conditions of the heat exchanger. 3. Rf values in the tables tend to be used without adequate engineering, resulting in exchangers that are much larger C4 Fouling of Heat Exchanger Surfaces C4. Table 3. TEMA fouling resistances for water (m2K/kW) [4] Temperature of heating medium Temperature of water Up to 115 C C4. Table 4. TEMA fouling resistances for oil refinery streams in shell-and-tube exchangers, (m2K/kW) [4] 115–200 C Crude and vacuum unit gases and vapors Over 50 C Atmospheric tower overhead vapors 0.18 Water velocity m/s Water velocity m/s Light naphthas 0.18 Vacuum overhead vapors 0.35 1.0 and less 1.0 and less 50 C Over 1.0 Over 1.0 Crude and vacuum liquids Crude oil Cooling tower and artificial spray pond 0–120 C 120–175 C Velocity (m/s) Velocity (m/s) Treated make up 0.088 0.088 0.17 0.17 Untreated 0.35 0.17 0.53 0.35 Dry 0.53 0.35 0.35 0.53 0.35 0.35 City or well water 0.17 0.17 0.35 0.35 Salta 0.53 0.35 0.35 0.88 0.70 0.70 <0.6 River water 0.6–1.2 >1.2 175–230 C <0.6 0.6–1.2 >1.2 230 C and over Minimum 0.35 0.17 0.53 0.35 Velocity (m/s) Average 0.53 0.35 0.70 0.53 <0.6 0.6–1.2 >1.2 <0.6 0.6–1.2 >1.2 Muddy or silty 0.53 0.35 0.70 0.53 Dry 0.70 0.53 0.53 0.88 0.70 0.70 Hard (over 250 ppm) 0.53 0.53 0.88 0.88 Salta 1.1 0.88 0.88 1.2 1.1 1.1 Engine jacket 0.17 0.17 0.17 0.17 a Gasoline 0.35 Condensate 0.088 0.088 0.088 0.088 Naphtha and light distillates 0.35–0.53 Treated boiler feedwater 0.17 0.088 0.17 0.17 Kerosene 0.35–0.53 Boiler blowdown 0.35 0.35 0.35 0.35 Light gas oil 0.35–0.53 Seawater 0.09 0.09 0.18 0.18 Heavy gas oil 0.53–0.88 Brakish water 0.35 0.18 0.54 0.35 Heavy fuel oils 0.88–1.2 Distilled or closed cycle Velocity (m/s) Assumes desalting at approximately 120 C Asphalt and residuum 4. 5. 6. 7. than required. For example, Fig. 1 includes a summary of the percent overdesign of all cases submitted to HTRI in 2006. As can be seen from the figure, most exchangers are 50–500% too large, based primarily on the assumed fouling resistances. This results in unnecessary capital expense and exchangers that foul due to poor design. Rf values are only available for a limited number of process fluids and process conditions. Tabulated Rf values provide only limited information about the influence of process parameters such as flow velocity, fluid, and wall temperature on the fouling resistance. These parameters have a considerable influence on the deposition of foulants matter onto the heat transfer surface. Using constant fouling resistances, the transient character of the fouling process is ignored. Conditions in the initially overdesigned heat exchanger often promote deposition, thus making fouling a self-fulfilling prophecy. The TEMA values do not apply for heat exchanger types other than conventional shell and tube heat exchangers, e.g., plate heat exchangers, compact heat exchangers or finned tubes. Some fouling resistances for other heat exchanger types are given in Tables 6–8. To demonstrate the significance of the selected fouling resistance on the sizing of heat exchangers, Table 9 shows the excess heat transfer surface required for several heat exchanger types, if a typical TEMA fouling resistance of 0.18 m2K/kW is used for each of the two heat exchanging fluids. As shown in the following Vacuum tower bottoms 1.8 Atmosphere tower bottoms 1.2 equation, the percentage excess surface area for a fixed heat duty increases with increasing clean heat transfer coefficient. Af ¼ 1 þ k c Rf ð3Þ Ac Obviously, the impact of the fouling resistance is more severe for heat exchangers with high overall heat transfer coefficients. To account for unreliable design procedures and operational problems, heat exchangers are typically overdesigned by 70–80%, from which 30–50% is attributed to fouling [8]. While the installation of excess heat transfer surface may extend the operation time of heat exchangers, it provides no remedy against the deposition of dirt. Fluid pretreatment, antifouling installations, and regular cleaning will still be required in most cases. Industrial practice and state of the art of such fouling mitigation and of heat exchanger cleaning are outlined in this chapter. 1.2 Mechanisms of Heat Exchanger Fouling Because of the great variety of fouling mechanisms it is useful to divide fouling according to the key physical/chemical processes into five major categories: 1. Crystallization Fouling ● Precipitation and deposition of dissolved salts, which at process conditions become supersaturated at the heat 81 82 C4 Fouling of Heat Exchanger Surfaces C4. Table 5. Fouling resistances for various processing streams in shell-and-tube exchangers, (m2K/kW) Hydrocarbons Gases and vapors Fuel oil no.2 0.35 Fuel oil no.6 0.88 Transformer oil 0.18 Lube oil 0.18 Hydraulic oil 0.18 Quench oil 0.7 Pitch 0.8 Tar 0.9 Vegetable oil 0.53 Steam (oil free) 0.0 Steam (oil contaminated) 0.18 Refrigerant vapor (oil contaminated) 0.35 0.0 Alcohol vapor 0.09 Organic vapor 0.18 Ammonia 0.35 Carbon dioxide 0.18 Combustion gas (coal) 0.18–0.35 Combustion gas (natural gas) 1.8 Diesel exhaust gas 1.8 Synthesis gas 0.18–0.35 Compressed air 0.18 Natural gas 0.18–0.35 Nitrogen 0.18–0.35 2. 3. 4. 5. Stabil column overhead product Liquids Refrigerant 0.10–0.18 Organic heat transfer liquid 0.18–0.35 Ammonia (oil free) 0.18 Ammonia (oil contaminated) 0.53 Methanol solution 0.35 Ethanol solution 0.35 Glycol solution 0.35 LPG, LNG 0.18–0.35 MEA- and DEA solution 0.35 DEG- and TEG solution 0.35 Stable column side stream 0.18–0.35 Stable column bottom stream 0.18–0.35 Caustic solutions 0.35 Black liquor 0.7–1.4 6. transfer surface. Supersaturation may be caused by the following processes: (a) Evaporation of solvent (b) Cooling below solubility limit for solution with normal solubility, e.g., increasing solubility with increasing temperature (c) Heating above the solubility limit for solutions with inverse solubility such as CaCO3, CaSO4, Ca3(PO4)2, CaSiO3, Ca(OH)2, Mg(OH)2, MgSiO3, Na2SO4, Li2SO4, and Li2CO3 in water (d) Mixing of streams with different composition (e) Variation of pH which affects the solubility of CO2 in water (f) Solidification fouling due to cooling below the solidification temperature of a dissolved component (e.g., solidification of wax from crude oil streams) Particulate Fouling ● Deposition of small suspended particles such as clay, silt, or iron oxide on heat transfer surfaces of any orientation ● Gravitational settling of relatively large particles onto horizontal surfaces Chemical Reaction Fouling Deposit formation at the heat transfer surface by a chemical reaction in which the surface material itself does not participate (polymerization, food processing). Corrosion Fouling The thermal resistance of corrosion layers is usually low because of the relatively high thermal conductivity of oxides. However, the increased surface roughness may promote fouling due to other fouling mechanisms. Biological Fouling Biological fouling refers to the development and deposition of organic films consisting of microorganisms and their products such as bacteria (microbial or microbiofouling) and the attachment and growth of macroorganisms such as mussels, algae, etc. (macro-biofouling) on the heat transfer surfaces. Microbial fouling always precedes fouling by macro-organisms, with the microorganisms acting as the nutrient source for the macro-organisms. Suspensions of seaweed and other organic fibres often cause fouling. Many types of bacteria will deposit slime on the heat transfer surfaces and other types of foulants can adhere to these deposits. Larger growth restricts the fluid flow and often causes pitting of the metal. This type of fouling is common in untreated water such as sea, river, or lake water. Microbiological fouling is a particularly serious problem as the microbes may be introduced into the water cycle not only by the fluid, but also from the ambient air in the cooling tower. Temperatures between 15 C and 50 C in cooling towers are ideal for microbial growth. Both dead and alive microorganisms adhere to the heat transfer surfaces and form a layer of slime with a thermal conductivity similar to that of water. As a consequence of the filtering effect of biological layers, more suspended particles amass in the deposit. Mixed Fouling Fouling mechanisms within each category may be described with similar models. Generally, several fouling mechanisms occur at the same time, nearly always being mutually reinforcing. Exceptions are the combination of crystallization and particulate fouling, where particles of the crystallizing matter accelerate fouling, whereas particles from other material may lead to reduced fouling due to a weakening of the deposit structure [9]. Figures 2 and 3 show typical effects of surface temperature and flow velocity on most of the above fouling mechanisms. Fouling of Heat Exchanger Surfaces C4 C4. Fig. 1. Impact of fouling resistance on 2000 shell and tube heat exchangers designed from 2003–2008 1.3 Sequential Events of Fouling The above fouling mechanisms generally occur in five consecutive steps: (i) Initiation Period or Delay Period When the new or cleaned heat exchanger has been taken into operation, the initially high heat transfer coefficients may remain unchanged for a certain time. During this time, nuclei for crystallization are formed or nutrients for biological growth are deposited. This delay period may last anytime from few seconds to several days. According to [10], no delay period occurs for particulate fouling. For crystallization fouling and for chemical reaction fouling, the initiation period decreases with increasing surface temperature, as supersaturation and/or reaction rate increase [11]. Generally, it is reported that the delay time, before deposition starts, decreases with increasing roughness of the heat transfer surface. (ii) Mass Transport To form a deposit at the heat transfer surface it is necessary that at least one key component is transported from the fluid bulk to the heat transfer surface. In most cases, this occurs by diffusion. For the transport of particles to the wall, inertia effects and thermophoretic forces have to be considered, as well. (iii) Formation of Deposit After the foulant has been transported to the heat transfer surface, it must stick to the surface (for particulate fouling) or react to the deposit forming substance (e.g., CaCO3). (iv) Removal or Auto-Retardation Depending on the strength of the deposit, erosion occurs immediately after the first deposit has been laid down. Furthermore, several mechanisms exist, which cause auto-retardation of the deposition process. For the thermal boundary condition of constant temperature difference between heated and cooled fluid, the growth of deposit causes a reduction of the driving temperature difference between heat transfer surface and fluid. C4. Table 6. Fouling resistances in plate and frame heat exchangers, (m2K/W) [5] Fluid Fouling resistance (m2 K/kW) Water Demineralized or distilled 0.009 Soft 0.017 Hard 0.043 Treated cooling tower water 0.034 Coastal sea water 0.043 Ocean sea water 0.026 River water 0.043 Engine jacket 0.052 Lube oil 0.017–0.043 Vegetable oil 0.017–0.052 Organic solvents 0.009–0.026 Steam 0.009 General process fluids 0.009–0.052 (v) Aging Every deposit is subjected to aging. Aging may increase the strength of the deposit by polymerization, recrystallization, dehydration, etc. Biological deposits get poisoned by metal ions and may be washed away by the bulk flow. Aging is the least investigated and understood step and is usually ignored in modelling attempts. Depending on the process parameters and the dominant fouling mechanism, the fouling rate can be either constant or decreasing with time (see Fig. 4). For hard, adherent deposits such as silicates and some polymerization products, steps iv and v may be ignored and the growth rate of deposits is constant or continuously decreasing with time. For weaker deposits (e.g., particles >1 mm), the fouling resistance approaches a constant (or asymptotic) value which may or may not allow acceptable operation of the process. 83 84 C4 Fouling of Heat Exchanger Surfaces C4. Table 7. Fouling resistances for combustion gases on finned surfaces (m2K/W) [6] Fouling resistance (m2 K/kW) Flow velocity m/s Natural gas 0.09–0.53 30–40 Propane 0.18–0.53 25–30 Butane 0.18–0.53 18–24 Clean turbine gas 0.18 15–21 Moderately clean turbine gas 0.27–0.5 Light oil 0.36–0.7 Diesel oil 0.53 Heavy oil 0.53–1.24 Crude oil 0.7–2.7 Coal 0.89–8.85 Fuel C4. Fig. 2. Effect of flow velocity on the fouling resistance for flow of water C4. Table 8. Fouling resistances in evaporators, (m2K/W) [7] Fouling resistance (m2 K/kW) Boiling medium Hydrocarbon C1–C4 0–0.18 Higher hydrocarbons 0.18–0.5 Olefins and polymerizing hydrocarbons 0.5–0.9 Heating medium Condensing steam 0–0.09 Condensing organic vapor 0.09–0.18 Organic liquid 0.09–0.052 C4. Fig. 3. Effect of surface temperature on the fouling resistance for flow of water C4. Table 9. Excess surface area for various heat exchanger applications, Rf = 0.36 m2K/kW Application Clean overall coefficient Excess area Gas/gas shell & tube heat exchanger 50 W/m2K 1.8% Liquid/gas shell & tube heat exchanger 150 W/m2K 5.4% Liquid/liquid shell & tube heat exchanger 1000 W/m2K 36% Liquid/liquid plate & frame heat exchanger 3000 W/m2K 108% Water-cooled shell & tube steam condenser 4500 W/m2K 162% C4. Fig. 4. Possible fouling resistance versus time curves Fouling of Heat Exchanger Surfaces C4 C4. Fig. 6. Total annual costs of a double pipe heat exchanger arrangement as a function of the flow velocity C4. Fig. 5. Fouling resistance in shell and tube heat exchangers as a function of flow velocity and water quality [13]. Water quality decreasing from 1 to 4 1.4 Approximate Influence of Operating Conditions on Fouling in Industrial Heat Exchangers Many correlations have been recommended for the prediction of individual fouling mechanisms [12]. However, these correlations are generally not applicable to industrial conditions where a combination of fouling mechanisms and foulants occurs. Comparing fouling data from a range of industries, the following approximate influence of process parameters on industrial fouling has been found: (a) Fouling usually increases linearly with increasing foulant concentration in the fluid bulk. (b) The fouling resistance nearly always decreases with increasing wall shear stress due to increased removal forces. As an average, it was found that the fouling resistance is proportional to the flow velocity to the power of 1.5. Figure 5 shows the effect of dirt content and of flow velocity on the fouling resistance for cooling water [13]. (c) For many fouling mechanisms, the fouling resistance increases with increasing surface temperature (see e.g., Fig. 3). For crystallization and chemical reaction fouling, this trend frequently follows an Arrhenius relationship dRf E ¼ Ke =RTS dt ð4Þ For biological fouling, a maximum is observed for temperatures around 35 C. (d) Fouling was found to increase with increasing roughness of the heat transfer surface. To date, not even these simple rules are considered in the design of heat exchangers, even though they could significantly improve some heat exchanger optimization procedures. This is demonstrated in Fig. 6, which shows the sum of annual operating and capital service costs of an arrangement of multiple double pipe heat exchangers as a function of the flow velocity in the pipes. One curve has been calculated according to Martin [14] for a constant fouling resistance, the second is for the case where the fouling resistance is velocity dependent as suggested above. The optimum flow velocity shifts from 0.8 to about 1.3 m/s and the total annual costs are reduced by 10% despite the higher friction losses. 1.5 Costs due to Heat Exchanger Fouling Despite the enormous costs associated with heat exchanger fouling, only very limited research has been done to determine accurately the economic penalties due to fouling and to attribute these costs to the various aspects of heat exchanger design and operation. However, reliable knowledge of fouling economics is desirable to evaluate the cost-efficiency of various mitigation strategies. The total fouling related costs consist of 1.5.1 Capital Expenditure According to Thackery [15], total capital cost due to fouling in England added up to £100 million in 1978, which corresponds to US$190 million. For the United States, Garrett-Price et al. found that capital costs excluding costs for antifouling equipment were US$960–280 million in 1982 [3]. (a) Excess Heat Transfer Surface Area Thackery [15] found that design excess surface area for fouling varies between 10–500%, with an average around 30%. This result was confirmed by Garrett-Price et al. [3], who obtained a similar value for the USA and by Steinhagen et al. for New Zealand [2]. Investigations by Heat Transfer Research Inc. and TEMA among the major North American heat exchanger manufacturers showed excess surface areas between 11% and 67% [8]. Excess area of 30–40% may correspond to 25% additional capital cost. To estimate the absolute costs of excess heat transfer area in the United Kingdom, Pritchard [16] took the value of 85 86 C4 Fouling of Heat Exchanger Surfaces the process plant built in the UK. As much as 6.5% of the process plant hardware consisted of heat exchangers. If each heat exchanger has 30–40% extra surface area to allow for fouling, he concluded that additional costs were £5 million in 1968 and £20 million in 1977. The corresponding American figure is $US320 million per year for 1982 [3]. (b) Transport and Installation Costs As a result of additional surface area, heat exchangers become bigger and heavier. Therefore costs for stronger foundations, provisions for extra space, increased transport and installation costs must be considered. Woods et al. [17] assume that installation costs tend to increase with the size of the heat exchanger and are usually 2–3 times the delivered costs. Adding these extra costs to the costs for excess heat transfer surface may increase the costs for oversized equipment to $640–960 million per year [3]. (c) Capital Costs for Antifouling Equipment These costs include expenses for online and off-line cleaning equipment, extra cost for providing non-fouling heat exchangers such as scraped surface or fluidized bed heat exchangers, pretreatment plants, cleaning-in-place equipment, dosing pumps and tanks for antifouling chemicals. 1.5.2 Fuel Costs Costs for extra fuel only occur if fouling leads to extra fuel burning in furnaces or boilers or if more secondary energy such as electricity or process steam is needed to overcome the effects of fouling. Thackery [15] estimated additional UK fuel costs in 1978 as £100–200 million ($US290–480 million). Garrett-Price et al. [3] calculate that 1–5% of the energy consumed by the industrial sector is used to overcome fouling. The result leads to fouling related fuel costs between $US700 and $US3,500 million. 1.5.3 Maintenance Costs Maintenance costs are costs for removing fouling deposits and costs for chemicals or other operating costs of antifouling devices. According to Pritchard [16] and Thackery [15], about 15% of the maintenance costs of process plant could be attributed to heat exchangers and boilers and of that 50% was probably due to fouling. Garrett-Price et al. [3] quote a figure of $US2,000 million for annual sales of companies supplying heat exchanger online and off-line cleaning equipment, chemicals, and cleaning services in the USA for 1982. 1.5.4 Costs due to Production Loss Because of planned and unplanned plant shutdowns due to fouling in heat exchangers, large production losses are possible. These costs are often considered to be the main cost of fouling. For example: Sart and Eimer [18] state that the loss of production for 1 day shutdown of a 1300 MW power plant is about $US500,000; Taborek [13] estimates that shutdown losses of a large oil refinery are about $US1.5 million per day. In addition to production losses during plant shutdown and start-up, penalties for not keeping to a deadline and the loss of customers must be considered. Garrett-Price et al. [3] suggested that an upper limit for loss of production costs may be estimated by assuming that the loss of production has to be less than the cost of providing redundant exchangers. For the US in 1984, this would be $US200 million. According to Thackery, [15] 1978 costs due to production losses in the UK are about £100 million ($US190 million). The above fouling-related costs will have to be inflated to current prizes. For crude oil heat exchangers, more recent information is available in [19]. 2 Consideration of Fouling in the Design of Heat Exchangers 2.1 Preliminary Remarks Not all heat exchangers have serious problems with fouling; many of them operate satisfactorily for long periods of time without being cleaned. If fouling is anticipated, however, some allowance must be provided in the design of a heat exchanger. Regardless of the approach, the selection of appropriate values still relies more on engineering judgement from past experience than on the application of results from experimental and theoretical research. It is important to keep in mind that heat exchanger fouling can be effectively mitigated at the design stage of the heat exchanger. To design for reliable operation, (i) Select a suitable heat exchanger type (ii) Try to avoid operating conditions which promote fouling (iii) Attempt an optimum design with adequate velocities in the heat exchanger and which avoids hot spots, bypass flow or dead zones (iv) Design for easy cleaning Additional guidance is included in Sect. 3. Due to their frequent occurrence and economic importance, detailed best practice guidelines have been prepared by ESDU [19–21] for fouling in crude oil preheat exchangers, and for seawater and fresh water as C4. Table 10. Reboiler selection guide [8] Anticipated fouling Kettle or internal boiler Horizontal shell-side thermosyphon Vertical tube-side thermosyphon Forced flow No fouling Good Good Good Expensive Moderate Risky Good Best Expensive Heavy Poor Risky Best Good Very heavy Poor Poor Risky Best Fouling of Heat Exchanger Surfaces cooling media. These reports present the state-of-the-art of fundamental aspects and industrial practice. 2.2 Selection of Heat Exchanger Type If fouling will be significant, it may well control the selection of the type of heat exchanger and its size. This is very clearly demonstrated in Table 10, which recommends different reboiler types depending on the severity of fouling [7]. Other examples are: ● Shell and tube heat exchangers are not particularly suitable for fouling conditions; however, good design practices [22–26] and special baffle and tube design may be applied to reduce fouling. ● Plate and frame heat exchangers may be attractive as they can be disassembled for cleaning and sterilizing. ● Since there are no local low velocity regions in spiral plate heat exchangers, these heat exchangers perform well for fluids with a high concentration of suspended solids. ● Scraped heat exchangers improve the heat transfer by continuously removing deposit from the heat transfer surfaces with rotating blades. ● Fluidized bed heat exchangers can be used where the fluidized particles remove deposit from the embedded tubes. ● Direct contact heat transfer may be a suitable alternative. ● Highly compact heat exchangers are normally avoided for severe fouling conditions, as they are difficult to clean. 2.3 Material Selection The second most important point is the proper selection of the heat exchanger material, as already minor corrosion may considerably increase other fouling mechanisms. In addition, the pipe material itself can also have an effect on fouling. For example, biofouling is reduced in brass tubing, as shown in Fig. 7 for seawater fouling [27], and crude oil fouling can be minimized by careful material selection [26]. Surface roughness increases the contact surface area such that the true contact area is much larger than the apparent C4. Fig. 7. Influence of pipe material on biofouling [27] C4 surface area. As a result of this difference, stronger adhesion should occur on rough surfaces. This is confirmed by measurements with Kraft black liquor in electropolished tubes shown in Fig. 8 [28]. Surface coatings for reducing the adhesion of deposits on heat transfer surfaces have attracted increased interest in recent years. For example, organic materials such as PTFE and Säkaphen have indeed been shown to reduce fouling from various fluids, for example during seawater evaporation and heat transfer to Kraft black liquor. The main reason why such materials/ coatings are not more widely used is that they are poor heat conductors and form an additional resistance to heat transfer which is comparable to the TEMA fouling resistance for cooling water. If very thin coatings were used, the resistance against erosion or other mechanical stress would be greatly diminished. These problems may be avoided with several novel coating methods, such as Ion Beam Implantation, Magnetron Sputtering, Multi-Arc Ion Plating, Filtered Cathodic Vacuum Arc Plating or electroless Ni-P-PTFE plating which have been investigated in recent years [29–33]. These thin and stable coatings have been found to reduce scale formation during convective and boiling heat transfer as well as the adhesion of bacteria. 2.4 Shell and Tube Heat Exchangers Experience has shown that higher flow velocities and lower tube surface temperatures generally tend to reduce fouling. Therefore, arrangements that eliminate stagnant or low velocity regions have less overall fouling. As a general rule, the more fouling and more corroding fluid should be placed on the tubeside. The inside of tubes can be cleaned much easier than the outside and the tubes can be made from exotic alloys at lower cost than the shell. The orientation of a heat exchanger influences the ease by which it can be cleaned and can effect particulate fouling. If particulate fouling is anticipated, a vertical down-flow orientation will permit the solids to move through the exchanger. If a horizontal orientation is unavoidable, place the slurry on the C4. Fig. 8. Reduction of heat transfer coefficient during the evaporation of Kraft black liquor in pulp mills [28] 87 88 C4 Fouling of Heat Exchanger Surfaces C4. Table 11. Cooling water flow velocities in condensers [29] Pipe material Recommended velocity Minimum velocity Arsenical copper <1.5 m/s 1.0 m/s Admiralty 1.4–2.0 m/s 1.0 m/s Aluminum brass 1.8–2.2 m/s 1.0 m/s 9010 cupro-nickel 1.8–2.5 m/s 1.5 m/s 90/30 cupro/nickel 2.4–3.5 m/s 1.8 m/s Cu 1.5–2.0 m/s 1.0 m/s Steel 2.0–4.0 m/s 1.0 m/s C4. Fig. 10. Helixchanger Baffles (courtesy ABB Lummus) C4. Fig. 11. Twisted Tubes (courtesy Brown Fintube Company) C4. Fig. 9. Sketch of heat exchanger geometry and observed deposit formation [8] tube-side and ensure down-flow for multiple tube pass designs. While placing a slurry on the shell-side of a horizontal heat exchanger is not recommended, some success has been reported for vertical-cut double-segmental baffles because they allow the sediment to travel through the exchanger. While heat exchangers used to be designed for tube-side flow velocities around 1 m/s, modern design velocities are about 2.0 m/s. Table 11 shows optimum and minimum cooling water velocities for condensers of various pipe materials [34]. Based on 20 years of experience in the design of heat exchangers, Gilmour [35] states that ‘‘for most applications, only negligible fouling occurs if the heat exchanger is well designed. It is obvious that the majority of poorly performing shell and tube heat exchangers were caused by mistakes in the design of the shell-side flow path.’’ He especially emphasizes that zones with low flow velocity and bypass flows should be avoided under any circumstances. If half-moon baffles are used, the baffle cut should not exceed 20% of the shell inside diameter. Vertical baffles should only be used for condensation or evaporation duties but not for sensible heat transfer situations, because they allow a stratification of flow and hence a sedimentation of suspended particles. Figure 9 [8] shows qualitatively the deposit formation in two shell and tube heat exchangers for identical heat duty. The smaller heat exchanger is designed with appropriate baffle spacing and baffle cut, and hence has higher heat transfer coefficients and less fouling. Helical flow baffles, as shown in Fig. 10, have been used successfully because they avoid both, flow stratification and stagnant flow zones [36]. Reduced fouling has also been reported for the EM-baffle design developed by Shell Global Solutions [37]. Successful installations of heat exchangers with twisted tubes (Fig. 11) have been reported which may reduce deposit formation both, on the shell and on the tube-side [38]. It is often assumed that finned tubes tend more to fouling because of low flow velocity zones at the base of the fins. While these problems may occur for fouling mechanisms which depend strongly on the flow velocity (such as biological fouling and particulate fouling), there are a number of applications where fouling was even reduced by the use of finned tubes. This effect is explained by the nonuniform thermal expansion of finned tubes due do the temperature profile along the fins, which may reduce the strength of hard and adherent deposits. In [39] numerous investigations on fouling on finned tubes are compared with respect to the effects of fin geometry on deposit formation. When selecting finned tubes for fouling duties it should always be considered that mechanical cleaning of finned surfaces may be difficult or even impossible. A fairly recent solution for heat transfer involving severely fouling liquids is the fluid bed heat exchanger, which has been described by Klaren [40]. Small solid particles (glass, ceramic, metal) are fluidized inside parallel tubes by the upward flow of liquid. The solid particles regularly break through the viscous boundary layer, so that good heat transfer is achieved in spite of relatively low flow velocities. More importantly, the solid particles have a slightly abrasive effect on the wall of the heat exchanger tubes, thus removing most deposits at an early stage. Fluid bed heat exchangers have been installed in water C4 Fouling of Heat Exchanger Surfaces treatment plants, paper mills, food and dairy plants, geothermal plants and in various chemical plants. In all cases, a substantial reduction in fouling has been achieved. 2.5 Other Heat Exchanger Types The widespread installation of compact heat exchangers has been hindered by the perception that the small passages are stronger affected by the formation of deposits. Obviously, compact heat exchangers are unsuitable for fluids containing large particulate material or debris. However, several investigations demonstrated that the high shear forces, low wall superheat and homogeneous flow distribution typical for compact heat exchangers reduce the formation and adhesion of deposits on the heat transfer surfaces. The use of more corrosion resistant materials with smoother heat transfer surfaces further reduces the formation of deposits. Most compact heat exchangers have to be cleaned chemically. Unfortunately, there is very little published information about fouling and cleaning of compact heat exchanger types. As indicated by Eq. (3), the excess heat transfer surface area increases with increasing clean heat transfer coefficient for a constant heat duty. This places a heavy penalty on compact heat exchanger types, such as plate and frame heat exchangers, if, because of ignorance or because of cautiousness, the TEMA fouling resistances for shell and tube heat exchangers are used. Typical clean overall heat transfer coefficients for plate and frame heat exchangers are about 3000 W/m2K, for shell and tube heat exchangers about 1000 W/m2K. A design fouling resistances of 0.3 m2K/kW then corresponds to 30% overdesign for a shell and tube heat exchanger and to 90% overdesign for a plate and frame heat exchanger. 2.5.1 Plate and Frame Heat Exchangers The application of plate heat exchangers in the chemical process industry is increasing rapidly, where they begin to replace tubular heat exchangers in several traditional applications. Cooper [36] investigated cooling water fouling using an APV model R405 plate heat exchanger. The water was chemically treated before entering the heat exchangers. As shown in Fig. 12, the fouling resistance in the plate and frame heat exchanger is significantly lower than in the shell and tube heat exchanger, despite the typically lower flow velocities. If the flow velocity is increased, the fouling resistance decreases similarly as it is found for shell and tube heat exchangers. Novak [42] studied the fouling behavior of Rhine River water near Mannheim (Germany), and of Öresund seawater in Sweden. For both waters, mainly biological fouling was observed. The fouling resistances increased almost linearly over the observed period of time. Table 12 summarizes the measured effect of flow velocity on the fouling rate. Typical values for fouling resistances in plate heat exchangers are given in Table 6. Most manufacturers of plate and frame heat exchangers recommend that the excess surface should not exceed 25% of the heat transfer surface area calculated for the clean duty. Due to the nonuniformity of flow distribution and deposit formation, measured pressure drop increases are significantly higher than values predicted using an average deposit thickness calculated from the fouling resistance. The actual plate geometry (angle, amplitude, and wavelength of corrugations) affects the formation of deposits [43]. Delplace et al. found that deposition from whey protein solutions on chevron plates is only half of that of straight corrugations, for otherwise identical conditions [44]. 2.5.2 Plate-Fin Heat Exchangers Plate-fin heat exchangers are brazed/welded compact heat exchangers with a heat transfer surface density of about ten times that of tubular heat exchangers. Typical applications are cryogenic, chemical/petrochemical, and hydrocarbon offshore installations. Molecular sieves and 100 mm filters are used in cryogenic installations to remove particulate matter or components that may freeze-out on the heat transfer surfaces. Systematic investigations have been performed on particulate fouling [45] and on river water fouling [46]. C4. Table 12. Fouling rates of Rhine river water for a surface temperature of 25 C [33] Type C4. Fig. 12. Comparison of fouling in plate and frame, and in shell and tube heat exchangers [41] u, m/s t, Pa dRf/dt, 104 m2K/kWh Plate heat exchanger 0.13 6.7 7.4 Plate heat exchanger 0.19 14.5 4.3 Plate heat exchanger 0.77 190.0 0.6 Spiral plate exchanger 0.43 7.5 5.0 89 90 C4 Fouling of Heat Exchanger Surfaces For 3 mm ferric oxide particles suspended in water, no blockage of plain fin or wavy fin channels was observed. Wavy fin channels fouled more than plain fin channels. All experiments showed asymptotic behavior. Higher deposition rates were obtained for non isothermal conditions and at higher bulk temperatures. Maximum deposition occurred at a Reynolds number of about 1500 [45]. Fibrous and biological material partially block the inlet of the aluminum plate-fin test sections when used with river water, which was filtered through a 1 mm mesh. Some deposition was found at locations where corrosion of the aluminum had occurred. In the wavy fin test section, a thin, uniform deposit of fine mud was observed. Pressure drop for the plain finning increased linearly with time, whereas asymptotic behavior was found for the wavy finning. The initial slope of the relative pressure drop vs. time curves was 5.8·108s1 for the plain fins and 1.71·107s1 for the wavy fins. For the latter, an initial deposition rate of 4.8·1012 s m2K/W and an asymptotic fouling resistance of 6·106m2K/W was measured [46]. 2.5.3 Printed Circuit Heat Exchanger The passages in Printed Circuit Heat Exchangers (PCHEs) are typically between 0.3 mm and 1.5 mm deep. The specific design leads to volumetric heat transfer areas of 500–2,500 m2/m3, which is an order of magnitude higher than shell and tube heat exchangers. Experiments are described in [47] to compare the fouling related drop in performance of a PCHE and of a double pipe heat exchanger (DPHE). The cooling water treated against corrosion, scale formation and biofouling, and a 0.5/1.0 mm strainers was installed to reduce particulate fouling. For operating times of 500–660 h, no change in thermal effectiveness was observed for the PCHE, but the pressure drop increased by up to 55% due to the deposition of particulate material. The addition of a stainless steel mesh insert for the removal of fibrous material significantly reduced the increase in pressure drop. No deposition was observed in the parallel DPHE. PCHEs have been used for gas cooling using seawater [47]. 200 mm strainers have been installed upstream of the heat exchanger and chlorine was added to counter biofouling. No operational problems have been reported. Another application involved the heating of tail gas in a nitric acid plant using condensing steam. After 18 months of operation, no indication of channel blockage could be detected. 2.6 Effect of Fouling on Pressure Drop The formation of deposits on the heat transfer surfaces causes an increase of the frictional pressure drop due to increased surface roughness and restricted cross-sectional flow area. According to Chenoweth [8], more heat exchangers are taken out of service because of excessive pressure drop than because of reduced heat transfer. 2.6.1 Tube-Side Pressure Drop A rough estimate of the tube-side pressure drop can be made if it is assumed that the deposit is distributed evenly at the tube inside. The frictional pressure drop in cylindrical tubes is calculated from Eq. (5): Dp r u2 ¼x 2di DL the friction factor for smooth tubes x ¼ 0:0056 þ 0:5 Re0;32 Polymer Compact Heat Exchangers Polymer heat exchangers are used for low pressure operations involving corrosive gases or liquids. The low surface energy and the smooth surface of their construction materials (polypropylene, fluoropolymer etc.) reduce the stickability of most deposits. Since clean heat transfer coefficients are already low (150–250 W/m2K), these heat exchangers react less sensitively to an additional fouling resistance than metallic heat exchangers. ð6Þ and for rough tubes x ¼ 0:014 þ 1:056 Re0;42 ð7Þ If the fouling resistance and the thermal conductivity of the deposit are known, the inside diameter of the fouled pipe can be determined by Eqs. (8) and (9): di di ln ð8Þ Rf ¼ 2ld df 2ld Rf ð9Þ df ¼ di exp di The pressure drop for the fouled tube is obtained by using Eq. (5) in conjunction with Eqs. (7) and (9). It is generally found that the above equations under-predict the effect of fouling on pressure drop, since they assume a uniform distribution of deposit over the total heat transfer surface. C4. Table 13. Ratio of fouled to clean shell-side pressure drop [48] Shell diameter/baffle spacing Deposit heat transfer coefficient 2.5.4 ð5Þ 1.0 2.0 5.0 1/Rf = 6000 W/m2K 1.06 1.20 1.28 1/Rf = 2000 W/m2K 1.19 1.44 1.55 1/Rf < 1000 W/m K 1.32 1.99 2.38 1.12 1.38 1.55 1/Rf = 2000 W/m K 1.37 2.31 2.96 1/Rf < 1000 W/m2K 1.64 3.44 4.77 Laminar flow 2 Turbulent flow 1/Rf = 6000 W/m2K 2 Fouling of Heat Exchanger Surfaces 2.6.2 Shell-Side Pressure Drop The effect of fouling on the shell-side pressure drop can be estimated using Table 13 from Coulson et al. [48]. 3 HTRI Fouling Mitigation by Design Method Based on almost 50 years of experience as some of the world’s leading heat exchanger design experts, Heat Transfer Research Incorporated (HTRI) [22–26] have developed a design methodology that yields smaller, more cost-effective shell and tube heat exchangers with extended run times between cleanings. While this methodology has, so far, only been validated for crude oil processing, its rigorous approach can be taken as an example for other fluids and heat exchangers types. These techniques were developed by HTRI with help from industry through the HTRI Exchanger Design Margin Task Force (EDMTF). The goal of the EDMTF is to develop the design philosophy for adding margins to heat exchangers to allow for process uncertainties and fouling. Experience has shown that fouling may be mitigated for many services through proper heat exchanger design and operation. For the experienced designer, fouling resistances are not used when operating data for identical or similar services are available. In these cases, designing with the proper attention to velocity (or shear stress) and wall temperature can prevent significant fouling whereas ‘‘the mere use of a high fouling resistance will generally engender a high degree of fouling.’’ A small design margin may be added to the design to address design uncertainties. Rarely is this margin in excess of 30%. More than 30% excess margin calls for a root cause analysis of the problem followed by a fouling (or design) mitigation strategy. Except for rare cases of intentional high variability in throughput, more than 30% excess margin in a heat exchanger design indicates the presence of unresolved engineering issues and can often be a significant source of hidden cost to the owner. It is good practice to design for an allowable pressure drop derived by reducing the maximum available pressure drop in the clean condition by the amount of excess margin anticipated. This permits any excess margin to be applied in such a way that design shear rates and wall temperatures are not reduced. The maximum available pressure drop in the clean condition is estimated as the maximum available pressure drop divided by the fractional pressure drop increase when the exchanger is operated in the fouled condition. 3.1 Crude Oil Best Practice Operating Conditions The fluid scope for this design methodology is: ● Medium-to-high boiling point liquid hydrocarbon mixture with API gravity less than 45 C4 ● Heavy particulate matter (e.g., catalyst fines) absent ● Reasonable salt content (no desalter malfunctions) a) Minimum Liquid Velocity ● Tube-side velocity of 2 m/s. This velocity limit is applicable for tubes with outside diameters of 19.05 mm and 25.4 mm. Increase velocity to 2.2 m/s for tube diameters of 31.75 mm and 38.1 mm to maintain shear stress. ● Shell-side cross flow stream should be at least 0.6 m/s. If the shell-side flow is fully longitudinal, the minimum shell-side velocity should be 1.2 m/s. For longitudinal flow bundles, tubes removed for entrance/exit considerations at the shell nozzles should be replaced in the bundle proper with plugged dummy tubes or rods of the same diameter to maintain a uniform flow field and minimize bypass streams. The bundle-to-shell diameter ratio is to be made as close to 1.0 as practical under TEMA [4] clearance rules. b) Maximum Temperature ● The maximum tube wall temperature should be 300 C. Shell-side design with cross-flow baffles ● The B-stream fraction according to TEMA nomenclature [4] should be at least 0.65. ● Single-segmental baffles should be selected. If the shell-side pressure drop is prohibitively high, double-segmental, helical, EMbaffle, rod baffle, squared, or no-tube-in-window (NTIW) baffle configurations may be considered. ● Baffle cut orientation should normally be horizontal for TEMA type E and J shells. Baffle cut orientation for TEMA type F and G shells should be vertical. If slurry must be placed on the shell-side of a horizontal heat exchanger, consider vertical cut double-segmental baffles to allow the sediment to exit the shell. ● Baffle cut for single-segmental designs should be 20–25% of the shell inside diameter, where 20% is preferred. It may be increased up to 25% to reduce leakage streams. ● The ratio of window velocity to cross-flow velocity (including leakage streams) should be less than 2.0 for designs with tubes in the window (1.0–1.5 is preferred). For no tubes in window designs, the ratio of window velocity to cross flow velocity should be less than 3.0 (1.5–2.0 is preferred). Refinement of this guideline is an area of research. 3.2 Cooling Tower Water Best Practice Operating Conditions For the case of those cooling water streams which are closely regulated in the plant for velocity control and are kept reasonably clean with a water maintenance program, fouling mitigation strategies apply. The cooling water temperatures should be designed and operated to not exceed a maximum bulk temperature of 50 C or a maximum wall temperature of 60 C. In addition, there must be sufficient velocity to maintain any particulate in suspension as well as to produce enough wall shear to stabilize any fouling which does occur. There are many 91 92 C4 Fouling of Heat Exchanger Surfaces sources for information on minimum cooling water velocities for design, such as those given in Table 11. In reality, the exact minimum value for any cooling water system is so dependent upon the contaminants dissolved in the water that one single value for this purpose can only be regarded as an approximation. In the final analysis, the judgment as to minimum design water velocities while adhering to prudent water temperature limitations must be made by those knowledgeable about the water used. 3.3 Excess Surface/Coefficient Adjustments ● If both fluids are within the scope outlined above, approximately 20–25% excess surface should be provided instead of applying fouling resistances. This design margin may be reduced when the designer has confidence in the fluid properties, predictive methods, and successful mitigation of fouling (usually based on prior experience for a similar service). ● If only one fluid is operating under the best practice conditions, a fouling resistance should be selected for the fluid outside scope. For non-fouling fluids outside scope, a fouling resistance of 0.000088 m2K/W is recommended to compensate for heat transfer surface changes during start-up. For the fluid within scope, the heat transfer coefficient is multiplied by 0.83 and no fouling resistance is used. As above, the design margin may be reduced based upon operating experience. 3.4 Design Recommendations 3.4.1 Shell-Side Bundle Geometry Exit/Entrance Constraints ● Where impingement protection is required, use impingement rods. One row of rods is acceptable for 90 tube layouts, two rows for staggered pitch. Impingement plates should be avoided. ● Large baffle end spaces and correspondingly low local velocity sometimes occur due to geometry constraints. When the end baffle space is greater than or equal to 1.5 times the space between baffles, the area back from the first baffle to 1.5 times the baffle spacing is to be considered 65% effective regardless of baffle type or orientation. All remaining area to the tube-sheet is to be considered ineffective for heat transfer. Additional area should be provided in the bundle proper as compensation. An annular distributor may be considered if the affected surface area is large. 3.4.2 Allowable Pressure Drop Pressure drop should be provided as required to meet the minimum critical velocities noted in Sect. 3.1. If the pressure drop (and hence the flow velocity) is too low, fouling may become inevitable and fouling mitigation impractical. 3.4.3 Longitudinal Baffles If a longitudinal baffle is used in heavy fouling service where shell-side pressure drop in one shell exceeds 35 kPa (70 kPa with a ‘‘kempchen’’ style of seal), the baffle shall be welded to the shell. Note that welding the longitudinal baffle to the shell requires a shell inside diameter of at least 0.7 m and, for the bundle to be removable, U-tubes must be used with the U-bends in the horizontal plane (normally two or more tube passes per shell pass). The designer should investigate differential thermal stresses across the shell. In general, a welded longitudinal baffle is probably acceptable where the shell-side temperature difference across one shell does not exceed 90 C. For leaf seal construction, shell-side operating temperature differentials of 195 C across one shell have been accommodated with proper mechanical design. These rules are for 6.7 m straight-length tube bundles and will vary with bundle length. Bundle slide rails in both top and bottom portions of the bundle need to be provided. The following segmental-baffle construction features may be considered to improve shell-side performance: ● American Petroleum Institute Standard 660 requires that a seal device (dummy tubes, rods, or strips) be implemented from 25–75 mm from the baffle tips, and for every 5–7 tube pitches thereafter. The number of seals may have to be increased to limit the bundle and pass lane leak streams. ● Where the tube-to-baffle diametral tolerance (as specified by TEMA [4]) is 0.8 mm, the tolerance may be reduced to 0.4 mm if required to reduce the leak stream between the tube and baffle hole. ● The TEMA [4] baffle-to-shell diametral clearance may be reduced to limit the baffle-to-shell leakage stream. A clearance of 0.0035–0.004 times the shell diameter is achievable for shells rolled from plate, but use this extra tight clearance only if necessary, as it is difficult to guarantee compliance. Extra tight clearance is not recommended for shells made from pipe (typically NPS 24 and smaller). ● Baffled TEMA [4] F and G shells may be considered to increase shell-side velocity, reduce the number of shells in series, and/or improve the baffle-spacing-to-shell-diameter aspect ratio. 3.5 Example for Fouling Mitigation by Design To demonstrate the potential savings of the design methods outlined in this section, the following example will be used. This example is for the last shell-and-tube heat exchanger in the crude oil preheat train prior to the fired heater. Selection of material is important, and stainless steel or high chrome steel should be selected for the design. The process conditions are summarized in Table 14a. C4 Fouling of Heat Exchanger Surfaces 3.5.1 Original Design The original heat exchanger is a TEMA type AES consisting of two shells. The design and performance parameters for the exchanger unit are given in Table 14b. 3.5.2 3.5.4 Operation History with Original Design This service was a consistent high fouling problem and would lose about 57% of its performance capacity within the first 6 months after cleaning, resulting in excess energy (fired heater fuel) and related costs of about €62.000 per month averaged over a 2 year turnaround cycle. 3.5.3 from adhering to the outside of the tubes and allow it to be carried through the exchanger without deposition. However, to do this required an appropriate redesign of the heat exchanger. Root Cause Analysis of Performance At the next turnaround, the bundles were pulled for cleaning. Prior to cleaning, visual bundle inspection revealed a ‘‘fuzzy’’ looking coating on the outside of the tubes consisting of oil and coking fines from the vacuum unit. The coating was slightly sticky but did not solidly adhere to the surface and could be easily wiped away. The tube-side fouling appeared to be slight. In addition, analyzing the fouling performance monitor over the course of the 2-year turnaround cycle indicated a performance plateau at about 6 months after which the fouling seemed to stabilize for the next 1.5 years. These data strongly indicated shear rate controlled fouling at the shell-side. From the above data, it was estimated that a shell-side velocity slightly greater than 1.5 m/s should keep the fouling New Design Using the procedures outlined in this section, a replacement heat exchanger was designed for this service as given in Table 14c. The new design consists of a horizontal welded long baffle on the shell-side, shell nozzles located at the rear of the shell beyond the bundle U-bends so that there are no erosion concerns, and horizontal U-bends with a vertical channel pass partition to produce a removable, two tube pass bundle in a welded long baffle F-shell. Both the original and new designs employed segmental baffles on the shell-side. 3.5.5 Final Outcome The new design used no preset fouling resistances but instead used the allowable pressure drop to produce the higher shear rate necessary to inhibit deposition. A minimum of 15% excess surface was thought prudent to handle design uncertainties in the new configuration. The new exchanger performed at or above expected design over the 2-year turnaround cycle producing an average €68.000 per month cost savings over the original heat exchanger. C4. Table 14a. Process conditions for design example Fluid Flow rate Location Stream Designation kg/s Temperature in Shell-side Heavy Vacuum Gas Oil 71 Tube-side Crude Preheat 88 Temperature out C Allowable DP C kPa 366 338 100 289 311 70 C4. Table 14b. Original heat exchanger design Number of shells TEMA Number of passes Fouling resistance Velocity m/s DP design kPa Size Type Shell Tube Shell Tube Shell Tube Shell 2 AES 1 2 0.00123 0.0007 0.37 1.22 8.5 Uc/Uf Tube 32 1.95 DP design kPa Uc/Uf 1016 mm 6.1 m C4. Table 14c. Improved heat exchanger design Number of shells TEMA Number of passes Fouling resistance Size Type Shell Tube Shell Tube Shell Tube Shell Tube 1 AFU 2 2 – – 1.85 2.38 91 58 610 mm 6.1 m Velocity m/s 1.16 93 94 C4 Fouling of Heat Exchanger Surfaces C4. Fig. 14. Recirculation of cooling water 4.2 C4. Fig. 13. Fouling resistance as a function of flow velocity and surface temperature during start-up of a new or cleaned heat exchanger 4 Online Mitigation Methods The following section provides an overview of the broad categories of mitigation methods, and describes some general approaches. For more detailed information see [49]. 4.1 Start-Up Procedures The use of constant fouling resistances in the design of heat exchangers leads to initially oversized equipment. Heat duties in new or cleaned heat exchangers can, therefore, be considerably higher than the design specifications. In most chemical processes, however, product inlet and outlet temperatures, product flow rate and cooling water inlet temperature are specified. If this is the case, the heat exchanger is usually controlled via the flow rate of the cooling water. To reduce the heat duty, the water flow velocity must be reduced. Figure 13 shows that this procedure may cause a considerable increase of fouling as compared to fouling under design operating conditions. Point ‘‘A’’ refers to the design values of flow velocity and heat transfer surface temperature. As the heat exchanger is initially overdesigned, the cooling water flow velocity is throttled which also causes an increase of the heat transfer surface temperature, see point ‘‘B.’’ However, fouling at ‘‘B’’ is considerably worse and deposits created during this part of the operation may not be removed completely, even if the flow velocity is increased, later. Therefore, by specifying high fouling resistances, fouling may become a self-fulfilling prophecy. If part of the cooling water is recirculated, as shown in Fig. 14, the flow velocity and the cooling water inlet temperature can be increased to meet the required heat duty. The anticipated fouling (‘‘C’’) will be similar to the design value (‘‘A’’), but a price is to be paid to provide the higher flow velocity. Chemical Fouling Mitigation Methods Since about 1920, a number of companies have specialized in the mitigation of fouling and corrosion, mainly for the flow of cooling water and hydrocarbons. These companies have gained considerable expertise and have developed a wide range of additives and equipment. Services include the supply of chemicals as well as the analysis of cooling water, the evaluation of potential fouling and corrosion problems, and complete treatment programs including continuous monitoring of the system. In what follows in this subsection, only a small selection of methods to reduce fouling by chemical means is discussed. For the final selection of the treatment as well as for the dosage of treatment chemicals, specialists should be consulted. More details may be found in [49] provided by industrial fouling mitigation companies. Commercial antifoulants usually contain a number of components. These polyfunctional antifoulants are more versatile and effective since they can be designed to combat various types of fouling that can be present in any given system. Antifoulants are designed to prevent equipment surfaces from fouling, but they are not designed to clean up existing deposits. Therefore, antifoulant addition should be started immediately after equipment is cleaned. 4.2.1 Scale Formation In general, there are three alternatives available to mitigate or to prevent scale deposition due to high concentration of scaleforming ions in aqueous solutions: Removal of Scaling Species Scaling species may be removed by ion exchange and by chemical treatment. In the latter treatment, carbonic acid, and calcium hardness are removed by the addition of chemicals. If the lime treatment is used: CaðHCO3 Þ2 þ CaðOH Þ2 ! 2 CaCO3 þ 2H2 O CO2 þ CaðOH Þ2 ! CaCO3 þ H2 O ð10Þ ð11Þ During slow decarbonization (1–3 h reactor residence time), the calcium carbonate precipitates as silt, during fast decarbonization (5–10 min reactor residence time) it precipitates in the form of particles. With the exception of installations with high Fouling of Heat Exchanger Surfaces calcium hardness or large throughput, chemical removal of scaling species is not used anymore. Instead, ion exchangers are used in which the ‘‘harmful’’ scaling species in the fluid are replaced by ‘‘harmless’’ ions (for example Ca++ or Mg++ by Na+). Ion exchangers are usually manufactured from styrene based polymers. The so-called cationic exchangers contain weak and strong acids; the anionic exchangers contain weak and strong alkaline groups. With these two variations, all cations and anions can be removed from the fluid. Ion exchangers have to be regenerated regularly with the appropriate salt solution. According to [50], chemical decarbonization leaves a residual hardness of 17–30 ppm as CaCO3, ion exchange can reduce the hardness down to 2 ppm as CaCO3. Both methods of fluid treatment have high capital and operating costs. In the oil industry, desalters are installed at the beginning of the crude oil heat exchanger train to replace salty water, which may otherwise cause scale formation at higher temperatures. The solubility of scale-forming constituents increases with decreasing pH. Many treatment programs, therefore, involve the addition of acid (usually H2SO4) to the system to maintain a pH in the region of 6.5–7.5. If the system contains corrosion-resistant materials, a pH may be selected at which no scaling will occur. The Langelier Saturation Index or the Ryznar Stability Index [51] are commonly used to determine the value of pH to be adjusted. Scale Inhibitors Growth of crystals or the nucleation of crystals can be inhibited by the addition of scale inhibitors. Many proprietary compounds are available for scale control. Chelating agents (for example EDTA) complex strongly with the scaling cations and hence inhibit their deposition at the heat transfer surface. Inhibitor and scalant must be available in stoichiometric ratios. Processes, which are based on physical rather than on chemical reactions are those that stabilize supersaturated solutions by adsorption at the crystal nuclei (for example polyphosphates) or that modify or weaken the crystalline structure (for example polycarboxylic acid). Table 15, which has been adopted from Harris and Marshall [52], shows the ability of additives to C4. Table 15. Ability of various additives to maintain CaCO3 in solution [52] % Inhibition at dose level Additive maintain CaCO3 in solution. Lists of additives to reduce crystallization from hard waters have been compiled by Harris and Marshall [52] and by Krisher [53]. 4.2.2 2.5 ppm 5.0 ppm 7.5 ppm 10 ppm Polyphosphate 98% 98% 99% 100% Aminophosphonic acid 97% 96% 95% 94% Acetodiphosphonic acid 83% 82% 83% 90% Polyacrylate 30% 65% 84% 93% Polymaleic acid 26% 35% 44% 56% EDTA 15% 20% 20% 20% Particulate Fouling Particulate fouling is usually mitigated by the addition of surfactants or dispersants. If the surface tension is reduced, large particle agglomerates can break down into smaller particles, which tend less to sedimentation. Dispersants impart like charges to both the heat transfer surface and the particles and reduce deposition. For cooling water applications polyacrylates or polysulfonates are used with molecular weights between 2000 and 3000 g/mol. According to [53], the addition of polyphosphates to reduce scaling may cause a slight reduction of the dispersion of particulates. 4.2.3 pH Control C4 Chemical Reaction Fouling Chemical reaction fouling increases exponentially with increasing heat transfer surface temperature according to an Arrhenius term, see Eq. (4). As activation energies E are fairly high for chemical processes, even a modest reduction of the heat transfer surface temperature due to process or design modifications may already cause a considerable reduction of fouling. Particles suspended in the fluid (e.g., from upstream corrosion) can act as catalysts. Reaction fouling may be mitigated by removing these particles. Especially for oil refining processes a number of chemical additives to reduce reaction fouling have been developed. Most antifoulants have several functions. Generally they are oxygen scavengers, metal deactivators and dispersants [54]. For autoxidation-induced fouling, antioxidants can be added to consume oxygen or react with oxidation products in a way as to prevent the chain reaction of the autoxidation process, or metal deactivators are added to chelate metal ions thereby preventing their catalytic effect on the autoxidation process. Once insolubles form by either autoxidation or thermal decomposition, dispersants can be added to minimize agglomeration of small insoluble polymeric or coke-like particles into larger particles or deposit, or sticking of particles to the tube wall [55]. Antioxidants Even very small amounts of oxygen can cause or accelerate polymerization. Accordingly, antioxidant type antifoulants have been developed to prevent oxygen from initiating polymerization. Antioxidants act as chain-stoppers by forming inert molecules with the oxidized free radical hydrocarbons. Metal Deactivators Traces of metals are invariably present in hydrocarbon streams, which may catalyze polymerization reactions. For example transition metal ions, such as Cu, Fe, Zn, and Mn are powerful hydroperoxide decomposers and provide a steady source of free 95 96 C4 Fouling of Heat Exchanger Surfaces radicals for oxidation chain initiation. By complexing the metal ion, it can be prevented from participating. Thus chelating compounds are used as metal deactivators [55]. Dispersants Dispersants or stabilizers prevent insoluble polymers, coke, and other particulate matter from agglomerating into large particles which can settle out of the process stream and adhere to the metal surfaces of process equipment. They also modify the particle surface so that polymerization cannot readily take place. Dispersants generally play an important role in antifoulant programs. The feedstock or hydrocarbon stream may already contain polymerized materials which, if allowed to agglomerate, would deposit. In most applications it is not possible to fully eliminate oxygen- or metal-induced reactions and dispersants are necessary to prevent the polymerized materials from agglomerating and depositing on heat transfer surfaces [54, 56]. Dispersants are believed to function by absorbing on the surface of materials which are insoluble in the organic fluid and converting them to stable colloidal suspensions. They generally contain polar groups which absorb on the particle surface and nonpolar hydrocarbon-soluble groups to affect dispersion by their solubilization. Mayo et al. [57–62] argue that it is the solubilizing properties of dispersants which are most important in reducing deposit formation. Figure 15 shows the performance of the feed/effluent heat exchanger in an oil refinery with and without chemical treatment. 4.2.4 Biofouling The environment in cooling towers and cooling systems is particularly conducive to the growth of microorganisms in water and on surfaces of the system. Microorganisms attach and grow on surfaces, and produce polysaccharides, which increase the C4. Fig. 15. Reformer feed/effluent exchanger performance [63] stickability of suspended matter and hence promote further deposition. Biological growth is usually controlled by addition of biocides. In recent years, chlorine has most widely been used, which reacts with water to hydrochloric and hypochlorous acid: Cl2 þ H2 O ! HCl þ HOCl ð12Þ Hypochlorous acid is an extremely powerful oxidant that easily diffuses through the cellular walls of microorganisms. It is assumed [64–66] that HClO oxidizes the active sites of certain enzyme sulfhydryl groups, which constitute intermediate steps in the production of adenosine triphosphate (ATP). The system ATP-ADP allows conversion of carbohydrates and hence the energy supply for living organisms. Contrariwise to other, nonoxidizing biocides, chlorination also weakens the biofilm matrix allowing the removal of biofilms from the heat transfer surface by fluid shear forces. Continuous application of chlorine at concentrations between 0.1 and 0.5 ppm has shown to be a reliable but costly method to avoid deposition. Cheaper but less effective is a dosage of 1–10 ppm for 15 min in intervals of 4 h. However, it was found that biofilm growth is accelerated after a shock chlorination, see Fig. 16. Biological fouling control with chlorination has the disadvantage that chlorine has to be added continuously, since it does not only react with microbes but also with process contaminants such as H2S or NH3. Chlorine concentration in water exceeding 0.5 ppm may give rise to corrosion problems, especially for stainless steel equipment. Due to the biocidal action of chlorine, there are increasing restrictions on the effluent chlorine concentration. For these reasons, chlorine is increasingly replaced by other chemicals such as methylene-thiocyanate or chlorophenoles, see Waite and Fagan [68]. Even though the addition of hypochlorous acid provides an effective method against the growth of a wide range of bacteria and algae, there are a number of species that can only be controlled by excessively high HOCl concentrations (>30 ppm). Since this may cause operational problems, compounds have been developed to eliminate these species, which can be added to the chlorinated water. Grade and Thomas [69] discuss treatment programs, which are effective against bacteria and algae. Generally, it is recommended to C4. Fig. 16. Effect of shock chlorination on the growth of biological matter at heat transfer surfaces [67] Fouling of Heat Exchanger Surfaces vary biocide treatment regularly to avoid immunization of microorganisms. Because of the toxic effect of copper ions on biological matter, another method to reduce bacterial growth is the use of piping with a copper content above 60% or the addition of copper sulfate to the water. For potable water, the copper concentration must be below 1 ppm. 4.2.5 Corrosion Fouling Generally, it is desirable to have a thin, passivating oxide layer on the heat transfer pipes. Epstein [11] mentions that this oxide layer is removed if the flow velocity exceeds 30 m/s. Excessive corrosion can be controlled by the addition of corrosion inhibitors (chromate or polyphosphate based) or by control of the pH. Chromate is a highly efficient and cost effective inhibitor. However, the toxicity of chromates in the environment has restricted their use. This also holds for zinc based inhibitors. Under some circumstances, corrosion inhibitors (such as phosphates) themselves can be the source of fouling in heat exchangers as they increase the total salt content of the water. However, this can be mitigated by careful control of parameters such as inhibitor concentration, flow velocity and surface temperature [70]. 4.2.6 C4 slag. Magnesium oxide can minimize fouling of coal-fired boilers by acting as a catalytic inhibitor to retard the formation of SO3 and reacting to MgSO4 which is inert and has a high melting point. Often, the amount of MgO required, 0.4–3% of the fuel burned, makes the practice uneconomical. However, using fine, particle-size magnesia dispersions at rates of 0.005–0.015% (weight) of the fuel has reportedly reduced fouling. For oil-fired boilers, additives are used to control SO3 related problems, high temperature fouling, high temperature corrosion. 4.3 Mechanical Fouling Mitigation Methods A number of mechanical mitigation techniques have been developed which generally are based on one of the following mechanisms: (a) Short-time overheating of the heat transfer surfaces. The different thermal expansion of tubes and tube deposits may cause cracking of the deposit (b) Mechanical vibration of heat transfer surfaces (c) Acoustical vibration of heat transfer surfaces (d) Increased shear stress at fluid deposit interface. (e) Reduced adhesion of deposits Gas-Side Fouling [3] Removal of contaminants which promote fouling, such as sodium, sulfur, or vanadium, from fuels prior to combustion and contaminant removal from combustion gases are two approaches to mitigate gas-side fouling. Water washing has helped to overcome some of the fouling problems experienced with residual oils in marine applications by removing sodium and sediment. Inorganic sulfur can be removed from coal by gravity settling or by froth floatation if the mineral particles are well above micron size. Electrostatic precipitators, mechanical collectors, fabric filters or wet scrubbers can be used to remove particles from combustion gas streams. Removal of gaseous constituents, which is considerably more difficult than particle removal, may involve limestone addition, wet scrubbing without sulfur recovery, MgO systems with sulfur recovery or use of dry sorbent systems. Under certain conditions, chemical fuel additives or chemical flue gas additives can mitigate the effects of gas-side fouling and corrosion. Many proprietary additives have been marketed, with varying degrees of success in mitigating fouling. Fuel additives to improve combustion efficiency in boilers and to keep gas-side heat transfer surfaces clean by reducing soot and slag formation have been developed by companies such as Betz [71], Dearborn, Drew [72], and Nalco [73]. Additives that have been used to control gas-side fouling in boilers include aluminum oxide, ammonium bicarbonate, magnesium oxide, magnesium carbonate, silica, and zinc. For coal-fired boilers, additives are used for fly ash conditioning for electrostatic precipitation, convective tube fouling and coal-ash 4.3.1 Liquid Flow Most of the commonly used fouling mitigation techniques have been developed for the tube-side liquid in shell and tube heat exchangers. Even though attempts have been made to develop mechanical online mitigation devices for non-tubular heat exchangers, their installation has not penetrated the market. Reversal of Flow Direction Regular reversal of the flow direction in conjunction with a short-time increase of the flow velocity is sometimes used as a method to mitigate the formation of weak deposits. Figure 17 shows that this procedure reduces the fouling resistance, but C4. Fig. 17. Continuous cleaning by reversal of flow direction [74] 97 98 C4 Fouling of Heat Exchanger Surfaces only for a short period of time. A much better performance could be achieved by operating at a higher flow velocity. Gas Rumbling Deposits with moderate stickability to the heat transfer surfaces (e.g., particulate, and some biological deposits) can be dislocated and washed out by increasing the fluid shear forces for a short time, in regular time intervals. This can be achieved by increasing the flow velocity, if enough pump capacity is available. More effective is, however, to introduce compressed air or nitrogen into the liquid system. The resulting highly turbulent gas-liquid two-phase flow can provide shear forces and pressure fluctuations, which are substantially higher than for singlephase flow. Gas rumbling is commonly used in cooling water applications. efficiency is always accompanied by an increased pressure drop per unit length; therefore, these inserts work best for flow in the laminar or transitional flow regime. In combination with further reduction of flow velocity (i.e., tube passes) design variations may be possible where significant improvements of heat transfer can be achieved with no or little increase in pressure drop. Typical inserts are twisted tapes, coils (Fig. 18) and wire matrix inserts (Fig. 19). The potential of some of these inserts with respect to reducing deposit formation is reported in [49]. Figure 20 shows the effectiveness of the TURBOTAL system in reducing fouling in a crude oil preheater [77]. Ultrasound On the laboratory scale, some success has been achieved in removing/inhibiting deposits by ultrasonic vibrations. So far, however, technical limitations have prevented the extrapolation of these results into industrial practice. Tube Inserts Tube corrugations and tube inserts can increase the plain tube heat transfer coefficient by a factor of 2–15 [49]. This is achieved by reducing the average thermal boundary layer thickness. As deposition rates for most fouling mechanisms are inversely dependent on fluid wall shear stress and heat transfer surface temperature, reduction of the viscous and thermal sublayer thickness may also considerably reduce fouling. It must be considered that, for constant mass flux, the increased thermal C4. Fig. 20. Crude oil fouling mitigation with Turbotal inserts [77] C4. Fig. 21. Continuous cleaning with wire brush system C4. Fig. 18. Spiral insert (SPIRELF system) [75] C4. Fig. 19. Cal-Gavin wire insert to increase heat transfer for flow in pipes [76] C4. Fig. 22. Typical layout of sponge ball cleaning system [79] Fouling of Heat Exchanger Surfaces Continuous Transport of Cleaning Devices Through Tubes These methods require major modifications of the flow system and are, therefore, best implemented in the design stage. However, they have the advantage that exchangers may be kept clean over long periods of time. All systems work best if applied to an initially clean heat exchanger. A number of companies (MAN, Water Services of America, KALVO [78], ATCS) have developed continuous tube cleaning systems using small nylon brushes which are inserted into each tube, see Fig. 21. These brushes are pushed through the tubes by the fluid flow. For continuous operation and optimum cleaning efficiency, the flow direction has to be reversed about every 8 h. Life expectancy of the brushes is about 5 years. It is claimed that the time for amortization is between 8 and 16 months. There are many examples for the successful application of the brush tube cleaning system. However, their most effective installation is in smaller, water-cooled heat exchangers, for example, for the central air-conditioning systems of office buildings, hotels, or hospitals. For large installations, more consistent results were obtained with a system where sponge balls with a rough surface are circulated through the heat exchanger, see Fig. 22. The diameter of the sponge balls is slightly larger than the inside diameter of the tubes and the system is designed such that each tube sees a sponge ball every 5–10 minutes. Since the diameter of the sponge balls decreases with time and because of inevitable ball losses through the screening system, the sponge balls have to be replaced regularly. For hard and adherent deposits, carborundum coated sponge balls can be used. According to the manufacturers, application of sponge ball systems may reduce the fouling resistance to close to 0 m2K/kW. The application of sponge ball systems is limited to temperatures below 120 C. Several companies, for example, TAPROGGE or CQM supply sponge ball systems and complete maintenance packages with different levels of complexity, size, and cost. Online cleaning systems are not effective against stones, clamshells, etc. and need upstream devices to remove debris and macroscopic organic matter from the incoming water. 4.3.2 Gas Flow C4 dislodge and frequently require shutdown for their removal. Jet soot blowers come in two types: (i) The fixed position rotating type is installed inside the heat exchanger and (ii) the retractable type periodically passes an externally mounted nozzle through the heat exchanger. The fixed position soot blowers require little additional floor space, but they can usually not be used if the temperature exceeds 1000 C. As more than 100 soot blowers may be installed in large fired boilers, steam, and pressurized air consumption may cause considerable costs. ● According to the manufacturers, installation, and operation costs of sonic soot blowers are only 10% of those of jet soot blowers. Sonic soot blowers perform best in the cooler regions of furnaces or in other apparatus where glassy phases of deposits are not encountered. They operate by emitting sound pressure waves that loosen the particulates and allow them to be carried away with the gas stream. Under normal operations, sonic horns need only sound for 15–30 s every 10–30 min. Horns are constructed of materials that can withstand temperatures up to 1000 C. Sonic soot blowers may not, however, be able to loosen the harder deposits that can be removed by the high velocity steam, air or water jets. Sonic soot blowers are available at sonic or infrasonic range. For very sticky deposits or if jet soot blowing may cause the temperature to drop below the acid dew point, 5 mm diameter cast iron spheres may be poured over the pipe arrangement. For extremely severe gas-side fouling problems, fluidized bed technology should be considered as an alternative. The control of operating conditions is a very important consideration in the prevention of gas-side fouling. Some of the most important controls are: ● Maintain surface temperature above acid dew-point temperature ● Control amount of excess air, which governs the conversion of SO2 to SO3 and hence the amount of H2SO4 formed ● Control combustion parameters such as fuel injection pattern, fuel injection schedule and fuel viscosity ● Use fuel/air premixing to eliminate soot production ● Quench hot flue gases to solidify molten and soft particles to prevent attachment at cooler heat transfer surfaces The control of combustion conditions is a difficult task due to the great variability in the quality of fuel supplies. Variability of fuel characteristics is a particular problem for those industries that burn waste products. Online mechanical techniques vary greatly, but soot blowers are the most popular for gas-side use [80]. Some of other techniques such as scrapers, rappers, and chains work well in special applications but are not as readily available. Two common types of soot blowers are jet soot blowers and sonic soot blowers. 4.3.3 ● The jet type of soot blower operates by emitting pulses of steam, air or water at programmed intervals directed at the tubes and/or down tube lanes to dislodge the deposits and re-entrain them in the gas stream. These soot blowers work best if used frequently, thus avoiding the build-up of material. When build-up occurs, it insulates the surface from the coolant, allowing a temperature rise that can produce a glassy deposit. Glassy deposits are much harder to When it comes to commercial mitigation of scale formation, one of the most frequently and emotionally discussed topics are devices, which claim to reduce scaling by magnetic, electronic, or catalytic means. To-date, no conclusive scientific proof or theory for the mechanisms, which may be responsible for the beneficial effects of such technologies, has been found. A considerable number of investigations have been reported in the literature; many of them claim some sort of success with the Other Devices for Fouling Mitigation 99 100 C4 Fouling of Heat Exchanger Surfaces applied technology. Most of the research-related literature originates from the former Soviet Union, the UK and the USA, while several systematic investigations have been performed by public and private organizations in Austria, Germany, and Switzerland. German Industry Standards (DIN) have been formulated for performance evaluation of physical water conditioners. Pilot plant and laboratory scale investigations have provided contradicting results. For example, [81, 82] report that the installation of magnets considerably reduced cooling water fouling, whereas [83, 84] found no effect of the water conditioner. Even the mechanisms of scale inhibition are highly disputed. There are claims that clatherate formation or impact on the nuclear spin of dissolved ions will reduce the chemical reaction on the surface; or that very high frequency current favors bulk precipitation of scale-forming materials and hence weakly adhering particulate deposit rather than a strong crystalline layer. Other investigators believe that minute changes in local pH may affect the CaCO3 equilibrium in the solution. More recently, claims have been made that the key mechanism is the release of iron ions or iron oxide into the water, which has an adverse effect on the growth behavior of crystals. Another plausible explanation is that the electrical field, together with dissolved impurities, changes the crystal form of CaCO3 from Calcite to Aragonite. Some agreement exists that magnetic or electromagnetic fields are effective for a relatively narrow range of flow velocities only [85]. Manufacturers of such equipment have impressive reference lists of successful installations, where the formation of crystalline deposits has been substantially reduced or even avoided. However, it is also fair to say that there have been numerous cases where no improvement has been achieved. Until the applications and limitations of these installations have been clearly established, no general statement can be made about their economic evaluation with respect to other available scale prevention methods. While most suppliers of physical water treatment facilities recommend installation of their devices at a relatively short distance upstream of the heat exchanger which is to be protected, others claim ‘‘memory effects’’ in the fluid of up to 6 months. 5 Cleaning of Heat Exchangers Periodical cleaning of heat exchangers will be necessary, even if the heat exchanger is well-designed and the fluid treatment is effective. Additionally, conditions in the heat exchanger may deviate from the design conditions due to changes in flow rates and temperatures, plant failures, ingress of air and bacteria, changes in the fluid composition or upstream corrosion, which all may promote fouling. If a heat exchanger or pipeline suffers from deposit formation, this can be the start of a whole series of problems. Corrosion processes may take place under the deposit, fouling rates may be increased due to the surface roughness of the deposit or irregular behavior of the exchanger may be observed due to build-up and removal of deposits. It is, therefore, advantageous to remove non-protective deposits soon after the onset of their formation. Heat exchangers may be cleaned by chemical or mechanical methods or by a combination of both. 5.1 Chemical Cleaning Methods Chemical cleaning methods have a number of advantages over mechanical methods, namely: (a) (b) (c) (d) (e) They are relatively quick. Surfaces do not experience mechanical damage. Chemical solutions reach normally inaccessible areas. They are less labor intensive than mechanical cleaning. Cleaning can be performed in situ. 5.1.1 The Basic Process Most chemical cleans consist of five distinct processes, each being monitored for results before proceeding to the next. The five stages are: 1. The alkaline clean primarily aims to remove the organic portion of the deposit (oil, fat) in order to render the inorganic surface hydrophilic. This is necessary to make the following acid cleaning effective. 2. Before and after each chemical step, high flow water flushes are required to physically remove loose or softened material. 3. Once the surface is hydrophilic, the deposit is softened and/ or dissolved by application of the appropriate acid blend. This blend usually contains an inhibitor, which prevents corrosion of the base metal by the acid. The analysis of the spent acid strength and the concentration of dissolved scale species indicate whether the acid clean is completed. 4. After the acid stage, water rinsing is required to remove loose debris, sludge, and residual acid. Water rinsing may be accompanied by inert gas purging and sequestrant addition, depending on the cleaning technique and the plant configuration. 5. After the acid and rinse stages, the base metal which has been exposed as a result of the cleaning operation is in a very active state. If left and exposed to the atmosphere, the surface would rapidly reoxidize in an uncontrolled fashion. A passivation process is performed to form a tightly adherent, protective oxide film on the base metal. Particular applications may require modifications of the above sequence. The selection of the cleaning agent and the cleaning procedure strongly depend on the type of deposit, the material and configuration of the installation and on economical and environmental considerations. 5.1.2 Cleaning Procedure Among the many possible choices available for cleaning procedures are ambient temperature treatments, high temperature treatments, fill-and-soak techniques, circulating techniques, onstream techniques, vapor phase techniques, foam techniques and emulsion techniques. Soaking treatments are effective in many instances. Their application generally reduces equipment costs while increasing chemical costs and downtime costs. C4 Fouling of Heat Exchanger Surfaces Obviously, it is advantageous to circulate the cleaning agent in order to improve evenly mixing of the chemicals and to reduce concentration profiles near the fouled surfaces. Circulation also increases physical disintegration of the deposit by mechanical scouring. As chemical reaction rates increase exponentially with temperature, the cleaning process may be improved if the cleaning agent is heated. Foaming reduces the cleaning agent requirements and increases the effectiveness of cleaning. Also, the foaming treatment may be faster in some cases. It allows for good contact in large shell and tube heat exchanger. Research on the mechanisms of chemical cleaning of heat transfer surfaces is far less developed than research of fouling mechanisms. Nevertheless, some first modelling has been attempted, assuming that the cleaning process is an inverse fouling process. 5.1.3 Cleaning Agents Table 16 shows typical deposits that can be removed chemically [86]. Deposits that can not be removed are given in Table 17. Table 18 lists a number of chemicals used for cleaning. Sulfuric acid and hydrochloric acid are the most widely used chemical cleaning agents. When used properly, they are safe, relatively low-cost materials. However, these mineral acids are highly ionized and strong, which may cause rapid corrosion if the solution is insufficiently inhibited. Therefore, weaker organic acids and chelating agents are coming into wider use. Generally, a mixture of several chemicals is used to attack complex deposits. Dispersants are added to disperse oils or fats and to allow better penetration of the deposit. Sometimes, the addition of small quantities of a second cleaning agent (e.g., the addition of 0.25% ammonium bifluoride or 0.5% sodium bromate to citric solutions) may considerably increase the effectiveness of the cleanup [87]. The type of cleaning agent to be chosen has a major effect on the economics of the cleaning job. The selection of cleaning chemicals is not only depending on the type of deposit, but also on the exchanger material and the cleaning conditions. In many cases, chemical cleaning of heat exchangers involves the use of C4. Table 16. Typical deposits removed by chemical cleaning [86] Organic Oil, grease, fat, waxes, soft carbon, tars, silt, vegetation, biological matter, polymers, resins, paints Inorganic Rust, magnetite, calcium carbonate, calcium sulfate, magnesium hydroxide, calcium phosphate, silica, magnesium silicate, copper, copper oxides, alumina, nickel oxides C4. Table 17. Intractable deposits [86] Glasses, ceramics, hard carbon, inert plastics, vulcanized rubber, rubber latex acids. Although some metal loss is inevitable, the addition of inhibitors greatly reduces corrosion. It must be emphasized that inhibitors are only suitable for specific metal under specific conditions. Personal danger and disposal problems have to be C4. Table 18. Common types of chemicals utilized for in-situ chemical cleaning [87] Acids Alkalis Complexing agents Hydrochloric Caustic Soda EDTA Nitric Ammonia Gluconates Sulfuric Trisodium phosphate Hydrofluoric Sodium metasilicate Citric Soda ash Formic Sulphamic Oxidants Solvents Others Potassium permangangate Aromatic Biocides Sodium bromate Aliphatic Surfactants Sodium nitrite Chlorinated Inhibitors Sodium hypochlorite Emulsifiers Antifoams Ammonium persulfate Dewatering formulations Dispersants Hydrazine bifluoride C4. Table 19. Scale and deposit removal [87] Deposit Cleaning method Calcium sulfate Boil with Na2CO3 solution, treat with inhibited acid Calcium carbonate Inhibited acid Magnesium hydroxide Inhibited acid Calcium Inhibited acid phosphate sludge Magnesium silicate Inhibited acid + small % of HF Sodium Hydrofluoric acid aluminum silicate Ferric oxide (Fe2O3) Inhibited acid or ammoniated citric acid Ferrous oxide (Fe3O4) Inhibited acid or ammoniated citric acid. Add 0.25–0.5% stannous chloride for protection against ferric ion attack. Ammoniated EDTA Copper Ammoniated bromate, ammoniated EDTA Organic material High velocity liquids or circulate 20% chromic acid heated to 95 C. Hot alkaline solutions useful for removing light oils, grease, or other sludge materials 101 102 C4 Fouling of Heat Exchanger Surfaces considered, too. Table 19 shows some deposits and scales with the recommended cleaning agents [87]. For plants in operation, the timing of cleaning operations is of economical importance. Energy losses, production losses and safety aspects have to be compared with cleaning costs and losses due to shutdown. Table 20 shows typical application of some of the most common cleaning agents. C4. Table 20. Chemical cleaning agents [87] Agent Application Hydrochloric acid General removal of rust and scale for non-stainless steel piping Inhibited HCL Same as above Sulfuric acid General usage for stainless steel for removal of rust and scale. H2SO4 is dangerous to personnel and must be used with caution Inhibited H2SO4 Same as above Hydroxyacetic acid General acidizing. Safer than H2SO4 Formic acid Often used as 1% formic, 2% hydroxy-acetic acid solution for cleaning of supercritical ‘‘oncethrough’’ boilers where stainless steel is the prevalent material of construction and chloride ions must be avoided. Also used for non-ferrous metals as a 1–2% solution. Must be heated to 95 C. Safter than mineral acids Citric acid Used as 0.01 solution to chelate iron. Used at ambient temperature or slightly warm Ammoniated citric acid Very safe (corrosion and handling) cleaning agent. By changing pH and adding sodium nitrite, the same solution. may be used for passivation. pH is adjusted by adding NH3 and resulting solution is effective for copper removal Hydrofluoric acid Used for new piping and for stainless steel where chloride ions are critical as a 3–5% solution. Also used for silica deposit removal. Dangerous! Sulphamic acid Fairly safe. Used at a 5–10% solution for removal of iron oxides. Must be maintained below 60 C or decomposes to ammonium bisulfate Ammoniated bromate Use for removal of copper. Does not attack scale or iron oxides. For each kg of copper use 0.9 kg NaBrO3 1.4 kg (NH4)2CO3 4.5 l NH4OH 30% 5.1.4 OnStream Chemical Cleaning In most cases, chemical cleaning is done while the heat exchanger is off-line. However, there have been several attempts to develop chemicals that can be used for onstream cleaning to avoid expensive plant shutdown. Examples for these chemicals are complexing agents which can be added during operation of boilers. Shock dosage of chlorine (>15 ppm) is often used to remove bio-deposits while the exchanger is onstream. However, it was found that biofilms regrow at an accelerated rate after the chlorine dosage. As chlorination has come under increasing regulatory control, methods to use chlorine more efficiently and to minimize the amount of chlorine discharged to the water ways become increasingly important. 5.1.5 Problems Associated with Chemical Cleaning Problems associated with chemical cleaning of heat exchangers are due to the danger of handling (burn, toxic), due to elevated application temperatures, due to the costs of cleaning agents, due to the chemical attack on the heat exchanger material (overcleaning, uneven cleaning, corrosion) and due to disposal problems. Acids and alkalis must be neutralized, organic materials may be burned and fluorides must be reacted to inactive solid residues. Some of the organic acids, such as citric acid and gluconic acid are biodegradable. 5.2 Mechanical Cleaning Methods For the following cleaning methods, heat exchangers have to be taken off-line and dismantled. Some of the deposits may then be removed manually, for example from the water box. Steamblasting and hydro-blasting with pressures up to 1500 bar are probably the most common mechanical cleaning methods, see [49]. They can be performed completely manually or semiautomatically in cleaning stations. If deposits are very tenacious, sand can be added to the pressurized water to increase the cleaning efficiency. Both, steam- and hydro-blasting are labor intensive and keep the exchanger off-line for a considerable time. Blasting may not completely eliminate all deposits and some significant roughness can remain. The shell-side of tube bundles can only be cleaned completely if the tubes are arranged in-line. The particular geometry of twisted tubes provides flow lanes for pressurized water or steam which facilitates cleaning. Experienced maintenance crews are required and strict safety regulations must be obeyed due to the danger of handling equipment at very high pressures. Phosphoric acid Less aggressive than sulfuric acid and more aggressive than sulphamic acid. Use for general removal of oxides and scales, particularly for stainless steel Ammoniated EDTA Use for removal of iron oxides or copper, as a 5–10% solution. Safe material! Sodium salt Use for removal of water hardness scales as a 5–10% solution C4. Fig. 23. CONCO cleaning device [89] Fouling of Heat Exchanger Surfaces While blasting is the only available alternative for the shellside of the tube bundle, several cleaning methods can be used for the inside of straight tubes. The continuous cleaning sponge ball system described in detail in Sect. 4.3 can also be used as a transportable, off-line cleaning system, particularly if used with corundum-coated sponge balls. Very dirty and plugged tubes can be cleaned with drills equipped with drill bits, brushes, or bit-brush combinations. To avoid damage of the heat transfer surfaces, cleaning must be done carefully, thus increasing costs for labor and downtime. Using air- or hydropressure, rubber plugs or metal scrapers can be shot through the tubes. These techniques are considerably faster than the above methods, cleaning up to 15,000 tubes in 24 h. Rubber plugs fail for hard deposits. Shooting metal scrapers through the tubes at a water pressure of 35 bar and a scraper velocity of 3–6 m/s results in the removal of most deposits [88]. An example of those scrapers is shown in Fig. 23. In general, water pressure systems are safer than air pressure systems, due to the compressibility and subsequent rapid expansion of gases. Most mechanical cleaning methods remove not only the deposit but also the protective oxide layer. Under certain circumstances, this may create a corrosion problem. On the other hand, regular cleaning removes deposit and avoids flow conditions, which promote corrosion due to chemical reaction or stagnant flow. For very severe fouling problems, a combination of chemical and mechanical cleaning may be recommended. 6 CF E K R Re Rf s u tw x 1,2 Symbols Cleanliness factor Activation energy (J/mol) Constant Universal Gas Constant, 8.314 J/(mol K) Reynolds Number Fouling resistance (m2K/W) Deposit thickness (m) Flow velocity (m/s) Wall shear stress (N/m2) Friction factor Fluid 1, fluid 2 Subscript/Superscripts c Clean d Deposit f Fouled 7 Bibliography 1. Steinhagen R, Müller-Steinhagen HM, Maani K (1993) Fouling problems and fouling costs in New Zealand industries. Heat Transfer Eng 14(1):19–30 2. Steinhagen R, Müller-Steinhagen HM, MaaniK (1990) Heat exchanger applications, fouling problems and fouling costs in New Zealand Industries. Ministry of Commerce Report RD8829 1–116 3. Garrett-Price BA, et al. (1985) Fouling of heat exchangers – characteristics, costs, prevention, control and removal. Noyes Publications, Park Ridge, New Jersey C4 4. 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Wilfried Roetzel Helmut-Schmidt-Universität, Universität der Bundeswehr Hamburg, Hamburg, Germany 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3 2 Temperature Calculation of Heat Exchanger Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Temperature Calculation of a Single Heat Exchanger. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Temperature Calculation of Heat Exchanger Networks with Sequential Flow Arrangements . . . . . . 106 Temperature Calculation of General Heat Exchanger Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.1 3.2 3.3 Synthesis of Heat Exchanger Networks with the Pinch Design Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 The Problem Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 The Composite Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Pinch Design Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 2.1 2.2 2.3 1 Introduction Many process industries are energy-intensive. A large amount of heat energy applied to process streams is normally dissipated through cooling utilities. It is possible to reuse the heat energy of hot process streams for heating cold process streams by means of additional heat exchangers. Such a system is called heat recovery system. The heat recovery system consists of a set of heat exchangers including heaters, coolers, condensers, reboilers, or other equipment and attachments for heat transfer between process streams. It can be treated as a heat exchanger network with different kinds of exchangers in which hot process streams can be cooled by the cold streams to be heated, and vice versa. In this way, the heating and cooling loads from external sources (hot and cold utilities) can be dramatically reduced. However, the reduction in utility costs is often accompanied by the increase in investment costs. Therefore, a balance between utility costs and investment costs should be established. The optimal design of a heat exchanger network is to structure a system capable of performing the prescribed tasks at the minimum total annual costs, which is the sum of the utility costs and investment costs [1]. Because of its structural characteristics, it is also named the synthesis of heat exchanger networks. A further extension of the network synthesis is the optimal retrofit design of existing networks. Principally, the methodologies of optimal design of heat exchanger networks do not focus on the determination of detailed parameters of heat exchangers of a network. It takes the network as a system and determines the network configuration and heat loads of the exchangers used in the network for the further detailed unit design. The well-known synthesis methodologies are the Pinch design method [2], mathematical programming [3], and stochastic or heuristic algorithms such as genetic algorithm [4], simulated annealing algorithm [5] and Tabu search procedure [6]. The genetic algorithm was also combined with simulated annealing algorithm for the synthesis of multistream VDI-GVC (ed.), VDI Heat Atlas, DOI 10.1007/978-3-540-77877-6_8, # Springer-Verlag Berlin Heidelberg 2010 heat exchanger networks [7, 8]. This chapter introduces only the fundamental theories of the design of heat exchanger networks. 2 Temperature Calculation of Heat Exchanger Networks 2.1 Temperature Calculation of a Single Heat Exchanger For a single heat exchanger, the heat load can be determined by _ p Þc ð#00c #0c Þ ¼ FkAD#LM ð1Þ _ p Þh ð#0h #00h Þ ¼ ðMc Q_ ¼ ðMc where the subscripts ‘‘h’’ and ‘‘c’’ denote hot stream and cold stream, #0 and #00 are inlet and outlet temperatures, k is the _ the overall heat transfer coefficient, A the heat transfer area, M mass flow rate, and cp the specific heat capacity at constant _ p Þ is also named heat capacity pressure. The product term ðMc flow rate. The correction factor F is the ratio of the real mean temperature difference to the logarithmic mean temperature difference of the counterflow heat exchanger D#LM (see also > Chap. C1), D#LM ¼ ð#0h #00c Þ ð#00h #0c Þ ln½ð#0h #00c Þ=ð#00h #0c Þ ð2Þ If ð#0h #00c Þ ð#00h #0c Þ, the arithmetic mean can be used, 1 D#LM ½ð#0h #00c Þ þ ð#00h #0c Þ 2 ð3Þ Equation (1) is used to determine the exchanger size according to known stream temperatures. In > Chap. C1 the two flow streams are denoted with indexes ‘‘1’’ and ‘‘2,’’ as defined for the channels of each flow arrangement. For heat exchanger networks the notations ‘‘h’’ and ‘‘c’’ is more appropriate. 106 C5 Heat Exchanger Networks For an existing heat exchanger, the outlet stream temperatures are given by 00 vhh vhc #0h #h ¼ ð4Þ vch vcc #00c #0c If the parameters appearing in the above equations depend on temperature, they can be modified with newly calculated outlet stream temperatures. The procedure will be repeated until the iteration deviation is less than the required accuracy. or in the matrix form 2.2 00 0 Y ¼ VY 0 Temperature Calculation of Heat Exchanger Networks with Sequential Flow Arrangements ð5Þ 00 in which Y and Y are the inlet and outlet temperature vectors of the exchanger, respectively, and 2 3 NTU ð1Rh Þ NTU ð1Rh Þ h ð1Rh Þe h 1e NTU ð1Rh Þ NTU ð1Rh Þ v v 6 7 V ¼ hh hc ¼ 4 1Rh eNTUh ð1Rh Þ 1Rh e h 5 ð6Þ h vch vcc Rh ½1e 1Rh 1Rh e NTU ð1Rh Þ h 1Rh e NTU ð1Rh Þ h _ p Þh ðMc _ p Þc Rh ¼ 1=Rc ¼ ðMc _ p Þh NTUh ¼ Rc NTUc ¼ FkA ðMc Special cases: ð7Þ ð8Þ e NTUh 1 e NTUh Rh ! 0 : V ¼ 0 1 1 0 Rh ! 1 : V ¼ 1 e NTUc e NTUc 1 0 ðFkAÞ ! 0 : V ¼ 0 1 ð9Þ ð10Þ ð11Þ For sequential flow arrangements the stream temperatures can be calculated from their entry positions. One of such arrangements is shown in Fig. 1, in which each cross-point of hot and cold streams indicates a possible heat exchanger. Hot streams are to be cooled down and cold streams are to be heated up. The hot and cold streams Hi and Ci ði ¼ 1; 2; 3; Þ are arranged according to the network structure to be calculated. Usually they are arranged in the order of their supply temperatures, beginning with the highest temperatures. The calculation begins from the upper left exchanger and the calculated outlet stream temperatures of an exchanger become the inlet stream temperatures of the following exchangers. Thus, Eq. (4) can be applied to the exchangers sequentially, and the exit stream temperatures of the network can be finally obtained. Example 1 This example was taken from the network design given by Ravagnani et al. [9]. The original problem data is listed in Table 1. The network design given by Ravagnani et al. [9] is shown in Fig. 2, where the data in brackets are the heat capacity flow rates in the branches. Its sequential relation is illustrated in Fig. 3. The calculation begins from EX4. _ p Þh ðMc _ p Þc ¼ 33:33=20 ¼ 1:6665 EX4: Rh ¼ ðMc k ¼ ð1=ah þ 1=ac Þ1 ¼ ð1=1:333 þ 1=0:917Þ1 ¼ 0:54327 kW=m2 K _ p Þh ¼ 1 0:54327 202:23=33:33 ¼ 3:2963 NTUh ¼ FkA ðMc ð1 Rh Þe NTUh ð1Rh Þ ð1 1:6665Þ e 3:2963ð11:6665Þ ¼ 1 1:6665 e 3:2963ð11:6665Þ 1 Rh e NTUh ð1Rh Þ ¼ 0:42852 vhh ¼ vhc ¼ 1 vhh ¼ 1 0:42852 ¼ 0:57148 1 Rh 1 1:6665 vcc ¼ ¼ 1 Rh e NTUh ð1Rh Þ 1 1:6665 e 3:2963ð11:6665Þ ¼ 0:04762 C5. Fig. 1. Heat exchanger network with sequential flow arrangement. vch ¼ 1 vcc ¼ 1 0:04762 ¼ 0:95238 C5. Table 1. Problem data [9] q0 ( C) q00 ( C) _ cp ðkW=KÞ M aðkW=m2 KÞ H1 175 45 10 2.615 H2 125 65 40 1.333 C1 20 155 20 0.917 Stream C2 Steam Cooling water 0.57 Heat exchanger cost = 1,200 A Cost ($/kW year) 40 112 15 0.166 180 179 5.000 110 15 25 2.500 10 $/year (A in m ). Correction factor F ¼ 1 for all heat exchangers including heaters and coolers. 2 Heat Exchanger Networks C5 C5. Fig. 2. A network design given by Ravagnani et al. [9], 117,069 $/year. 2.3 In general cases the heat exchanger networks might have loops and the inlet stream temperatures of some exchangers might be unknown. An easy way is the use of iteration method. However, for complex networks the convergence of the iteration method might not be ensured. An alternative solution is the matrix method [10, 11]. Consider a heat exchanger network with N 0 stream entrances, N 00 stream exits and NEX heat exchangers. Each exchanger has two channels: the hot stream channel and the cold stream channel; therefore, the number of channels N ¼ 2NEX . The channel indexes are related to the exchanger indexes, i.e., the index of the hot stream in the ith exchanger is 2i 1, and that of the cold stream is 2i. The indexes of the network entrances and network exits can be arbitrarily labeled. Extending Eq. (5) to the whole network yields, C5. Fig. 3. Heat exchanger network with the sequential flow arrangement. Temperature Calculation of General Heat Exchanger Networks Y00EX ¼ VY0EX 64:99 0:42852 0:57148 125 #00h ¼ ¼ 120:0 20 0:95238 0:04762 #00c in which, 2 The outlet stream temperatures of other exchangers can be obtained with the same method and the results are listed in Table 2. The heating and cooling loads and heat transfer areas of the heater HU1 and cooler CU1 are calculated by Eq. (1). _ p Þ ð#0h #00h Þ ¼ 10 ð57:02 45Þ ¼ 120:2 kW CU1: Q_ ¼ ðMc h ð#0h #00c Þ ð#00h #0c Þ ð57:02 25Þ ð45 15Þ D#LM ¼ ¼ ln½ð#0h #00c Þ=ð#00h #0c Þ ln½ð57:02 25Þ=ð45 15Þ ¼ 31:00 C 1 1 2 k ¼ ð1=ah þ 1=ac Þ ¼ ð1=2:615 þ 1=2:5Þ ¼ 1:2781 kW=m K 2 _ A ¼ Q=ðkFD# LM Þ ¼ 120:2=ð1:2781 1 31:00Þ ¼ 3:034 m _ p Þc ð#00c #0c Þ ¼ 20 ð155 145Þ ¼ 200 kW HU1 :Q_ ¼ ðMc ð180 155Þ ð179 145Þ D#LM ¼ ¼ 29:27 C ln½ð180 155Þ=ð179 145Þ k ¼ ð1=5 þ 1=0:917Þ1 ¼ 0:7749 kW=m2 K A ¼ 200=ð0:7749 1 29:27Þ ¼ 8:818 m2 ð12Þ 6 V¼4 Vi ¼ vhh;i vhc;i vch;i vcc;i 2 6 ¼4 V1 .. 0 . 0 7 5 ð13Þ VNEX NTU ð1Ri Þ i ð1Ri Þe NTU ð1Ri Þ i 1Ri e NTU ð1Ri Þ i Ri ½1e NTU ð1Ri Þ i 1Ri e ði ¼ 1; 2; ; NEX Þ _ p Þh;i ðMc ðFkAÞi ; NTUi ¼ Ri ¼ _ p Þc;i _ p Þh;i ðMc ðMc 3 NTU ð1R Þ 3 i i 1e NTU ð1Ri Þ i 1Ri e 7 1Ri 5 NTU ð1Ri Þ i 1Ri e ð14Þ ði ¼ 1; 2; ; NEX Þ ð15Þ Y0EX and Y00EX are the temperature vectors containing the inlet and outlet stream temperatures of NEX exchangers, respectively, h iT Y0EX ¼ #0h;1 ; #0c;1 ; #0h;2 ; #0c;2 ; ; #0h;NEX ; #0c;NEX ð16Þ 107 108 C5 Heat Exchanger Networks h iT Y00EX ¼ #00h;1 ; #00c;1 ; #00h;2 ; #00c;2 ; ; #00h;NEX ; #00c;NEX ð17Þ To illustrate the interconnections among the streams, the following four matching matrices need to be introduced [12]: Interconnection matrix G: N N matrix whose elements gij are defined as the ratio of the heat capacity flow rate flowing from channel j into channel i to that flowing through channel i. Entrance matching matrix G0 : N N 0 matrix whose elements gik0 are defined as the ratio of the heat capacity flow rate flowing from the entrance k to channel i to that flowing through channel i. Exit matching matrix G00 : N 00 N matrix whose elements gli00 are defined as the ratio of the heat capacity flow rate flowing from channel i to the exit l to that flowing out of exit l. Bypass matrix G000 : N 00 N 0 matrix whose elements glk000 are defined as the ratio of the heat capacity flow rate flowing from entrance k to exit l to that flowing out of exit l. In a heat exchanger network, there might be such a knot at which the streams mix and split again, which can be defined as a mixer. If there is a mixer before channel i or exit l, then, in the above definitions of the matrices, the denominator should be the heat capacity flow rate flowing through the mixer. By the use of the aforementioned matrices, the stream temperatures in the network can be obtained by Y0EX ¼ ðI GVÞ1 G0 Y0N Y00N ¼ ð18Þ Y00EX ¼ VY0EX ¼ VðI GVÞ1 G0 Y0N G000 Y0N þ G00 Y00EX ¼ ½G000 þ G00 VðI GVÞ1 G0 Y0N in which I is the unit matrix, Y0N and Y00N are two vectors containing the stream temperatures at the network entrances and exits before entering the external heaters and coolers. A more complicated problem is the temperature calculation of multistream heat exchangers and their networks. For general cases a numerical procedure should be adopted. However, if the stream arrangement in a multistream heat exchanger is onedimensional, e.g., parallel flow and counterflow, an analytical solution of the stream temperatures can be obtained [13]. Example 2 The network shown in Fig. 4 is the optimal solution of the design problem given by Table 1. The indexes of channels, entrances, and exits are labeled in Fig. 4. The entrance temperature vector is Y0N ¼ ½175 125 20 40T . For EX1, EX1: R1 ¼ _ p ÞH1 10 ðMc ¼ ¼ 0:5 _ p ÞC1 20 ðMc k1 ¼ ð1=aH1 þ 1=aC1 Þ1 ¼ ð1=2:615 þ 1=0:917Þ1 ¼ 0:6789 kW=m2 K NTU1 ¼ ðFkAÞ1 1 0:6789 51:65 ¼ ¼ 3:5066 _ p ÞH1 10 ðMc ð1 R1 Þe NTU1 ð1R1 Þ 1 R1 e NTU1 ð1R1 Þ ð1 0:5Þ exp½3:5066 ð1 0:5Þ ¼ ¼ 0:09481 1 0:5 exp½3:5066 ð1 0:5Þ vhc;1 ¼ 1 vhh;1 ¼ 1 0:09481 ¼ 0:90519 vhh;1 ¼ ð19Þ ð20Þ C5. Table 2. Calculation results of example 1 qh0 ( C) qc0 ( C) A (m2) Rh NTU*h q00h ( C) q00c ( C) EX4 125 20 202.23 1.6665 3.2963 64.99 120.00 EX3 125 40 147.81 EX1 175 120.00 52.78 1.2003 3.2713 65.00 112.02 0.5000 3.5834 125.00 145.00 EX2 125.00 40 #0h ( C) #00h ( C) 291.74 1.0590 #00c ( C) 4.5538 Q_ (kW) 57.02 #0c ( C) D#LM ( C) A (m2) CU1 57.02 45 15 25 120.2 31.00 3.034 HU1 180 179 145 155 200 29.27 8.818 C5. Fig. 4. Optimal design of heat exchanger network, 108,072 $/year. 111.99 Heat Exchanger Networks 1 R1 1 0:5 ¼ 1 R1 e NTU1 ð1R1 Þ 1 0:5 exp½3:5066 ð1 0:5Þ ¼ 0:54740 vcc;1 ¼ vch;1 ¼ 1 vcc;1 ¼ 1 0:54740 ¼ 0:45260 The calculations for EX2, EX3, and EX4 are similar, which yields, 2 0:09481 6 6 0:45260 6 6 6 0 6 6 6 0 V¼6 6 6 0 6 6 0 6 6 6 0 4 0 0:90519 0 0 0 0 0 0 0 0 0 0:96465 0:03535 0 0 0 0 0 0 0:38690 0 0 0 0 0 0:84706 0:15294 0 0 0 0 0 0 0:33214 0:66786 0 0 0 0 0:95847 0:04153 0 0 0 0 0 0 0:34782 0:65218 0 According to the stream arrangement and channel indexes shown in Fig. 4, the matching matrices are 2 3 0 0 0 0 0 0 0 0 6 0 0 0 6:968=20 0 13:032=20 0 0 7 6 7 61 0 0 0 0 0 0 07 6 7 60 0 0 0 0 0 0 07 7 G¼6 60 0 0 0 0 0 0 07 6 7 60 0 0 0 0 0 0 07 6 7 40 0 0 0 0 0 0 05 0 0 0 0 0 0 0 0 2 3 1 0 0 0 60 0 0 07 6 7 60 0 0 07 6 7 60 0 1 07 7 G0 ¼ 6 60 1 0 07 6 7 60 0 1 07 6 7 40 1 0 05 0 0 0 1 2 3 0 0 1 0 0 0 0 0 6 0 0 0 0 19:276=40 0 20:724=40 0 7 7 G00 ¼ 6 40 1 0 0 0 0 0 05 0 0 0 0 0 0 0 1 G000 ¼ 0 The calculation of Eqs. (18–20) yields, 2 3 2 3 175:00 126:69 6 121:63 7 6 145:78 7 6 7 6 7 2 3 6 126:69 7 6 55:43 7 55:43 6 7 6 7 6 20:00 7 00 6 122:26 7 00 6 65:00 7 7 6 7 6 7 Y0EX ¼ 6 6 125:00 7; YEX ¼ 6 56:52 7; YN ¼ 4 145:78 5 6 7 6 7 6 20:00 7 6 121:29 7 112:00 6 7 6 7 4 125:00 5 4 72:89 5 40:00 112:00 The matrix calculation can also be performed with Microsoft Excel# by the use of matrix multiplication function MMULT and matrix inverse function MINVERSE. The calculation of hot and cold utilities depends on the calculated exit stream temperatures of the network Y00N and their target values Y00N . In this network, streams H1 and C1 should be further cooled and heated, respectively: _ p Þh ð#0h #00h Þ ¼ 10 ð55:43 45Þ ¼ 104:34 kW CU1: Q_ ¼ ðMc ð#0h #00c Þ ð#00h #0c Þ ð55:43 25Þ ð45 15Þ ¼ ln½ð#0h #00c Þ=ð#00h #0c Þ ln½ð55:43 25Þ=ð45 15Þ ¼ 30:22 C k ¼ ð1=ah þ 1=ac Þ1 ¼ ð1=2:615 þ 1=2:5Þ1 ¼ 1:2781 kW=m2 K 2 _ A ¼ Q=ðkFD# LM Þ ¼ 104:34=ð1:278 1 30:22Þ ¼ 2:702 m _ p Þc ð#00c #0c Þ ¼ 20 ð155 145:78Þ ¼ 184:35 kW HU1: Q_ ¼ ðMc 3 7 7 0 7 7 7 0 7 7 7 0 7 7 7 0 7 7 0 7 7 0:61310 7 5 0:54740 D#LM ¼ C5 D#LM ¼ ð180 155Þ ð179 145:78Þ ¼ 28:91 C ln½ð180 155Þ=ð179 145:78Þ k ¼ ð1=5 þ 1=0:917Þ1 ¼ 0:7749 kW=m2 K A ¼ 184:35=ð0:7749 1 28:91Þ ¼ 8:228 m2 3 Synthesis of Heat Exchanger Networks with the Pinch Design Method The parameters of a heat exchanger network can be classified into three sets: (1) Design parameters, e.g., flowsheet of the network, heat exchanger type, heat transfer area, and other structural parameters. (2) Operation parameters, e.g., supply stream temperatures and flow rates. Their values might be disturbed or passively changed but cannot be regulated. (3) Control parameters, e.g., bypass flow rates and flow rates in stream split branches. Their values can be manually or automatically regulated by controlling units. A fundamental synthesis problem can be stated as: For given operation parameters of a heat recovery system, find the design parameters and control parameters of the heat exchanger network in their feasible regions so that the target temperatures of the process streams and other additional constraints (e.g., pressure drop, flow rate, and size limitations) can be fulfilled; meanwhile the sum of investment and operation costs reaches the minimum. In a typical synthesis task, the supply temperatures, heat capacity flow rates (or mass flow rates) and target temperatures of the process streams, and the temperature levels of the available hot and cold utilities are given as the operation parameters. The heat transfer coefficients of the process streams and utility mediums as well as the equipment and utility costs are previously specified. The design and control parameters to be optimized include: (1) the flowsheet of the heat exchanger network, (2) the area of each heat exchanger in the network, and (3) the heat capacity flow rates of hot and cold streams in each heat exchanger. As the number of possible flowsheets could be astronomical figures, traditional optimization solvers are not suitable for such a task. In the past 3 decades, many synthesis methodologies have been developed. As a practical procedure, the Pinch design method is introduced in this section in detail. 3.1 The Problem Table The problem table proposed by Linnhoff and Flower [14] is used to find the position of the Pinch and the minimum hot and cold utility duties. For a given synthesis task dealing with Nh hot streams and Nc cold streams, Let 109 110 C5 Heat Exchanger Networks 2 3 #0h;1 2 #00h;1 3 6 0 7 6 00 7 6 #h;2 7 6 # 7 6 7 00 6 h;2 7 0 Yh ¼ 6 . 7; Yh ¼ 6 . 7; 6 . 7 6 . 7 4 . 5 4 . 5 #0h;Nh #00h;Nh 2 0 3 2 0 #c;1 þ D#min #c ;1 6 0 7 6 0 6 #c ;2 7 6 #c;2 þ D#min 6 7 6 Y0c ¼ 6 . 7 ¼ 6 .. 6 . 7 6 . 4 . 5 4 2 #0c ;Nc #0c;Nc þ D#min and repeating the calculation. This can also be done by subtracting Q_ min from all heat inputs and outputs. After the modification, the minimum hot utility duty Q_ HU;min ¼ I1 and the minimum cold utility duty Q_ CU;min ¼ OSN is obtained. The position where the heat input is zero is called the Pinch. 3 7 7 7 7; 7 5 3 2 00 3 #00c ;1 #c;1 þ D#min 6 #00 7 6 #00 þ D# 7 min 7 6 c ;2 7 6 c;2 7 6 7 Y00c ¼ 6 ¼ .. 6 .. 7 6 7 4 . 5 4 5 . #00c ;Nc #00c;Nc þ D#min 3.2 Let j1 and j2 indicate the maximum and minimum temperature levels of the hot streams, respectively; k1 and k2 indicate those of the cold streams, so that ð21Þ in which D#min is the minimum temperature difference in the network. Let the set ST ¼ f#0h;1 ; #0h;2 ; ; #0h;Nh g [ f#00h;1 ; #00h;2 ; ; #00h;Nh g [ f#0c ;1 ; #0c ;2 ; ; #0c ;Nc g [ f#00c ;1 ; #00c ;2 ; ; #00c ;Nc g ð22Þ then define a temperature level vector Y ¼ ½ #1 #2 #NSN þ1 T #j1 ¼ maxf#0h;1 ; #0h;2 ; ; #0h;Nh ; #00h;1 ; #00h;2 ; ; #00h;Nh g ð31Þ #j2 ¼ minf#0h;1 ; #0h;2 ; ; #0h;Nh ; #00h;1 ; #00h;2 ; ; #00h;Nh g ð32Þ #k1 ¼ maxf#0c;1 ; #0c;2 ; ; #0c;Nc ; #00c;1 ; #00c;2 ; ; #00c;Nc g ð33Þ #k2 ¼ ð23Þ Di ¼ Ii Oi ¼ DH_ c;i DH_ h;i ( C_ h;ij ¼ C_ c;ij ¼ Nc X 0; ( _ p Þc;j ; ðMc 0; #00h;j H_ h;j ¼ j2 1 X DH_ h;i ð35Þ DH_ c;i þ OSN ð36Þ i¼j H_ c;k ¼ kX 2 1 i¼k C_ h;ij ð25Þ C_ c;ij ð26Þ 1. Do not use cold utilities above the Pinch 2. Do not use hot utilities below the Pinch 3. Do not transfer heat across the Pinch ð27Þ Therefore, for the network design there are three consequences: #iþ1 and #i #0h;j #iþ1 and #i #00c ;j others #0c ;j ð34Þ Because any network design that transfers heat across the Pinch will cause both heating and cooling duties larger than their minimum, there are three principles: j¼1 _ p Þh;j ; ðMc ; #00c;Nc g 3.3 j¼1 DH_ c;i ¼ ð#i #iþ1 Þ ; #0c;Nc ; #00c;1 ; #00c;2 ; ð24Þ in which DH_ h;i ¼ ð#i #iþ1 Þ minf#0c;1 ; #0c;2 ; The points for the composite curve of hot and cold streams are ð#j ; H_ h;j Þ ðj ¼ j1 ; j1 þ 1; ; j2 Þ and ð#k ; H_ c;k Þ ðk ¼ k1 ; k1 þ 1; ; k2 Þ, respectively, in which H_ h;j and H_ c;k are enthalpy flow rates of the hot and cold streams in the jth (or kth) subnetwork, in which the temperature levels #i 2 ST ði ¼ 1; 2; ; NSN þ 1Þ and #1 > #2 > > #NSN þ1 . The streams in each temperature interval ½#i ; #iþ1 constitute a subnetwork SNi ði ¼ 1; 2; ; NSN Þ. The heat transport difference between the heat input Ii and heat output Oi in SNi can be calculated by means of Eq. (24), Nh X The Composite Curves others ð28Þ At first, assume a zero heat input to SN1 , that is, I1 ¼ 0. If there is no additional connection between SNiþ1 and heat utility, the heat input of SNiþ1 should be equal to the heat output of SNi , Iiþ1 ¼ Oi ð29Þ The assumption I1 ¼ 0 might yield negative values of heat inputs and heat outputs of the sub-networks. This is not allowed because the heat cannot flow from a lower temperature region to a higher temperature region. The modification is performed by subtracting the minimum value of heat inputs/outputs to I1 , I1 ¼ Q_ min ¼ minfIi ; Oi ji ¼ 1; 2; ; NSN Þ ð30Þ Pinch Design Method 1. Divide the network at the Pinch into two parts 2. Design each part separately 3. Avoid the use of coolers in the part above the Pinch (hot end part); avoid the use of heaters in the part below the Pinch (cold end part) For the matching of streams there are the following two rules: 1. In the part above the Pinch, the number of the hot streams (including their branches) should be less than or equal to that of the cold streams (including their branches), that is, Nh Nc ðabove the PinchÞ ð37Þ otherwise, the stream splitting is necessary to ensure that Eq. (37) is fulfilled. Similarly, in the part below the Pinch, the inequality is inversed, Heat Exchanger Networks Nh Nc (below the Pinch) ð38Þ 2. For a match in the part above the Pinch, the heat capacity flow rate of the hot stream (or the branch of a hot stream) should be less than or equal to that of the cold stream (or the branch of a cold stream) to be matched, that is, _ p Þc (above the Pinch) ðMc _ p Þh ðMc ð39Þ otherwise, the stream splitting is necessary. For a match in the part below the Pinch, the inequality is inversed, _ p Þ (below the Pinch) ðMc c _ pÞ ðMc h Example 3 We use the problem data in Table 1 to illustrate the calculation of problem table and composite curves and let D#min ¼ 5K. The temperature intervals are formed according to the following temperatures, 175 45 20 þ 5 25 ; Y00h ¼ ; Y0c ¼ ¼ ; Y0h ¼ 125 65 40 þ 5 45 155 þ 5 160 Y00c ¼ ¼ 112 þ 5 117 Put the above temperatures into Eq. (23) and arrange them according to their magnitude; six subnetworks are obtained, NSN ¼ 6, and the temperature levels are, Y ¼ ½ 175 160 125 117 65 45 _ p Þ ¼ ð175 160Þ 10 ¼ 150 DH_ h;1 ¼ ð#1 #2 ÞðMc h;1 DH_ c;2 25 T I1 ¼ 0 _ _ D1 ¼ DHc;1 DHh;1 ¼ 0 150 ¼ 150 O1 ¼ I1 D1 ¼ 0 ð150Þ ¼ 150 SN2 : #2 ¼ 160; #3 ¼ 125 _ p Þc;1 ¼ ð160 125Þ 20 ¼ 700 ¼ ð#2 #3 ÞðMc _ p Þh;1 ¼ ð160 125Þ 10 ¼ 350 DH_ h;2 ¼ ð#2 #3 ÞðMc I2 ¼ O1 ¼ 150 D2 ¼ DH_ c;2 DH_ h;2 ¼ 700 350 ¼ 350 O2 ¼ I2 D2 ¼ 150 350 ¼ 200 ð40Þ In the Pinch design method D#min is an important parameter for the balance between the investment costs and utility costs. A large value of D#min would decrease the investment costs but increase the utility costs, and vice versa. Further more, the Pinch position could also change with D#min . The value of D#min can be optimized by taking the total costs of the network as the objective function. The Pinch design method focuses on the matches of streams near the Pinch because at that point the temperature difference is the minimum. For the matches away from the Pinch, the above rules must not be fulfilled. In some cases there might be multiple Pinches or no Pinch. A detailed description of the Pinch design method can be found in [15]. C5 The calculation results are provided in Table 3, where the modified heat input and output are denoted with ‘‘*’’. At the temperature level #3 ¼ 125 C, the heat input I3 ¼ 0, that means that there is no heat flowing through this interface. This position is the pinch at which the temperature difference reaches the given minimum value, D#min ¼ 5 C. The corresponding minimum heating duty is 200 kW, and the minimum cooling duty is 120 kW. The composite curves are shown in Fig. 5. The point data of the curves are also provided in Table 3. To design the network, the problem is divided into two parts at the Pinch as is shown in Fig. 6. In the part above the Pinch (the left part in Fig. 6), there is only one match: H1C1, i.e., Nh ¼ Nc ¼ 1, therefore, Eq. (37) is fulfilled. Since _ p ÞC1 ¼ 20 kW/K, Eq. (39) is also _ p ÞH1 ¼ 10 kW/K and ðMc ðMc valid and no splitting is necessary. In the part below the Pinch (the right part in Fig. 6), Nh ¼ Nc ¼ 2, which meets Eq. (38). The matches H1C1 and H2C2 can be considered due to their temperature intervals. Since _ p ÞC1 ¼ 20 kW/K, according to _ p ÞH1 ¼ 10kW/K and ðMc ðMc _ p ÞC1ðH1C1Þ Eq. (40), a splitting in C1 is necessary, ðMc 10 kW/K, and a new match H2C1 should be added with _ p ÞC1 ðMc _ p ÞC1ðH1C1Þ 10 kW=K, which _ p ÞC1ðH2C1Þ ¼ ðMc ðMc _ pÞ _ p ÞH2ðH2C1Þ ðMc yield a splitting in stream H2 with ðMc 10 kW=K . C1ðH2C1Þ _ p Þ ¼ 15 kW=K, then, For the match H2C2, since ðMc C2 Eq. (40) indicates _ p ÞH2ðH2C2Þ ¼ ðMc _ p ÞH2 15 kW=K ðMc _ p ÞH2ðH2C1Þ ðMc Equations (24–29) are applied to the following calculations. 30 kW=K This design step yields a network structure shown in Fig. 7. At first it is assumed that the branches are isothermally mixed, i.e., the split-flows of a stream at the branch outlets have the SN1 : #1 ¼ 175; #2 ¼ 160 DH_ c;1 ¼ 0 C5. Table 3. The problem table, D#min ¼ 5K SN q, qh ( C) DH_ c ðkWÞ DH_ h ðkWÞ D (kW) I (kW) O (kW) I* (kW) O* (kW) H_ h ðkWÞ qc ( C) H_ c ðkWÞ 1 175 0 150 150 0 150 200 350 3700 2 160 700 350 350 150 200 350 0 3550 155 3900 3 125 160 400 240 200 40 0 240 3200 120 3200 4 117 1820 2600 780 40 820 240 1020 2800 112 3040 5 65 700 200 500 820 320 1,020 520 200 60 1220 6 45 400 0 400 320 80 520 120 0 40 520 7 25 20 120 111 112 C5 Heat Exchanger Networks same temperature before they are mixed. Further more, as has been analyzed in the aforementioned problem table, the minimum cooling duty is 120 kW for stream H1; therefore, a cooler is added to stream H1. The detailed calculations for EX1 and EX4 are given as follows: _ p ÞH1 ð#0H1 #h;Pinch Þ ¼ 10 ð175 125Þ ¼ 500 kW EX1 :Q_ ¼ ðMc _ Mc _ p ÞC1 ¼ 120 þ 500=20 ¼ 145 C #00C1 ¼ #c;Pinch þ Q=ð ð#0H1 #00C1 Þ ð#h;Pinch #c;Pinch Þ D#LM ¼ ln½ð#0H1 #00C1 Þ=ð#h;Pinch #c;Pinch Þ ð175 145Þ ð125 120Þ ¼ ¼ 13:95 C ln½ð175 145Þ=ð125 120Þ k ¼ ð1=aH1 þ 1=aC1 Þ1 ¼ ð1=2:615 þ 1=0:917Þ1 k ¼ ð1=aH2 þ 1=aC2 Þ1 ¼ ð1=1:333 þ 1=0:166Þ1 ¼ 0:1476 kW=m2 K 2 _ A ¼ Q=ðkFD# LM Þ ¼ 1080=ð0:1476 1 18:35Þ ¼ 398:69 m More calculation results can be found in Fig. 7. The investment costs and utility costs can then be calculated according to the cost data in Table 1: EX1: CEX;1 ¼ 1; 200A0:57 ¼ 1; 200 52:780:57 ¼ 11; 508 $=year EX2: CEX;2 ¼ 1; 200 62:650:57 ¼ 12; 688 $=year EX3: CEX;3 ¼ 1; 200 133:470:57 ¼ 19; 527 $=year EX4: CEX;4 ¼ 1; 200 398:690:57 ¼ 36; 437 $=year _ p ÞH1 ð#00N ;H1 #00N ;H1 Þ$=year CU1: CU;1 ¼ 1; 200A0:57 þ 10ðMc ¼ 1; 200 3:030:57 þ 10 10 ð57 45Þ ¼ 0:6789 kW=m2 K 2 _ A ¼ Q=ðkFD# LM Þ ¼ 500=ð0:6789 1 13:95Þ ¼ 52:78 M _ p Þ ð#00C2 #0C2 Þ ¼ 15 ð112 40Þ ¼ 1; 080 kW EX4 : Q_ ¼ ðMc C2 0 00 _ _ p ÞH2ðH2C2Þ ¼ Q=ð# ðMc H2 #H2 Þ ¼ 1080=ð125 65Þ ¼ 18 kW=K D#LM ¼ ¼ ð#0H2 #00C2 Þ ð#00H2 #0C2 Þ ln½ð#0H2 #00C2 Þ=ð#00H2 #0C2 Þ ð125 112Þ ð65 40Þ ¼ 18:35 C ln½ð125 112Þ=ð65 40Þ C5. Fig. 5. Composite curves of Example 3. C5. Fig. 6. The Pinch decomposition. ¼ 3; 457 $=year HU1: CU;2 ¼ 1; 200 8:820:57 þ 110 20 ð155 145Þ ¼ 26; 150 $=year The total annual cost of the network is the sum of the above costs, Ctot ¼ 4 X n¼1 CEX;n þ 2 X n¼1 CU;n ¼ 109; 768$=year Heat Exchanger Networks C5 C5. Fig. 7. The structure design of the heat exchanger network, 109,768 $/year. As has been mentioned, the isothermal mixing is assumed in the above calculation, and Dtmin is also an empirical value. Therefore, it is possible to optimize the solution. Let x1 ¼ Q_ CU1 , _ p ÞEX2;c , and x4 ¼ ðMc _ p ÞEX3;h , and take x2 ¼ Q_ EX2 , x3 ¼ ðMc them as the controlling variables to be optimized. The optimal design can be obtained by means of the iteration procedure of the Newton method, @Ctot xi ¼ xi @ 2@xCi tot @xi2 Dx Ctot ðxi þ DxÞ Ctot ðxi DxÞ 2 Ctot ðxi þ DxÞ þ Ctot ðxi DxÞ 2Ctot ðxi Þ ði ¼ 1; 2; 3; 4Þ xi ð41Þ which yields the optimal network design with the total annual cost of 108,072 $/year, as is shown in Fig. 4. This procedure is simple, but might not converge in some cases. For such cases other optimization solvers can be used. Example 3 deals with only four process streams; therefore, it is suitable to use the Pinch design method. For more complicated synthesis problems, e.g., the synthesis of large-scale heat exchanger networks, the stochastic algorithms such as the hybrid genetic algorithm [16] and monogenetic algorithm [17] are recommended to solve the optimization problem. 4 C F H_ N N0 N 00 NEX NTU* R Y Symbols annual cost (monetary unit/year) correction factor of logarithmic mean temperature difference enthalpy flow rate (kW) number of stream channels number of stream entrances of network number of stream exits of network number of heat exchangers modified number of transfer units defined by Eq. (8) ratio of heat capacity flow rates temperature vector ( C) # D#LM temperature ( C) logarithmic mean temperature difference (K) Superscripts T transpose 0 inlet 00 outlet Subscripts c cold stream EX heat exchanger h hot stream N heat exchanger network excluding heaters and coolers N* heat exchanger network including heaters and coolers U utility 5 Bibliography 1. Masso AH, Rudd DF (1969) The synthesis of system designs - II. Heuristic structuring. AIChE J. 15:10–17 2. Linnhoff B, Mason DR, Wardle I (1979) Understanding heat exchanger networks. Comp Chem Eng 3:295–302 3. Grossmann IE, Sargent RWH (1978) Optimum design of heat exchanger networks. Comp Chem Eng 2:1–7 4. Lewin DR (1998) A generalized method for HEN synthesis using stochastic optimization - II. The synthesis of cost-optimal networks. Comp Chem Eng 22:1387–1405 5. Dolan WB, Cummings PT, LeVan MD (1989) Process optimization via simulated annealing: application to network design. AIChE J 35:725–736 6. Lin B, Miller DC (2004) Solving heat exchanger network synthesis problems with Tabu Search. Comp Chem Eng 28:1451–1464 7. Wei G-F, Yao P-J, Luo X, Roetzel W (2004) Study on multi-stream heat exchanger network synthesis with parallel genetic/simulated annealing algorithm. Chinese J Chem Eng 12:66–77 8. Xiao W, Dong H-G, Li X-Q, Yao P-J, Luo X, Roetzel W (2006) Synthesis of large-scale multistream heat exchanger networks based on stream pseudo temperature. Chinese J Chem Eng 14:574–583 9. Ravagnani MASS, Silva AP, Arroyo PA, Constantino AA (2005) Heat exchanger network synthesis and optimisation using genetic algorithm. Appl Therm Eng 25:1003–1017 10. Strelow O (2000) A general calculation method for plate heat exchangers. Int J Therm Sci 39:645–658 11. Chen D-Z, Yang S-S, Luo X, Wen Q-Y, Ma H-G (2007) An explicit solution for thermal calculation and synthesis of superstructure heat exchanger networks. Chinese J Chem Eng 15:296–301 113 114 C5 Heat Exchanger Networks 12. Roetzel W, Luo X (2005) Thermal analysis of heat exchanger networks. Archives Thermodynamics 26:5–16 13. Luo X, Li M-L, Roetzel W (2002) A general solution for one-dimensional multistream heat exchangers and their networks. Int J Heat Mass Transfer 45:2695–2705 14. Linnhoff B, Flower JR (1978) Synthesis of heat exchanger networks: I. Systematic generation of energy optimal networks. AIChE J 24: 633–642 15. Linnhoff B, Townsend DW, Boland D, Hewitt GF, Thomas BEA, Guy AR, Marsland RH. (1982) User guide on process integration for the efficient use of energy. Oxford: Institution of Chemical 16. Luo X, Wen Q-Y, Fieg G (2009) A hybrid genetic algorithm for synthesis of heat exchanger networks. Comp Chem Eng 33:1169–1181 17. Fieg G, Luo X, Jezowski J (2009) A monogenetic algorithm for optimal design of large-scale heat exchanger networks. Chem Eng Proc, 48:1506–1516 C6 Costs and Economy of Heat Exchangers C6 Costs and Economy of Heat Exchangers Bernhard Spang1 . Wilfried Roetzel2 1 2 BUCO Wärmeaustauscher International GmbH, Geesthacht, Germany Helmut-Schmidt-Universität, Universität der Bundeswehr Hamburg, Hamburg, Germany 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4 Thermodynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 2 2.1 2.2 Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Costs of Capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Energy Costs and Other Operating Expenses . . . . . . . . . 116 5 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 3 Economic Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 1 Introduction Heat exchangers are essential components in process technology. Therefore, the economic selection and design of heat exchangers plays an important role for the profitability of a process. In this connection profitability means the ratio of income to costs. Income and costs are value quantities (monetary units per unit time) which are linked to the physical variables used in engineering by cost coefficients. Applying the notion of profitability to heat exchangers allows either to compare marginal cost and marginal utility of a transferred heat flow or to consider the amount of heat transferred during a period of time as an externally specified quantity. The definition of marginal values in economics is given by W. H. Bartzsch [1]. In the former case the increase in income (usually in the form of lower energy costs) must be compared to the additional cost for the higher amount of transferred heat or for heat integration (> Chap. C5). The additional costs for increasing the heat transfer surface area of an exchanger for heat recovery entail lower energy costs. However, the heat flow rate per unit surface area decreases with increasing surface area (> Chap. C1). Consequently, a plot of the net amount of saved annual costs (saved energy costs less operating expenses including depreciation) versus the investment costs for the heat exchanger shows a maximum [2]. The actual heat exchanger should be smaller than at this maximum because the marginal return of the invested capital becomes just zero at this point. The optimal surface area of the heat exchanger for a requested return on investment can graphically be determined from the chart at the point where the gradient of the curve equals this return on investment. The following considerations are limited to the case where the amount of heat to be transferred is an externally specified quantity, given, for example, by the requirements for the proper functioning of the whole process. In this case the income is fixed, albeit usually not explicitly but only as an inseparable part of the income of the whole plant, and a cost-effectiveness study is limited to the minimization of costs by comparative cost methods. VDI-GVC (ed.), VDI Heat Atlas, DOI 10.1007/978-3-540-77877-6_9, # Springer-Verlag Berlin Heidelberg 2010 2 Costs The total costs Ctot (monetary units/year) can be subdivided into costs of capital CCA composed of the annual depreciation or amortization, the (imputed) interest, and the operating expenses for energy and supplies CE as well as the other operating expenses CS (for maintenance, repair, staff, and replacement of heat transfer fluids): Ctot ¼ CCA þ CE þ CS : 2.1 ð1Þ Costs of Capital The annual costs of capital depend on the capital requirements for the heat exchanger IEX (price or acquisition value), for pumps or compressors IP1 plus IP2 to convey the fluids through both channels of the exchanger, the number n of years of the recovery period, and the interest rate z: 1 z þ ðIEX þ IP1 þ IP2 Þ ¼ aðIEX þ IP1 þ IP2 Þ ð2Þ CCA ¼ n 2 where linear depreciation and a declining balance of zero are assumed. Equation (2) takes into account the fact that over the whole recovery period on average only half the capital employed is tied up. The value of the payback coefficient a falls usually between 0.1/year and 0.25/year (recovery period 5–20 years, interest rate 5–15%). While the recovery period and the interest rate are externally given, the capital requirements for the heat exchanger and pumps or compressors depend on the design of the exchanger. For the precise determination of I quotations from different manufacturers should be solicited. Several publications [2–5] give numerous methods and data for the estimation of acquisition costs of heat exchangers. However, these are associated with a high degree of uncertainity and are also not transferable offhand to other regions of the world. In order to estimate costs previously carried out projects or quotations for ‘‘similar’’ heat exchangers of different size or 116 C6 Costs and Economy of Heat Exchangers materials may be taken. The effect of the size on the equipment price IEX may be taken into account using the surface area A: mEX A ; ð3Þ IEX ¼ IEX0 A0 where IEX0 is the reference price of an exchanger with surface area A0. The value of the exponent mEX is usually less than 1 and is called degression exponent. Following the so-called 6/10-rule [6] a value of m ¼ 0.6 can be used for rough estimates. For shelland-tube heat exchangers with surface areas between 2 and 2,000 m2 a value of mEX ¼ 0.59 is recommended [7]. Accordingly, the pumping power L_ may be used as a reference variable for pumps or compressors: mP L_ : ð4Þ IP ¼ IP0 _L0 Values of mP ¼ 0.30 for small centrifugal pumps (0.35–30 kW), mP ¼ 0.67 for large centrifugal pumps (30–300 kW), and mP ¼ 0.84 for compressors (0.75–1,500 kW) are recommended by F. A. Holland and J. K. Wilkinson [7]. Different materials may be taken into account by correction coefficients for the price of the construction using a reference material. Values of such material correction coefficients for a shell-and-tube heat exchanger with a surface area of 140 m2 are given in Table 1 [2]. Both values for the tubes and for the whole heat exchanger are specified. Carbon steel is used as the reference material. For smaller heat exchangers the correction coefficients tend to be smaller and vice versa. Prices of the past have to be corrected by means of price indexes: Ij2 ¼ Ij1 j2 j1 ð5Þ with Ij1 and j1 as the price and the price index at a particular time in the past and Ij2 and j2 as the current price and the C6. Table 1. Material correction coefficients for a shell-and-tube heat exchanger [2] Material Unalloyed carbon steel Tubes Heat exchanger 1.0 1.0 Stainless steel 304L, welded 2.2 1.6 Stainless steel Cu/Ni-90/30, welded 2.4 1.6 Stainless steel Cu/Ni-70/30, seamless 2.9 1.8 Stainless steel 316L, welded 3.2 1.8 Titanium, 20 BWG, welded 3.6 1.9 E-Brite 26-1, welded 5.2 2.4 Titanium, welded 6.8 2.8 Monel 400, welded 7.5 3.0 Incoloy 825, welded 7.6 3.0 Carpenter 20/CB3, welded 8.6 3.3 Inconel 625, welded 15.1 5.0 Zirconium 20 BWG, seamless 15.8 5.2 Hastelloy C276, welded 18.2 5.9 Zirconium, seamless 25.1 7.7 current price index. A common index is the Chemical Engineering Plant Cost Index (CEPCI) which is published periodically in the magazine Chemical Engineering [8] or is available online [9]. The CEPCI contains subindexes for heat exchangers and tanks as well as for pumps and compressors. 2.2 Energy Costs and Other Operating Expenses The total costs for energy and supplies CE are composed of the pumping costs on both sides, of the additional energy costs CDT for increasing the temperature difference in the heat exchanger and of the costs of supplies CM . They are proportional to the annual operating time t (hours/year): _ 1 Dp1 M _ 2 Dp2 M þ ð6Þ CE ¼ cel t þ CDT þ CM r1 P1 r2 P2 with the price of electrical energy cel (monetary units/kWh) and _ i , the absolute pressure drop Dpi , the mean the mass flow rate M fluid density ri, and the pump efficiencies Pi on both sides (i = 1 or 2). The additional energy costs CDT for increasing the temperature difference in the exchanger result from the costs for combustibles, steam, or electrical energy. In many cases Eq. (6) may be simplified. While pumping costs always arise at least on one side, additional energy costs CDT for increasing the temperature difference do not occur for heat transfer between two process fluids or for cooling with fluids at ambient temperature. Moreover, for cooling with water there may be costs. Costs of supplies do not occur for heat transfer between process fluids or for cooling with air. The other operating expenses primarily include maintenance and cleaning costs. Although they are at least partially proportional to the annual operating time like the energy costs, it is usual practice to assume them to be proportional to the equipment price like the capital costs [10]: Cs ¼ sIEX : ð7Þ For cost estimation purposes with the objective of economic design this is justified as well because operating time-dependent or constant parts of the maintenance costs do not depend on the construction of the heat exchanger. Rough values for the coefficient s are given by Schnell [10]: s ¼ 0.01 to 0.02 for low maintenance requirements (no danger of fouling and corrosion), s ¼ 0.02 to 0.05 for medium maintenance requirements (planned maintenance and cleaning intervals), s ¼ 0.05 to 0.10 for high maintenance requirements (rapid fouling, high corrosion). Maintenance costs for the pumps may be taken into account accordingly. 3 Economic Design In general the following parameters are specified for the design of a heat exchanger: Costs and Economy of Heat Exchangers – Mass flow rate of one of both streams (process fluid) – Inlet and outlet temperature of the process fluid In many cases the inlet temperature of the fluid on the other side is also defined (supplies like air or water for cooling) or restricted to a few discrete values (heating steam). The objective of the economic design is the selection of a heat exchanger (type, heat transfer surface area, design details) and the specification of operating conditions (mass flow rate and inlet temperatures of supplies where necessary) in order both to meet above specifications and to minimize the annual total costs according to Eq. (1). Generally the total costs depend on many factors, some of them having only discrete values. The formal way for determining the minimum of the cost function Eq. (1) by means of analytical or numerical partial derivation with respect to all relevant variables would require either simple analytical relations or an extensive data base. This formal way is rarely justified because of the high costs for collection of the required data. In the special case of heat transfer between two process fluids mass flow rates and terminal temperatures of both streams are specified. Additional energy costs for increasing the temperature difference do not occur. The cost function is reduced to mEX _ 1 Dp1 M _ 2 Dp2 A M þcel t þ ð8Þ Ctot ¼ ða þ s ÞIEX0 r1 P1 r2 P2 A0 where costs of capital and maintenance for the pumps are neglected. According to > Chap. C1, Eq. (3), the required surface area A depends on the mean overall heat transfer coefficient k and the mean temperature difference D#m . The overall heat transfer coefficient k, in turn, depends on the geometry of the flow channels and the mean flow velocities (> Chap. C2 and Part G), and the mean temperature difference D#m depends on the flow arrangement (> Chap. C1). Pressure drops Dp1 and Dp2 depend on the mean flow velocities and the geometries of the flow paths, especially on their lengths (Part L). Minimization of the cost function Eq. (8) may be considerably simplified by using an analogy between heat transfer and pressure drop. Martin [11] has shown that an analogy following the generalized Lévêque equation may be used for the economic design of plate heat exchangers, tube bundles, packed beds, and other types of compact heat exchangers. 4 Thermodynamic Analysis The economic valuation on the basis of costs is expensive and unreliable. On the other hand, a thermodynamic analysis for minimization of the entropy production or of the exergy loss by means of entropy or exergy balances may be carried out easily and quickly. There is no general relation between entropy production or exergy loss on the one hand and total costs on the other hand. However, in cases where energy costs preponderate the thermodynamic analysis may provide indications for the most economic solution (see > Chap. C5 about the optimization of heat exchanger networks). An exergy balance for an adiabatic heat exchanger with two streams in steady-state operation according to > Chap. C1, Fig. 1, yields the exergy loss E_ V : _ 1 s100 s10 þ M _ 2 s200 s20 E_ V ¼ Tu M C6 ð9Þ _1 where Tu is the ambient thermodynamic temperature and M _ 2 are the mass flow rates of both streams. By heat losses and M to the surroundings an additional exergy loss is generated. This additional exergy loss, however, is usually small and may be neglected in most cases, especially if the heat exchanger is properly insulated. Evaluation of Eq. (9) for single-phase systems requires inlet and outlet temperatures and pressures of both streams in order to determine the specific entropies s10 ; s100 ; s20 ; and s200 . For wet vapor of a pure fluid, temperature or pressure and vapor quality at the inlet and outlet must be known; for mixtures, additionally the compositions of vapor and liquid must be known. For the single-phase model fluids ‘‘perfect gas’’ and ‘‘incompressible fluid,’’ which are good approximations for real gases at low pressures and liquids, respectively, the following simple equations for the calculation of the exergy loss may be used. They have been derived for constant heat capacities [12]. The exergy loss is composed of three parts: E_ V ¼ E_ V;Q þ E_ V;Dp;1 þ E_ V;Dp;2 : ð10Þ The first term E_ V ;Q represents the main exergy loss due to heat transfer at finite temperature difference. Included is a small fraction which is caused by the mixing of fluid parts of different temperatures at the outlet. For gases and liquids the exergy loss E_ V;Q is calculated according to 1 1 E_ V;Q ¼ Q_ 12 Tu 0: ð11Þ TM;2 TM;1 In Eq. (11) Q_ 12 means the heat flow rate transferred from stream 1 to stream 2 and TM,i means the logarithmic mean values of the thermodynamic inlet and outlet temperatures of stream i = 1 and 2: TMi ¼ Ti0 Ti00 T0 ln T i00 : ð12Þ i If stream 1 is the hot stream, Q_ 12 > 0 and TM1 > TM2. If stream 1 is the cold stream, Q_ 12 < 0 and TM1 < TM2. The second and third term in Eq. (10) represent the exergy loss due to frictional pressure drop of stream i ¼ 1 and 2, respectively. For gases this exergy loss is calculated according to 0 _ i Ri ln pi E_ V;Dp;i ¼ M pi00 ð13Þ where Ri is the specific gas constant and pi0 and pi00 are the gas pressures at the inlet and outlet of the heat exchanger. The following equation applies to liquids: _ i Dpi M E_ V;Dp;i ¼ ri TM;i ð14Þ _ i as the mass flow rate, ri the density, Dpi ¼ pi0 pi00 the with M absolute value of the pressure drop, and TM,i the logarithmic mean value of the temperature according to Eq. (12). 117 118 C6 Costs and Economy of Heat Exchangers Equating Eqs. (13) and (14) reveals that Eq. (14) can also be applied to gases provided the mean density is determined for the mean temperature according to Eq. (12) and the mean pressure pM ¼ p0 p00 0 ln pp00 : The considerations refer also to Eqs. (6) and (8). Unlike the general exergy balance Eq. (9), Eqs. (10–14) allow the separate evaluation of exergy losses caused by heat transfer with finite temperature difference and those caused by frictional pressure drop on both sides. This becomes important if they are covered by exergy sources which are energetically unequal (e.g., fuel oil for the exergy loss caused by finite temperature differences and electrical energy for the exergy loss caused by pressure drop). This is not so important if all exergy losses are eventually covered by the same source as in heat exchangers of thermal power plants. 5 a E_ V j I C m n z Symbols payback coefficient (1/year) exergy loss (W) price index price (monetary units) costs (monetary units/year) degression exponent number of periods (year) annual interest rate (1/year) 6 Bibliography 1. Bartzsch WH (1997) Betriebswirtschaft für Ingenieure, 6th edn. VDEVerlag, Berlin/Offenbach 2. Peters MS,Timmerhaus KD (1991) Plant design and economics for chemical engineers, 4th edn. McGraw-Hill, New York 3. Chisholm D et al. (1983) Costing of heat exchangers. Chap. 4.8 in: Heat Exchanger Design Handbook. Hemisphere Publishing Corporation, Washington 4. Purohit GP (1987) Heat exchangers, cost of double-pipe and multitube units. In: Encyclopedia of chemical processing and design, vol 25. Marcel Dekker, New York, pp 310–324 5. Vatavuk WM (1995) A potpourri of equipment prices. Chem Eng 102 (August): 68–73 6. Williams R (1947) ‘Six-tenths factor’ aids in approximating costs. Chem Eng 54:124–125 7. Holland FA, Wilkinson JK (1997) Process economics. Section 9 in: Perry’s chemical engineers’ handbook, 7th edn. McGraw-Hill, New York 8. Chemical Engineering. Access Intelligence LLC Inc., New York 9. Chemical Engineering Online Plant Cost Index, http://www.che.com/ pcitrial/ 10. Schnell H (1991) Technisch-wirtschaftliche Optimierung von Wärmeaustauschern. In: Wärmeaustauscher, Energieeinsparung durch Optimierung von Wärmeprozessen, 1st edn, Vulkan-Verlag, Essen, pp 348–353 11. Martin H (1998) Prediction of heat transfer from pressure drop in heat exchangers – a better tool for thermohydraulic and economic design. Proc Int Conf Heat Exchangers for Sustainable Development, Lisbon, Portugal, June 15–18, pp 249–256 12. Roetzel W (1983–2001) Lecture ‘‘Prozesse und Apparate der Enegietechnik’’., Helmut Schmidt University, University of the Federal Armed Forces Hamburg. See also Roetzel W (1985) Comments on the paper of A. L. London and R. K. Shah, Costs of irreversibilities in heat exchanger design. Heat Transfer Eng 5(3–4):5–17 and 6(2):73 Part D Thermophysical Properties D1 Calculation Methods for Thermophysical Properties D1 Calculation Methods for Thermophysical Properties Michael Kleiber1 . Ralph Joh2 1 2 Uhde GmbH, Bad Soden, Germany Siemens AG, Frankfurt, Germany 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 2 Systematics of Calculation Methods . . . . . . . . . . . . . . . . 122 3 3.1 3.2 3.3 3.4 3.5 3.6 Characteristic Property Constants. . . . . . . . . . . . . . . . . . 122 Critical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Acentric Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Normal Boiling Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Melting Point and Enthalpy of Fusion. . . . . . . . . . . . . . . 129 Standard Enthalpy of Formation and Gibbs Energy of Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Dipole Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 4 4.1 4.2 4.3 Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Density of Liquids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Density of Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Coefficient of Thermal Expansion . . . . . . . . . . . . . . . . . . . 133 5 Vapor Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6 6.1 6.2 Enthalpy Determination. . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Enthalpy of Vaporization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Specific Heat Capacity of Ideal Gases. . . . . . . . . . . . . . . . 136 1 Introduction For the description of the heat transfer, the knowledge of thermophysical properties is essential. They occur as parameters in particular equations and have usually a significant influence on the results. For example, the thermal conductivity, the dynamic viscosity, the density, and the specific heat capacity are important for the calculation of heat transfer in a single-phase forced convection. In case of natural convection, the movement of the fluid is caused by temperature differences in the gravitational field. Therefore, the temperature-dependence of the density is important to know. If a phase change happens (condensation or evaporation), the vapor pressure curve is necessary to determine the temperature at the interface between the two phases. The enthalpy of vaporization then determines the heat flux, whereas the surface tension is an important parameter to describe the formation of such an interface, for example, the bubble formation in a vessel containing a boiling liquid. In fluid mixtures, the heat transfer is always connected with a simultaneous mass transfer, where the particular diffusion coefficients are decisive for the evaluation. All these thermophysical properties depend on the thermodynamic state, which is characterized by two coordinates in the VDI-GVC (ed.), VDI Heat Atlas, DOI 10.1007/978-3-540-77877-6_10, # Springer-Verlag Berlin Heidelberg 2010 6.3 6.4 6.5 Real Gas Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Specific Heat Capacity of Liquids. . . . . . . . . . . . . . . . . . . . 138 Routes for Enthalpy Calculation . . . . . . . . . . . . . . . . . . . . . 140 7 7.1 7.2 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Dynamic Viscosity of Liquids . . . . . . . . . . . . . . . . . . . . . . . . 142 Dynamic Viscosity of Gases . . . . . . . . . . . . . . . . . . . . . . . . . . 144 8 8.1 8.2 Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Thermal Conductivity of Liquids . . . . . . . . . . . . . . . . . . . . 146 Thermal Conductivity of Gases . . . . . . . . . . . . . . . . . . . . . . 147 9 Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 10 10.1 10.2 10.3 Diffusion Coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Diffusion Coefficients in Gases . . . . . . . . . . . . . . . . . . . . . . 149 Diffusion Coefficients in Liquids . . . . . . . . . . . . . . . . . . . . 150 Diffusion in Multicomponent Mixtures . . . . . . . . . . . . . 151 11 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 12 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 single-phase region. Normally, it is convenient to use temperature and pressure. The temperature-dependence is usually strong, whereas the dependence on the pressure is not negligible, but comparably weak. Only the density of gases is an exception. For mixtures, the dependence on the concentration has to be taken into account. Values for thermophysical properties should, if possible, always be based on reliable experimental data. Extensive measurements have been performed for various technically important pure substances. These data have been collected in tables in > Chap. D2, for example, for water, carbon dioxide, nitrogen, or air, which is often treated like a pure substance. High-precision equations of state have been developed and published for these substances, which ensure the reproduction of all thermodynamic quantities with extraordinary accuracy [1]. The structure of these equations is not based on physical relationships but on the numerical optimization of the terms contributing to the equation. For a large number of other substances, values and correlations are listed in > Subchap. D3.1. However, the heat transfer must often be determined in fluids for which no measured data are available. For multicomponent mixtures, this is even the normal case. Therefore, 122 D1 Calculation Methods for Thermophysical Properties methods for the estimation of physical properties are required. In the following sections, a collection of simple correlation and estimation methods for the calculation of thermophysical properties of fluids is compiled. 2 Systematics of Calculation Methods Physical properties are determined by the internal structure of the molecules and the intermolecular forces between them. Therefore, most of the practical calculation methods are based on considerations in the molecular scale. Nevertheless, the step from the molecular scale to measurable thermophysical properties is extremely difficult. An independent calculation of properties without using experimental data points will not be possible in the near future. Instead, the molecular theories deliver the structure of the calculation methods, and parameters of the particular methods are adjusted to experimental data. The calculation methods, which are established today, are a combination of a theoretically founded structure and parameters determined by experimental data. It must be distinguished between correlation and estimation methods. The target of correlations is to reproduce a certain number of data points as exactly as possible, to interpolate between the data points safely and to extrapolate beyond the range covered by the data points in a reasonable way. Certainly, care must be taken for the latter case. Many correlations are so well established that the quality of the parameter adjustment can be taken as a consistency test, that is, data points are only accepted if the correlation can reproduce them within their experimental uncertainty. In contrast, estimation methods shall predict thermophysical properties with or without a few experimental information available. Accuracy is not the main focus of estimation methods; it is more important that unacceptably high deviations from the true values are avoided. In this chapter, only those estimation methods are listed, which can be recommended to a non-specialized user as a useful compromise between general applicability, accuracy in the sense mentioned above, and simplicity. The use of commercial programs is not necessary. All the calculation methods introduced are mainly founded on two basic elements, that is, the description of the structure of the molecules by group contribution methods and the calculation of molecular interactions by means of the principle of corresponding states. Group contributions are contributions of the particular functional groups of a molecule to a thermophysical property. It is usually assumed that the contributions of the structural groups are independent of the kind of structural groups in the neighborhood. Then, comparably few structural groups can describe a huge number of chemical substances. The success of the group contribution methods demonstrates that the assumption mentioned above is reasonably justified. The 3-parameter corresponding states principle is based on the assumption that intermolecular forces can be described by a generalized function, where the substance itself is characterized by few constant parameters. If a calculation function depending on these constants has been derived for a thermophysical property by adjustment to experimental data, this function can be applied to substances where the particular property is unknown. The use of the corresponding states principle is, in most cases, easier to perform than the use of group contributions. For mixtures, the composition must be introduced into the calculation equations. Essentially, there are two ways to do that. If the pure component data are reliable, so-called mixing rules can be used to evaluate the mixture data from the pure component values. These mixing rules are different for each property, and there are also different forms for different thermodynamic states. Less frequently, mixing rules are applied to the characteristic property constants of the components involved. In this way, a pseudo-pure component is generated with property constants that depend on the concentration of the mixture. The properties of the mixture are then determined with the corresponding pure component methods. Altogether, the combination of group contribution methods, the 3-parameter corresponding states principle and the mixing rules form a powerful but not perfect system of calculation methods for thermophysical properties of fluid substances. For all generalized calculation methods, the structural formula is sufficient for the characterization of a substance. Especially, it allows the group assignment of a molecule with structural groups. 3 Characteristic Property Constants Physical property estimation methods based on the 3-parameter corresponding states principle revert to the characteristic property constants critical temperature (Tc), critical pressure (pc), and acentric factor (o). These constants are mainly the basis of the cubic equations of state, which are valuable tools for the description of density and enthalpy of real gases. As the results of an estimation method mainly depend on the quality of the input data, it is worth to determine them carefully. However, the evaluation of critical data is related with a huge experimental effort, not to mention the fact that many substances already decompose before the critical point can be reached. In these cases, estimation methods are necessary. In the following section, a number of estimation methods for Tc, pc, and o are introduced. Other scalar properties such as normal boiling point (TNBP), critical volume (vc), melting point (Tm) and enthalpy of fusion (qm), standard enthalpy of formation (Dh0f ), and standard Gibbs energy of formation (Dg0f ) as well as the dipole moment (m), which are used in property estimation methods and process simulations, are also considered. In combination with the correlation and estimation methods for temperature-dependent properties, a system is formed where the optimal calculation method can be found to determine unknown properties with an arbitrary set of known data points for a substance. The extreme case would be to determine all the data required just on the basis of the structural formula as the only ensured information. This case occurs in practical applications; however, it should of course not be aspired, as uncertainties and error propagation might yield in bad results. The standard strategy should be to gain as much information as possible from databanks or experiments and to estimate only the missing information. Calculation Methods for Thermophysical Properties 3.1 Critical Data Critical temperature, critical pressure, and critical volume can be quite well-determined with group contribution methods. The methods of Joback [2] and Constantinou/Gani [3] are well-established in this area. A more complicated but accurate method has been developed by Rarey et al. [4]. The Joback method uses only the structural formula as input information. For the estimation of the critical temperature, the normal boiling point is additionally needed; if it is not known, it can be estimated from the structural formula as well (Sect. 3.3). The calculation equations are: X 2 1 X Tc TNBP ¼ 0:584 þ 0:965 DT DT ð1Þ K K X 2 pc ¼ 0:113 þ 0:0032 nA Dp ð2Þ bar X vc ¼ 17:5 þ Dv ð3Þ cm3 =mol The group contributions for DT, Dp, and Dv can be taken from Table 1. nA is the number of atoms in the molecule. The group assignment of the Joback method is simple, as the increments are directly listed. It is only distinguished between chain and ring increments; there is no difference between aromatic and aliphatic rings. It is worth mentioning that there are two kinds of OH groups for alcohols and phenols. The Constantinou/Gani method uses only the structural formula for all quantities as input information. The authors have introduced the so-called second-order groups, where special configurations of structural groups are assigned with their own group contributions which can simply be added to the normal ‘‘first-order’’ groups. However, acceptable results can also be obtained using only the first-order groups; the improvement achieved with the second-order groups turned out to be relatively small in tests. The calculation equations for the Constantinou/Gani method are: exp p c bar X X Tc ¼ DT;i þ DT;j 181:128 K i j 1:3705 0:5 vc m3 =kmol ¼ ¼ 0:10022 þ X i Dv;i þ X X i Dp;i þ X ð4Þ Dp;j ð5Þ j Dv;j 0:00435 ð6Þ j where the indices i and j represent the first-order and the second-order groups, respectively. The group contributions for DT, Dp, and Dv are listed in Tables 2 and 3. The first-order groups are molecular segments which can easily be assigned. Consistently, it is distinguished between aromatic (AC) and aliphatic carbon atoms. As mentioned above, the second-order groups are additive contributions to the first-order groups; they do not replace them. The quality of the estimation is usually very good for the critical temperature; in most of the cases, the true value is met within a few K. Poling et al. [2] indicate an average error of 1.1% of the absolute temperature for the Joback method, if the D1 normal boiling point is known. Only 1% of the test substances have an average error larger than 5%. The average error for the Constantinou/Gani method is reported to be somewhat higher (2.3%) due to the fact that the normal boiling point is not used as input information. Approximately, 11% of the tested substances had an average error larger than 5%. However, the Constantinou/Gani method is superior if the normal boiling point has to be estimated itself. For the critical pressure, the average errors are reported according to Poling et al. [2] to be 4.6% (Joback) and 5.5% (Constantinou/Gani). As the case may be, these errors can be transferred to the estimation of the vapor pressure (Sect. 5) or to the accuracy of cubic equations of state (Sect. 4.2). The critical volume is of less importance. It has an influence on the estimation of the density with the COSTALD method (Sect. 4.1), if no reference value is available. The average errors are reported to be 3.1% (Joback) and 3.7% (Constantinou/ Gani). The numbers reported for the average errors refer in all cases to molecules with more than three carbon atoms, since for substances with less carbon atoms property estimations do not make much sense, as usually experimental data are available. As for the Constantinou/Gani method only the structural formula is used as input, it is also possible to take similar substances with known critical data as reference and to exchange or add only the differing structural groups. Often, but not in every case, this procedure results in an improvement. The target of this procedure is in fact to reduce the probability of a large error. An example is shown below. If values for Tc, pc, and vc are available, it is strongly recommended to check the consistency of the values by calculating the critical compressibility factor pc vc Zc ¼ ð7Þ e c RT Zc is usually in the range 0.21 < Zc < 0.29. Example 1: Estimate the critical properties of m-xylene (Fig. 1). The normal boiling point is TNBP = 412.25 K. (a) Joback’s method The group assignment of m-xylene is given by: 4 x = CH– (ring) 2 x = C < (ring) 2 x –CH3 The group contributions are: X DT ¼ 4 ð0:0082Þ þ 2 ð0:0143Þ þ 2 ð0:0141Þ ¼ 0:0896 X Dp ¼ 4 ð0:0011Þ þ 2 ð0:0008Þ þ 2 ð0:0012Þ ¼ 0:0036 X Dv ¼ 4 ð41Þ þ 2 ð32Þ þ 2 ð65Þ ¼ 358 Thus, the critical data can be calculated to be: Tc ¼ 412:25 K=ð0:584 þ 0:965 0:0896 0:08962 Þ ¼ 622:32 K pc ¼ ð0:113 þ 0:0032 18 0:0036Þ2 bar ¼ 35:86 bar vc ¼ ð17:5 þ 358Þ cm3 =mol ¼ 0:3755 m3 =kmol 123 124 D1 Calculation Methods for Thermophysical Properties D1. Table 1. Group contributions of the Joback method Structural group DT Dp Dv DNBP DM DH DG –43.96 –CH3 0.0141 –0.0012 65 23.58 –5.10 –76.45 >CH2 0.0189 0.0000 56 22.88 11.27 –20.64 8.42 >CH– 0.0164 0.0020 41 21.74 12.64 29.89 58.36 >C< 0.0067 0.0043 27 18.25 46.43 82.23 116.02 =CH2 0.0113 –0.0028 56 18.18 –4.32 –9.63 3.77 =CH– 0.0129 –0.0006 46 24.96 8.73 37.97 48.53 =C< 0.0117 0.0011 38 24.14 11.14 83.99 92.36 =C= 0.0026 0.0028 36 26.15 17.78 142.14 136.70 CH 0.0027 –0.0008 46 9.20 –11.18 79.30 77.71 C– 0.0020 0.0016 37 27.38 64.32 115.51 109.82 –CH2–(ring) 0.0100 0.0025 48 27.15 7.75 –26.80 –3.68 >CH– (ring) 0.0122 0.0004 38 21.78 19.88 8.67 40.99 >C< (ring) 0.0042 0.0061 27 21.32 60.15 79.72 87.88 =CH– (ring) 0.0082 0.0011 41 26.73 8.13 2.09 11.30 =C< (ring) 0.0143 0.0008 32 31.01 37.02 46.43 54.05 –F 0.0111 –0.0057 27 –0.03 –15.78 –251.92 –247.19 –Cl 0.0105 –0.0049 58 38.13 13.55 –71.55 –64.31 –Br 0.0133 0.0057 71 66.86 43.43 –29.48 –38.06 –I 0.0068 –0.0034 97 93.84 41.69 21.06 5.74 –OH (alcohols) 0.0741 0.0112 28 92.88 44.45 –208.04 –189.20 –OH (phenols) 0.0240 0.0184 –25 76.34 82.83 –221.65 –197.37 –O– 0.0168 0.0015 18 22.42 22.23 –132.22 –105.00 –O– (ring) 0.0098 0.0048 13 31.22 23.05 –138.16 –98.22 >C=O 0.0380 0.0031 62 76.75 61.20 –133.22 –120.50 >C=O (ring) 0.0284 0.0028 55 94.97 75.97 –164.50 –126.27 –CH=O 0.0379 0.0030 82 72.24 36.90 –162.03 –143.48 –COOH 0.0791 0.0077 89 169.09 155.50 –426.72 –387.87 –COO– 0.0481 0.0005 82 81.10 53.60 –337.92 –301.95 =O 0.0143 0.0101 36 –10.50 2.08 –247.61 –250.83 –NH2 0.0243 0.0109 38 73.23 66.89 –22.02 14.07 >NH 0.0295 0.0077 35 50.17 52.66 53.47 89.39 >NH (ring) 0.0130 0.0114 29 52.82 101.51 31.65 75.61 >N– 0.0169 0.0074 9 11.74 48.84 123.34 163.16 –N= 0.0255 –0.0099 –N= (ring) 0.0085 0.0076 34 57.55 68.40 55.52 79.93 93.70 119.66 74.60 23.61 =NH –CN 0.0496 –0.0101 91 125.66 59.89 88.43 89.22 –NO2 0.0437 0.0064 91 152.54 127.24 –66.57 –16.83 –SH 0.0031 0.0084 63 63.56 20.09 –17.33 –22.99 –S– 0.0119 0.0049 54 68.78 34.40 41.87 33.12 –S– (ring) 0.0019 0.0051 38 52.10 79.93 39.10 27.76 (b) Method of Constantinou/Gani The group assignment of m-xylene is: 4 ACH 2 ACCH3 Second-Order-Groups cannot be assigned. The results for the group contributions are: X DT ¼ 4 ð3:7337Þ þ 2 ð8:213Þ ¼ 31:3608 X Dp ¼ 4 ð0:007542Þ þ 2 ð0:01936Þ ¼ 0:068888 X Dv ¼ 4 ð0:04215Þ þ 2 ð0:10364Þ ¼ 0:37588 Calculation Methods for Thermophysical Properties D1 D1. Table 2. Constantinou / Gani group contributions for first-order groups Structural group DT Dp Dv DNBP DH DG CH3 1.6781 0.019904 0.07504 0.8894 –45.947 CH2 3.4920 0.010558 0.05576 0.9225 –20.763 –8.030 8.231 CH 4.0330 0.001315 0.03153 0.6033 –3.766 19.848 C 4.8823 –0.010404 –0.00034 0.2878 17.119 37.977 CH2=CH 5.0146 0.025014 0.11648 1.7827 53.712 84.926 CH=CH 7.3691 0.017865 0.09541 1.8433 69.939 92.900 CH2=C 6.5081 0.022319 0.09183 1.7117 64.145 88.402 CH=C 8.9582 0.012590 0.07327 1.7957 82.528 93.745 C=C 11.3764 0.002044 0.07618 1.8881 104.293 116.613 CH2=C=CH 9.9318 0.031270 0.14831 3.1243 197.322 221.308 ACH 3.7337 0.007542 0.04215 0.9297 11.189 22.533 AC 14.6409 0.002136 0.03985 1.6254 27.016 30.485 ACCH3 8.2130 0.019360 0.10364 1.9669 –19.243 22.505 ACCH2 10.3239 0.012200 0.10099 1.9478 9.404 41.228 ACCH 10.4664 0.002769 0.07120 1.7444 27.671 52.948 9.7292 0.005148 0.03897 3.2152 –181.422 –158.589 ACOH 25.9145 –0.007444 0.03162 4.4014 –164.609 –132.097 CH3CO 13.2896 0.025073 0.13396 3.5668 –182.329 –131.366 CH2CO 14.6273 0.017841 0.11195 3.8967 –164.410 –132.386 CHO 10.1986 0.014091 0.08635 2.8526 –129.158 –107.858 CH3COO 12.5965 0.029020 0.15890 3.6360 –389.737 –318.616 CH2COO 3.8116 0.021836 0.13649 3.3953 –359.258 –291.188 HCOO 11.6057 0.013797 0.10565 3.1459 –332.822 –288.902 CH3O 6.4737 0.020440 0.08746 2.2536 –163.569 –105.767 CH2O 6.0723 0.015135 0.07286 1.6249 –151.143 –101.563 CH-O 5.0663 0.009857 0.05865 1.1557 –129.488 –92.099 CH2O (cyclic) 9.5059 0.009011 0.06858 2.5892 –140.313 –90.883 CH2NH2 12.1726 0.012558 0.13128 3.1656 –15.505 58.085 CHNH2 10.2075 0.010694 0.07527 2.5983 3.320 63.051 CH3NH 9.8544 0.012589 0.12152 3.1376 5.432 82.471 CH2NH 10.4677 0.010390 0.09956 2.6127 23.101 95.888 CHNH 7.2121 –0.000462 0.09165 1.5780 26.718 85.001 CH3N 7.6924 0.015874 0.12598 2.1647 54.929 128.602 132.756 OH CH2N 5.5172 0.004917 0.06705 1.2171 69.885 ACNH2 28.7570 0.001120 0.06358 5.4736 20.079 68.861 C5H4N 29.1528 0.029565 0.24831 6.2800 134.062 199.958 C5H3N 27.9464 0.025653 0.17027 5.9234 139.758 199.288 CH2CN 20.3781 0.036133 0.15831 5.0525 88.298 121.544 COOH 23.7593 0.011507 0.10188 5.8337 –396.242 –349.439 CH2Cl 11.0752 0.019789 0.11564 2.9637 –73.568 –33.373 CHCl 10.8632 0.011360 0.10350 2.6948 –63.795 –31.502 CCl 11.3959 0.003086 0.07922 2.2073 –57.795 –25.261 CHCl2 16.3945 0.026808 0.16951 3.9300 –82.921 –35.814 –53.332 CCl2 3.5600 CCl3 18.5875 0.034935 0.21031 4.5797 –107.188 ACCl 14.1565 0.013135 0.10158 2.6293 –16.752 –0.596 CH2NO2 24.7369 0.020974 0.16531 5.7619 –66.138 17.963 CHNO2 23.2050 0.012241 0.14227 5.0767 –59.142 18.088 ACNO2 34.5870 0.015050 0.14258 6.0837 –7.365 60.161 125 126 D1 Calculation Methods for Thermophysical Properties D1. Table 2. (continued) DT Dp Dv DNBP DH DG CH2SH 13.8058 0.013572 0.10252 3.2914 –8.253 16.731 I 17.3947 0.002753 0.10814 3.6650 57.546 46.945 Br 10.5371 –0.001771 0.08281 2.6495 1.834 –1.721 7.5433 0.014827 0.09331 2.3678 220.803 217.003 Structural group CHC 11.4501 0.004115 0.07627 2.5645 227.368 216.328 Cl- (attached to >C=C< ) CC 5.4334 0.016004 0.05687 1.7824 –36.097 –28.148 ACF 2.8977 0.013027 0.05672 0.9442 –161.740 –144.549 –679.195 –626.580 2.6446 –313.545 –281.495 2.8881 –258.960 –209.337 1.9163 –446.835 –392.975 HCON(CH2)2 7.2644 CF3 2.4778 0.044232 0.11480 CF2 1.7399 0.012884 0.09519 CF 3.5192 0.004673 COO 12.1084 0.011294 0.08588 CCl2F 9.8408 0.035446 0.18212 F CONH2 0.6115 1.1739 HCClF CClF2 1.2880 2.3086 4.8923 0.039004 0.14753 1.5974 0.014434 0.03783 1.0081 –223.398 –212.718 65.1053 0.004266 0.14431 10.3428 -203.188 –136.742 CONHCH3 –67.778 –182.096 CONHCH2 CON(CH3)2 36.1403 0.040149 0.25031 7.6904 CONCH3CH2 –65.642 –46.562 CON(CH2)2 C2H5O2 –189.888 6.7822 17.9668 0.025435 0.16754 5.5566 CH3S 14.3969 0.016048 0.13021 CH2S 17.7916 0.011105 0.11650 C2H4O2 –344.125 –241.373 3.6796 –2.084 30.222 3.6763 18.022 38.346 5.4248 CHS 2.6812 C4H3S 5.7093 C4H2S 5.8260 The critical data can be calculated to be: Tc ¼ 181:128 K ln 31:3608 ¼ 624:09 K pc ¼ ½ð0:10022 þ 0:068888Þ2 þ 1:3705 bar ¼ 36:34 bar vc ¼ ð0:37588 0:00435Þ m3 =kmol ¼ 0:37153 m3 =kmol (c) Method of Constantinou/Gani with toluene as reference substance The critical data of toluene are: Tc ¼ 591:75 K; pc ¼ 41:1 bar; vc ¼ 0:3156 m3 =kmol A backwards calculation to obtain the group contributions of toluene (Fig. 2) yields: X DT;toluene ¼ expð591:75=181:128Þ ¼ 26:233 X Dp;toluene ¼ ð41:1 1:3705Þ0:5 0:10022 ¼ 0:05843 X Dv;toluene ¼ 0:3156 0:00435 ¼ 0:31125 The difference in the structural formulas of toluene and m-xylene is that one ACH group has to be replaced by an ACCH3 group. Thus, the group contributions for m-xylene can be determined to be: X DT ¼ 26:233 ð3:7337Þ þ ð8:213Þ ¼ 30:7123 X Dp ¼ 0:05843 ð0:007542Þ þ ð0:01936Þ ¼ 0:070248 X Dv ¼ 0:31125 ð0:04215Þ þ ð0:10364Þ ¼ 0:37274 Therefore, the critical data can be estimated: Tc ¼ 181:128 K ln 30:7123 ¼ 620:3 K pc ¼ ½ð0:10022 þ 0:070248Þ2 þ 1:3705 bar ¼ 35:78 bar vc ¼ ð0:37274 0:00435Þ m3 =kmol ¼ 0:36839 m3 =kmol The experimental values for m-xylene are: Tc ¼ 617:05 K pc ¼ 35:4 bar vc ¼ 0:37516 m3 =kmol For all the three calculation options, the agreement between estimated and experimental values is remarkably good. The check of the critical compressibility factor yields Calculation Methods for Thermophysical Properties D1 D1. Table 3. Constantinou/Gani group contributions for second-order groups Structural group DT Dp Dv DNBP DH (CH3)2–CH –0.5334 0.000488 0.00400 –0.1157 –0.860 0.297 (CH3)3–C –0.5143 0.001410 0.00572 –0.0489 –1.338 –0.399 CH(CH3)CH(CH3) 1.0699 –0.001849 –0.00398 0.1798 6.771 6.342 CH(CH3)C(CH3)2 1.9886 –0.005198 –0.01081 0.3189 7.205 7.466 C(CH3)2–C(CH3)2 5.8254 –0.013230 –0.02300 0.7273 14.271 16.224 3-membered ring –2.3305 0.003714 –0.00014 0.4745 104.800 94.564 4-membered ring –1.2978 0.001171 –0.00851 0.3563 99.455 92.573 5-membered ring –0.6785 0.000424 –0.00866 0.1919 13.782 5.733 6-membered ring 0.8479 0.002257 0.01636 0.1957 –9.660 –8.180 7-membered ring 3.6714 –0.009799 –0.02700 0.3489 15.465 20.597 CHn=CHm–CHp=CHk 0.4402 0.004186 –0.00781 0.1589 –8.392 –5.505 CH3–CHm=CHn 0.0167 –0.000183 –0.00098 0.0668 0.474 0.950 0,1,2 CH2–CHm=CHn –0.5231 0.003538 0.00281 –0.1406 1.472 0.699 0,1,2 CH–CHm=CHn or C–CHm=CHn –0.3850 0.005675 0.00826 –0.0900 4.504 1.013 0,1,2 Ccyclic – Cm (C-chain attached to ring) 2.1160 –0.002546 –0.01755 0.0511 1.252 1.041 m>1 CH3CH3 2.0427 0.005175 0.00227 0.6884 –2.792 –1.062 CHCHO or CCHO DG –1.5826 0.003659 –0.00664 –0.1074 –2.092 –1.359 CH3COCH2 0.2996 0.001474 –0.00510 0.0224 0.975 0.075 CH3COCH or CH3COC 0.5018 –0.002303 –0.00122 0.0920 4.753 Ccyclic(=O) 2.9571 0.003818 –0.01966 0.5580 14.145 23.539 ACCHO 1.1696 –0.002481 0.00664 0.0735 –3.173 –2.602 –1.7493 0.004920 0.00559 0.1552 1.279 2.149 10.715 CHCOOH or CCOOH ACCOOH Values for k,l,m,n,p 0,1,2 6.1279 0.000344 –0.00415 0.7801 12.245 –1.3406 0.000659 –0.00293 –0.2383 –7.807 –6.208 2.5413 0.001067 –0.00591 0.4456 37.462 29.181 CO–O–CO –2.7617 –0.004877 –0.00144 –0.1977 –16.097 –11.809 ACCOO –3.4235 –0.000541 0.02605 0.0835 –9.874 –7.415 CHOH –2.8035 –0.004393 –0.00777 –0.5385 –3.887 –6.770 COH –3.5442 0.000178 0.01511 –0.6331 –24.125 –20.770 CHm(OH)CHn(OH) 5.4941 0.005052 0.00397 1.4108 0.366 3.805 CHm(cyclic)–OH 0.3233 0.006917 –0.02297 –0.0690 –16.333 –5.487 0,1 CHm(OH)–CHn(NHp) 5.4864 0.001408 0.00433 1.0682 –2.992 –1.600 0,1,2,3 CHm(NH2)–CHn(NH2) 2.0699 0.002148 0.00580 0.4247 2.855 1.858 0,1,2 CHm(cyclic)–NHp–CHn(cyclic) 2.1345 –0.005947 –0.01380 0.2499 0.351 8.846 0,1,2 CHm–O–CHn=CHp 1.0159 –0.000878 0.00297 0.1134 –8.644 –13.167 –5.3307 –0.002249 –0.00045 –0.2596 1.532 –0.654 0.4408 –0.329 –2.091 –0.1168 CH3COOCH or CH3COOC COCH2COO, COCHCOO or COCCOO AC–O–CHm CHm(cyclic)–S–CHn(cyclic) 4.4847 CHm=CHn–F –0.4996 0.000319 –0.00596 CHm=CHn–Br –1.9334 –0.004305 0.00507 CHm=CHn–I ACI –2.2974 0.009027 –0.00832 –0.6776 2.8907 0.008247 –0.00341 –0.3678 CHm(NH2)–COOH 35:4 105 0:37516 103 ¼ 0:259 8:3143 617:05 11.989 which is a reasonable value between 0.21 and 0.29. 0,1,2 12.373 0,1,2 0,1,2 12.285 14.161 11.207 12.530 11.740 3.2 0,1,2 0,1,2,3 0,1,2 –0.4453 ACBr Zc ¼ –0.3201 0,1,2 0,1,2 Acentric Factor The simple 2-parameter principle of corresponding states says that it is possible to set up a generalized equation of state valid 127 128 D1 Calculation Methods for Thermophysical Properties D1. Fig. 3. Structural formula of pentyl cyclohexane. D1. Fig. 1. Structural formula of m-xylene. and hydrogen (o = 0.216), the so-called quantum gases, have negative acentric factors. Methane and the noble gases argon, krypton, xenon, and neon have values that are near zero. In other cases, o 0 can strictly be excluded. If a value like this is evaluated, the conclusion must be that the vapor pressure curve or the critical point or both of them are wrong. 3.3 Normal Boiling Point D1. Fig. 2. Structural formula of toluene. for all substances with only two specific parameters, for example, Tc and pc. The success of this approach was limited to simple, spherical molecules like Ar, Kr, Xe, or CH4, where vapor pressure and compressibility factor could be adequately reproduced. For other molecules, the 2-parameter principle of corresponding states yielded results with considerable deviations. Therefore, it was replaced by the extended 3-parameter principle of corresponding states, where a third parameter has been introduced, which gives additional information about the vapor pressure line. The most popular parameter of this kind is the acentric factor o, which is defined as ps ð8Þ o ¼ 1 log10 pc T=Tc ¼0:7 Physically, o takes into account the influence of the intermolecular forces depending on the orientation of the molecules. The parameter is used in many correlations for the estimation of thermophysical properties. Especially, o is decisive for the application of cubic equations of state (Sect. 4.2). The definition given in Eq. (8) makes sense, as the vapor pressure is a quantity with high significance and accessibility. The reference temperature T = 0.7 Tc has been chosen because it is often in the neighborhood of the normal boiling point. An estimation of o is therefore equivalent to an estimation of the vapor pressure curve or, respectively, the normal boiling point. Although estimation methods for the acentric factor are available (e.g., group contribution method of Constantinou/ Gani [5]), this concept is not recommended in this transaction, as it is, as mentioned above, a redundancy to the estimation of the normal boiling point. To avoid inconsistencies, it is instead recommended to evaluate o directly via the definition Eq. (8) from the vapor pressure equation. If a vapor pressure equation is not available at all, it is still possible to estimate the normal boiling point (Sect. 3.3) and the critical point (Sect. 3.1) and to determine the vapor pressure curve as described in Sect. 5. The acentric factor increases with the size of the molecule. Only in single cases, values o > 1 occur. Helium (o = 0.39) The normal boiling point is an easily accessible property and well known for a wide variety of substances. Even values from chemical catalogues, safety datasheets, or from the Internet (e.g., www.nist.gov) can give reasonable values, although highprecision data should not be expected. In case no information is available, the normal boiling point (NBP) can be estimated using the methods of Joback [2] or Constantinou/Gani [3], analogously to the estimation of the critical temperature. The corresponding relationships are: Joback: TNBP =K ¼ 198 þ X DNBP ð9Þ Constantinou/Gani: exp X X TNBP ¼ DNBP;i þ DNBP;j 204:359 K i j ð10Þ The corresponding group contributions can again be taken from Tables 1, 2 and 3. In both cases, the accuracy is much lower than for the estimation of the critical data. As for the critical data, the possibility of taking a reference substance with a similar structure can be made use of. Because of the high uncertainties of the normal boiling point estimation, this procedure is strongly recommended if possible to avoid large errors. Example 2: Estimate the normal boiling point of pentyl cyclohexane (Fig. 3). (a) Joback method The group assignment of pentyl cyclohexane is: 5 CH2 (ring) 1 CH (ring) 1 CH3 4 CH2 The group contribution can be added up to: X DNBP ¼ 5 ð27:15Þ þ 1 ð21:78Þ þ 1 ð23:58Þ þ 4 ð22:88Þ ¼ 272:63 Calculation Methods for Thermophysical Properties Thus, the normal boiling point is calculated to be: TNBP ¼ ð198 þ 272:63Þ K ¼ 470:63 K (b) Method of Constantinou/Gani The group assignment of pentyl cyclohexane is: 9 CH2 1 CH3 1 CH As second-order groups can be assigned: 1 6 membered ring 1 C-chain attached to ring The sum of the group contributions is: X DNBP ¼ 9 ð0:9225Þ þ 1 ð0:8894Þ þ 1 ð0:6033Þ þ 1 ð0:1957Þ þ 1 ð0:0511Þ ¼ 10:042 The normal boiling point is determined to be: TNBP ¼ 204:359 K ln 10:042 ¼ 471:41 K (c) Joback method with methyl cyclohexane as reference substance The normal boiling point of methyl cyclohexane (Fig. 4) is: TNBP ¼ 373:95 K: To evaluate the sum of group contributions for methyl cyclohexane, a backward calculation yields: X DNBP;Methylcyclohexan ¼ 373:95 198 ¼ 175:95 The difference in the structural formulas of pentyl cyclohexane and methyl cyclohexane is that four aliphatic CH2-groups have been added. In this way, the sum of group contributions for pentyl cyclohexane can be determined to be: X DNBP ¼ 175:95 þ 4 ð22:88Þ ¼ 267:47 Thus, what is obtained for the normal boiling point is: TNBP ¼ ð198 þ 267:47Þ K ¼ 465:47 K (d) Methode of Constantinou/Gani with methyl cyclohexane as reference substance The normal boiling point of methyl cyclohexane is: TNBP ¼ 373:95 K: D1 The difference in the structural formulas of pentyl cyclohexane and methyl cyclohexane is that four aliphatic CH2-groups have been added. Moreover, the contribution of the second-order group ‘‘C-chain attached to ring’’, which is only valid for m > 1, has to be supplemented. In this way, the sum of group contributions for pentyl cyclohexane can be evaluated to be: X DNBP ¼ 6:233 þ 4 ð0:9225Þ þ 0:0511 ¼ 9:9741 Thus, the result for the normal boiling point is: TNBP ¼ 204:359 K ln 9:9741 ¼ 470:02 K The experimental value for pentyl cyclohexane is: TNBP = 476.75 K. All the methods shown above yield a reasonable result. Again, the use of a reference substance does not necessarily guarantee a better result, but it lowers the probability of a large error. A new recommendable method for the estimation of the normal boiling point has been developed by Rarey et al. [6]. However, its group assignment is somewhat more complicated. 3.4 Melting Point and Enthalpy of Fusion Besides normal boiling point and liquid density at 20 C, the melting point is the thermophysical property which can be found most frequently and is often found in chemical catalogues and handbooks. The estimation of melting points is a very complex task, as is determined both by the enthalpy of fusion, which depends on intermolecular forces, and by the entropy of fusion, which is a function of the symmetry of the molecule. Therefore, the applicability of group contribution methods is limited, as information about the molecular symmetry is lost if a group contribution concept is applied. Joback [2] lists, in fact, group contributions for the melting point; however, the average error is expected to be more than 20 K even for simple molecules, which is not acceptable for practical applications. The enthalpy of fusion itself depends partly on the crystalline form that is transformed into a liquid, which can hardly be expressed in terms of mathematics for complex substances. In principle, the Clausius-Clapeyron equation can be applied, but information on the pressure dependence of the melting point is also usually missing. For aromatic compounds like benzene and naphthalene derivatives, the Walden rule [6, 7] can be applied: e Dhm ðTm Þ=Tm M 13 cal: K1: mol1 ¼ 54:4 J: mol1: K1 ð11Þ For the group contributions of methyl cyclohexane, a backward calculation yields: X DNBP;Methylcyclohexan ¼ expð373:95=204:359Þ ¼ 6:233 3.5 D1. Fig. 4. Structural formula of methyl cyclohexane. The enthalpy of formation Dh0f and the Gibbs energy of formation Dg0f are decisive for the calculation of enthalpies of reaction and chemical equilibria. For heat exchange calculations of chemical reactors, they are relevant as well, as these quantities determine the maximum possible product temperature or the heat to be removed. The reference state for Dh0f and Dg0f is T0 = 298.15 K and p0 = 1 atm in the ideal gas state. In process simulation, the enthalpy of formation is also taken as the reference state for the calculation of enthalpies Standard Enthalpy of Formation and Gibbs Energy of Formation 129 130 D1 Calculation Methods for Thermophysical Properties (Sect. 6.4), so that these enthalpies are then consistent if chemical reactions are considered. Further explanations, especially for the switch to liquid and solid phases, can be found in the textbook of J. Gmehling and B. Kolbe [8]. In both cases, the problem of the difference of large numbers has to be taken into account. Small relative deviations of Dh0f or Dg0f can cause severe errors when differences are calculated. Therefore, estimation methods for these quantities must be taken as rough numbers for orientation. Analogously to the estimation of the critical data, the methods of Joback and Constantinou/Gani are recommended. The equations for calculation are: Joback [2]: X Dh0f ¼ 68:29 þ DH kJ=mol X Dg 0f ¼ 53:88 þ DG kJ=mol ð12Þ ð13Þ Constantinou/Gani [3]: X X Dh0f ¼ DH;i þ DH;j þ 10:835 kJ=mol i j ð14Þ X X Dg 0f ¼ DG;i þ DG;j 14:828 kJ=mol i j ð15Þ Example 3: Determine the enthalpy of formation and the Gibbs energy of formation for ethyl acetate with the Joback method (structural formula in Fig. 7).The group assignment of ethyl acetate is 2 CH3 1 CH2 1 COO Thus, one gets for the group contributions: X DH ¼ 2 ð76:45Þ þ 1 ð20:64Þ þ 1 ð337:92Þ ¼ 511:46 DG ¼ 2 ð43:96Þ þ 1 ð8:42Þ þ 1 ð301:95Þ ¼ 381:45 The values finally obtained are: Dh0f ¼ 68:29 511:46 ¼ 443:17 kJ=mol Dg 0f ¼ 53:88 381:45 ¼ 327:57 kJ=mol The values obtained from databanks are Dh0f = 444.5 kJ/mol and Dg0f = 328 kJ/mol. The excellent agreement can be explained by the fact that ethyl acetate is very well known from esterification reactions. 3.6 Dipole moment Substance Formula Hydrogen chloride HCl (m/10–30 Cm) Debye 3.44 1.03 Carbon monoxide CO 0.40 0.12 Carbon dioxide CO2 0.00 0.00 Water H2O 6.00 1.80 Ammonia NH3 4.97 1.49 Methane CH4 0.00 0.00 Ethanol C2H6O 5.67 1.70 Benzene C6H6 0.00 0.00 Chlorobenzene C6H5Cl 5.90 1.77 Nitrobenzene C6H5NO2 13.40 4.02 according to the geometry of the molecule. In the simplest case, this can be described as an electric dipole, which consists of two charges q of the same magnitude but with opposite sign, where the distance between them is r. The product of charge q and distance r is called dipole moment m: m ¼ rq where the second-order group concept is again applied. The group contributions for both methods can be found in Tables 1, 2 and 3. X D1. Table 4. Some numbers for the dipole moment Dipole Moment For polyatomic molecules containing atoms with different electronegativity, the charge distribution can be asymmetric ð16Þ As the charges are smaller than the elementary charge, that is, approximately 1020 C, and the distances like an atom, that is, 1010 m, the order of magnitude of dipole moments is 1030 m. Usually, the unit debye is used: 1 debye = 3.3356 · 1030 Cm. Some values are given in Table 4. For complex molecules, higher electrical moments may occur, for example, the quadrupolar moment, which consists of two pairs of charges with opposite sign. Dipole moments can be determined by measurement of the electric capacity or by molecular simulations. 4 Density 4.1 Density of Liquids The density of liquids is one of the most important quantities for equipment design. There are considerable demands on the accuracy. Simple equations of state do usually not fulfill these requirements; therefore, direct correlations for the liquid density on the saturation line are used. The most popular one is the Rackett equation rliq A ¼ ð17Þ kg=m3 B1þð1TC=K ÞD Currently, the PPDS equation " rliq rc T 0:35 T 2=3 ¼ þ A 1 þB 1 kg=m3 kg=m3 Tc Tc 4=3 # T T þC 1 þD 1 Tc Tc ð17aÞ is considered to be the most precise one. For this correlation, coefficients for approximately 270 substances are given in > Subchap. D3.1. Calculation Methods for Thermophysical Properties For the estimation of liquid densities or, respectively, specific liquid volumes on the saturation line, the COSTALD equation [9] has been widely applied: h i ð0Þ ðdÞ vs ¼ e ð18Þ r1 ¼ v vR 1 o vR ð0Þ vR ¼ 1 þ að1 Tr Þ =3 þ bð1 Tr Þ =3 þ c ð1 Tr Þ 1 ðdÞ þ d ð1 Tr Þ =3 ; 0:25 < Tr < 0:95 ¼ e þ fTr þ gTr2 þ hTr3 =ðTr 1:00001Þ; 0:25 < Tr < 1:0 Tr ¼ T =Tc ð19Þ ð20Þ ð21Þ where a ¼ 1:52816; b ¼ 1:43907; d ¼ 0:190454; g ¼ 0:0427458; e ¼ 0:296123; f ¼ 0:386914; h ¼ 0:0480645 At moderate pressures up to approximately 5 bar, the ideal gas law e pv ¼ RT ð0Þ vR ¼ 0:3799 ðdÞ vR ¼ 0:2277 vs ¼ 130:99 cm3 =mol ) rliq ¼ 657:9 kg=m3 The value given in the literature is 659 kg/m3. For a first approximation, liquids can be regarded as incompressible. If the pressure dependence plays a major role, the application of high-precision equations of state [1] would be desirable. If such an equation is not available, some equations for estimation are given in [2]. The evaluation of the density of liquid mixtures should be performed via the linear mixing rule for the specific volume: X e ð22Þ xi vi vmix ¼ i ¼ X i e aðT Þ RT 2 v b v þ 2bv b2 ð25Þ e aðT Þ RT v b v 2 þ bv ð26Þ Soave-Redlich-Kwong: p¼ It can be shown by mathematical rearrangement that these equations can be reduced to the search for the roots of a cubic function of the specific volume. In the subcritical region, they can deliver three real solutions for a given temperature and pressure, where the smallest solution describes the liquid phase and the largest solution represents the vapor phase. Nevertheless, the cubic equations are not suitable for the calculation of liquid densities, as long as no additional terms have been introduced into the equation [12]. The middle solution has no physical meaning. Above the critical point and at pressures far below saturation one gets one real and two complex solutions, where the real solution describes the fluid phase. The particular solutions can be obtained by application of the Cardanic formula [13] or by iteration. To evaluate gas densities with the PR or the SRK equation, critical temperature, critical pressure and acentric factor have to be known. Using the reduced temperature Tr = T/Tc, the following relationships can be set up: Peng-Robinson: aðT Þ ¼ ac aðT Þ 2 aðT Þ ¼ 1 þ 0:37464 þ 1:54226o 0:26992o2 1 Tr0:5 e 2 Tc2 R ac ¼ 0:45724 ð25aÞ pc e c RT b ¼ 0:0778 pc Soave-Redlich-Kwong: !1 xi r1 liq;i can be used for the calculation of gas phase densities of nonassociating compounds with sufficient accuracy. At higher pressures, the cubic equations of state like PengRobinson [10] (PR) and Soave-Redlich-Kwong [11] (SRK) are well-suited for nonassociating compounds, as they are sufficiently accurate and comparably easy to apply. The equations are derived from the van der Waals equation and can be written as follows: p¼ Example 4: Estimate the liquid density of n-hexane at T = 293.15 K with the COSTALD method: The given data are: Tc = 507.5 K v∗ = vc = 370 cm3/mol o = 0.299 M = 86.18 g/mol Using Eqs. (18)–(21), one can obtain: or, respectively: ð24Þ Peng-Robinson: c ¼ 0:81446; The characteristic volume v∗ is an adjustable parameter which can be fitted to one or more experimental data points. If no information is available, it is useful to replace it by the critical volume vc, which often yields reasonable results. rmix liq Density of Gases 2 4 vR 4.2 D1 ð23Þ Equation (22) is not exact, as the mixture influence, the so-called excess volume, is neglected. However, the error of Eq. (22) can hardly be larger than 2–3%. aðT Þ ¼ ac aðT Þ aðT Þ ¼ 1 þ 0:48 þ 1:574o 0:176o2 1 Tr0:5 e 2 Tc2 R ac ¼ 0:42748 pc e c RT b ¼ 0:08664 pc 2 ð26aÞ 131 132 D1 Calculation Methods for Thermophysical Properties If these equations are applied to mixtures, the parameters can be calculated via the mixing rules XX 0:5 e amix ¼ yi e yj aii ajj ð1 kij Þ ð27Þ i j bmix ¼ X e yi bi ð28Þ i The binary parameters kij can be set to zero as long as phase equilibria are not involved (Part D). For the calculation of vapor densities, their influence is negligible. Example 5: Determine the vapor density of R22 (chlorodifluoromethane) at T = 301.15 K, p = 11.308 bar using the Peng-Robinson equation. The following input data are given: Tc = 369.28 K pc = 49.88 bar o = 0.221 e ¼ 86:47 g=mol M Thus, one gets the following coefficients: að301:15 KÞ ¼ 1 þ 0:37464 þ 1:54226 0:221 0:26992 0:2212 2 1 ð301:15=369:28Þ0:5 ¼ 1:1408 8:31432 369:282 Pa m6 Pa m6 ¼ 0:864133 2 5 49:88 10 mol mol2 3 3 8:3143 369:28 m m ¼ 4:789 105 b ¼ 0:0778 mol 49:88 105 mol Pa m6 að301:15 K Þ ¼ aað301:15 KÞ ¼ 0:98581 mol2 ac ¼ 0:45724 The Peng-Robinson equation can be rearranged to ap p2 b2 pb 3 2 bp f ðZÞ ¼ Z þ Z 3 2 1 þZ e2T 2 e e2T 2 e R RT R RT 3 3 2 2 2 p b p b abp þ ¼0 þ e3 T 3 R e2T 2 R e3T 3 R ð29Þ with Z as the compressibility factor Z = pv/(RT). For this example, one gets: f ðZÞ ¼ Z 3 0:978372 Z 2 þ 0:133153 Z 0:003368 ¼ 0 In this example, the calculation procedure is as follows, starting with an estimated value of Z0 = 1 (ideal gas): Z0 ¼ 1 Z1 ¼ 0:87129 Z2 ¼ 0:82686 Z3 ¼ 0:82131 Z4 ¼ 0:82123 f ðZ0 Þ ¼ 0:15141 f ðZ1 Þ ¼ 0:03136 f ðZ2 Þ ¼ 0:00314 f ðZ3 Þ ¼ 4:606:105 f ðZ3 Þ ¼ 1:043:108 f 0 ðZÞ ¼ 3 Z 2 1:956744 Z þ 0:133153 The compressibility factor can then iteratively be determined either with the Cardanic formula or iteratively with Newton’s method, where f and f 0 are evaluated with an estimated value for Z. As long as the results for Z and the estimated value do not sufficiently agree, the calculation is repeated with a new estimated value Znþ1 ¼ Zn f ðZÞ f 0 ðZÞ Z1 ¼ 0:87129 Z2 ¼ 0:82686 Z3 ¼ 0:82123 Z4 ¼ 0:82123 Z4 ¼ 0:82123 o:k: The final result Z = 0.82123 corresponds to a specific volume v = 0.0018184 m3/mol and a density r = 47.55 kg/m3. The value obtained from a high precision equation of state is r = 48.02 kg/m3, corresponding to v = 0.001801 m3/mol and Z = 0.81326. Strongly polar and associating substances show large deviations from the ideal gas behavior even at low pressures, which is not in line with the cubic equations of state. The reason for this deviation is the formation of dimers or higher associates in the vapor phase. In these cases, the chemical theory [8] is a good tool for the description of the vapor phase nonidealities. Its main assumption is that the association is comparable to a chemical reaction. Normally, it is sufficient to regard only the formation of dimers, as it is the case for carboxylic acids. An exception is hydrogen fluoride, where hexamers are formed. Besides the overall mole fraction e y , a true mole fraction e z is defined, which considers the particular associates as own species. For the formation of dimers (D) from monomers (M) the following reaction can be defined: 2Mi ! Dii The equilibrium of this reaction can be described with the law of mass actions: KD ¼ fD fD0 ð fM =fM0 Þ 2 ð30Þ using the standard fugacity fD0 ¼ fM0 ¼ f 0 ¼ 1 bar ð31Þ The fugacity of a component i can be expressed with the fugacity zi and the pressure p: coefficient ’i , the true mole fraction e fi ¼ e zi ’ i p ð32Þ Thus, the equilibrium constant is given by: KD ¼ with the derivation f 0 ðZ0 Þ ¼ 1:17641 f 0 ðZ1 Þ ¼ 0:70571 f 0 ðZ2 Þ ¼ 0:56629 f 0 ðZ3 Þ ¼ 0:54971 f 0 ðZ3 Þ ¼ 0:54946 e z D ’D f 0 e zM2 ’2M p ð33Þ Values for KD can be obtained by the measurement of vapor densities and vapor heat capacities. KD depends on the temperature and can be correlated by B f0 ð34Þ ln KD ¼ A T bar In Table 5, some constants A and B for carboxylic acids are listed. Furthermore, for the calculation of the true mole fractions of monomers and dimers the fugacity coefficients are necessary. At low pressures, the behavior of the particular species can be Calculation Methods for Thermophysical Properties D1. Table 5. Equilibrium constants for vapor phase association Substance Formula A / bar–1 B/K bar–1 –7099 Formic acid HCOOH –18.117 Acetic acid CH3COOH –17.374 –7290 Propionic acid CH3–CH2–COOH –18.347 –7635 Butanoic acid CH3–CH2–CH2–COOH –16.636 –7000 considered to be ideal, that is, ’M ¼ ’D ¼ 1. With this assumption, one gets: KD p e zD KD ¼ 0 ¼ 2 e zM f ð35Þ As the sum of the true mole fractions must be 1 e zM ¼ 1 zD þ e ð36Þ one gets for given temperature and pressure 2 e KD ¼ 1 e zM zM or, respectively, e zM ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 þ 4KD 1 2KD ð37Þ ð38Þ The specific volume can then be determined by v¼ e e 1 M RT ¼ zD zM þ 2 e r p e ð39Þ Example 6: Calculate the vapor density of acetic acid (AA) at the normal boiling point (TNBP = 391.35 K). Given data: Association constants: A = 17.374 bar1, B = 7290 K bar1 Standard fugacity f 0 = 1bar e AA ¼ 60:05 g=mol M The results are: KD = 3.504 KD* = 3.55 e zM ¼ 0:408 e zD ¼ 0:592 and finally, for the specific volume: v¼ e 8:3143 391:35 1 M m3 =mol ¼ 101325 0:408 þ 2 0:592 r ¼ 0:0202 m3 =mol ) r ¼ 2:977 kg=m3 This result is in line with experimental values and exceeds the result obtained with the ideal gas equation by approximately 60%. 4.3 Coefficient of Thermal Expansion The coefficient of thermal expansion b is defined as 1 Dv b¼ v DT ð40Þ At standard conditions (273.15 K, 1.01325 bar), the coefficient of thermal expansion for ideal gases is 1 b ¼ 1=273:15K : D1 Example 7: At p = 1.013 bar and T = 273.15 K, the specific volume of helium is 0.02242 m3/mol. To which extent will the specific volume increase, if the gas is heated up by DT = 100 K? Dv ¼ v 5 1 DT ¼ 0:008207m3 =mol 273:15 K Vapor Pressure For many process calculations, the vapor pressure is the most important quantity. It is decisive for the determination of the number of separation stages of distillation columns and for the evaluation of temperature profiles in general. Therefore, data should be carefully searched, measured and correlated. Additionally, a good vapor pressure curve is helpful for the estimation of other thermophysical properties, especially of the enthalpy of vaporization (Sect. 6.1). Good data points for the vapor pressure should be correlated with deviations considerably less than 1%, the average deviation of a good data set should be by far less than 0.5%. Values with deviations greater than 1% should be regarded as outliers and removed from the database, as long as enough other data points are available. Exceptions are values below approximately 1 mbar, as their accuracy is much lower. It is recommended to set their weighting factor in the regression to 0 but keep an eye on the correct order of magnitude, when the vapor pressure curve is extrapolated to low temperatures. Vapor pressure curves are strictly monotonically increasing. They exist between triple point and critical point of a particular substance, where a vapor–liquid equilibrium is possible. For the description of vapor pressures several equations are available. The most frequently used one is the Antoine equation with three adjustable parameters ln ps B ¼Aþ Pa T þC ð41Þ It is appropriate for the reproduction of data sets within a certain temperature range. For thermodynamic reasons, both B and C must have a negative sign. There are many different notations in the literature, which has always to be taken into account. The Antoine equation (41) is well-known for its bad extrapolation behavior. The temperature range from the triple point to the critical point cannot be covered with sufficient accuracy. Often two equations are given for vapor pressures below and above 1 atm; however, such an approach usually implies a discontinuity in the junction point. There is a singularity at T = C, and in the vicinity of this point the application of the Antoine equation does not make sense. The Wagner equation [14] ln ps 1 ¼ Að1 Tr Þ þ Bð1 Tr Þ1:5 þC ð1 Tr Þ3 þDð1 Tr Þ6 pc T r ð42Þ with Tr ¼ T =Tc ð42aÞ 133 134 D1 Calculation Methods for Thermophysical Properties can describe the whole temperature range from the triple point to the critical point and should be applied for the precise adjustment of good data in sufficient quantity. The correct reproduction of the critical point is ensured by the mathematical form of Eq. (42). The only weakness of the equation is the extrapolation to low temperatures. In most cases, the ranges of the coefficients are A ¼ 9 ::: 5 B ¼ 10 :::10 C ¼ 10 :::10 C ¼ 20 :::20 If these conditions are not fulfilled, a critical check of the data should take place, especially for the critical point used. Further constraints and many good parameter sets have been set up by McGarry [15]. In the recent years, the so-called 3-6-form (Eq. (42); the numbers refer to the exponents of the last two terms) has mostly been replaced by the 2.5-5-form, which is considered to be slightly more accurate: ps 1 Að1 Tr Þ þ Bð1 Tr Þ1:5 þC ð1 Tr Þ2:5 ln ¼ pc T r ð42cÞ þDð1 Tr Þ5 The reasonable ranges for the coefficients stay the same. For Eq. (42c), coefficients for 275 substances are given in > Subchap. D3.1. The estimation of vapor pressures is one of the most difficult problems in thermodynamics. There are several methods based on the 3-parameter principle of corresponding states or group contributions [16–18]. A new method developed by Rarey et al. [19] yields good results but is difficult to apply. One of the most reliable methods is the application of the vapor pressure curve of Hoffmann-Florin [20], which has only two adjustable parameters: ps ð43Þ ln ¼ A þ B f ðT Þ Pa with f ðT Þ ¼ 1 T 7:9151 103 þ 2:6726 103 log10 T =K K T 0:8625 106 K ð43aÞ The equation can be fitted to two or more experimental data points. As a correlation equation it is not very accurate, but its extrapolation behavior is supposed to be quite good. Especially, it is superior to the widely used simplified Antoine equation with C = 0 in Eq. (41). If only one or, in the extreme case, no data point is available, normal boiling point and/or critical point can be estimated, and the parameters A and B can be adjusted to these artificial data. It should be emphasized that the two points for adjustment must be far away from each other to obtain significant coefficients. For two arbitrarily given data points of the vapor pressure curve (T1,ps1), (T2,ps2), the coefficients of the Hoffmann-Florin equation can be determined to be A ¼ ln ps1 ps1 f ðT1 Þ ln Pa ps2 f ðT1 Þ f ðT2 Þ ð44Þ B¼ lnðps1 =ps2 Þ f ðT1 Þ f ðT2 Þ ð45Þ Because of the exponential relationship between vapor pressure and temperature, a high accuracy in the estimation of vapor pressures should not be expected. Deviations of 5% have to be regarded as excellent. For the assessment of a vapor pressure estimation method, the number of substances where the method yields completely unusable results is decisive. In this context, especially, the method described above has considerable advantages in comparison with several group contribution methods. Example 8: Estimate the vapor pressure of chloroform at t = 41.7 C, t = 4.5 C, and t = 120.1 C. Using the Joback method, the estimated values for normal boiling point and critical point are: TNBP = 334.13 K (true value: 334.26 K) Tc = 532.11 K (true value: 536.45 K) pc = 49.8 bar (true value: 55.54 bar) With T1 = 334.13 K ps1 = 1.01325 bar T2 = 532.11 K ps2 = 49.8 bar we get A = 19.5596 B = 5233.61 The results are: ps(41.7 C) = 5.69 mbar ps(4.5 C) = 99.94 mbar ps(120.1 C) = 5.18 bar The values calculated with the Wagner equation (> Subchap. D3.1) are ps = 5.04 mbar (t = 41.7 C), ps = 100 mbar (t = 4.5 C), and ps = 5.01 bar (t = 120.1 C). As in this case, the quality of the normal boiling point or another reference value is usually decisive. The relatively large error in the critical pressure does not have a large influence in this example. The estimation of vapor pressures of mixtures does not make sense physically, as the concentrations of the vapor and liquid are different. Moreover, boiling point and dew point of a mixture are not identical. Azeotropic mixtures are often treated as a pure substance, but even this is only valid within a certain temperature range, as the azeotropic composition is temperaturedependent. The vapor–liquid equilibria of mixtures are explained in > Subchap. D5.1. 6 Enthalpy Determination Enthalpies are the key quantity for heat transfer problems, as the difference of the enthalpies of the particular streams determines the energy balance of the process and therefore the state of the outlet streams. Enthalpy changes can be caused: ● By a phase change. The most important one is the vapor– liquid transition, which is determined by the enthalpy of vaporization. ● By heating or cooling of a homogeneous phase. In this case, the most important quantity is the heat capacity of the particular phase. Calculation Methods for Thermophysical Properties ● By pressure change of a phase, which is, however, only relevant for gases. ● By mixing or separating mixture components. ● By chemical reaction. All of these processes can run in parallel, for example, in a heat exchanger with high pressure drop. Therefore, a thermodynamically consistent enthalpy description, which connects the vapor and the liquid region, is needed. This enthalpy is then calculated using the standard enthalpy of formation as the starting point to make the enthalpy consistent with respect to chemical reactions, the specific heat capacities of liquid and ideal gas, the enthalpy of vaporization, and the real gas correction. The difficulty is that the two heat capacities are not independent from each other and can be calculated in different ways. The consequences are explained in Sect. 6.5. 6.1 Enthalpy of Vaporization In Fig. 5, typical curvatures of the enthalpy of vaporization as a function of temperature are given. It is a strictly monotonic decreasing function, at low temperatures with a small slope, at high temperatures with an increasing slope. At the critical point, vapor and liquid become identical, and the enthalpy of vaporization approaches zero. A different curvature is shown by substances with association in the vapor phase, where a more or less well-defined maximum occurs (e.g., formic acid in Fig. 5). Enthalpies of vaporization can be very well correlated with the extended Watson equation 2 3 Dhv ¼ A ð1 Tr ÞBþCTr þDTr þETr J=kg ð46Þ with Tr ¼ T =Tc ð46aÞ The order of magnitude of their deviation should be approximately 0.5%; at temperatures in the vicinity of the critical point, where the values are low and the slopes are large, higher deviations can be accepted. The parameters C, D, and E are D1 needed only for a good data situation; otherwise, they could be set to zero. If C = D = E = 0, B = 0.38 is often a good first guess. For high precision data, the PPDS equation Dhv ¼ RTc ðAt1=3 þ Bt2=3 þ Ct þ Dt2 þ Et6 Þ ð46bÞ with ð46cÞ t ¼ 1 T =Tc is a very useful correlation tool. In > Subchap. D3.1, this equation has been fitted to approximately 275 substances. There is a peculiarity for the estimation of the enthalpy of vaporization. The Clausius-Clapeyron equation Dhv ¼ T ðv 00 v 0 Þ dps dT ð47Þ is an exact thermodynamic relationship, using the easily available quantities vapor pressure curve, bubble point volume, and dew point volume. In fact, most of the data points available have been evaluated this way and not by direct measurement. However, there are some restrictions for the application of the Clausius-Clapeyron equation in practical applications. It is important to check that only the temperature range is considered where the vapor pressure curve is validated. The most important vapor pressure equations Wagner (Eqs. (42) and (42c)) and Antoine (Eq. (41)) extrapolate badly to low temperatures. Even if data points are available, the relative errors, which of course have an influence on the slope, are often still quite large. As a rule of thumb, it is recommended not to apply the Clausius-Clapeyron equation for vapor pressures ps < 1 mbar. The term (v 00 – v 0 ) is decisive for the accuracy. v 0 is negligible in comparison with v 00 with the exception of the region just below the critical point. Moreover, in this region the quality of the correlations for the liquid density is low. If v 00 is determined with the ideal gas equation, the error can be tolerated in the low pressure region, but the curve has a concave curvature instead of a convex one, which becomes less and less acceptable when the saturation pressure increases. Therefore, v 00 is usually calculated with a cubic equation of state (Sect. 4.2). From test calculations, it can be concluded that D1. Fig. 5. Curvature of the enthalpy of vaporization as a function of temperature. 135 136 D1 Calculation Methods for Thermophysical Properties an error of 1%. . .2% might occur. In the region just below the critical point, the deviations are larger. As both v 00 and v 0 are much less accurate in the vicinity of the critical point and the term (v 00 –v 0 ) behaves as a difference of large numbers, the application of the Clausius-Clapeyron equation should be excluded in this area. As a rule of thumb, the application should be restricted to T < Tc – 30 K. Values outside the application range of the ClausiusClapeyron equation can be estimated by correlating values generated with the Clausius-Clapeyron equation in the valid range with Eq. (46) or (46b) and extrapolate this equation towards the critical point. For associating substances, it should be taken into account that the chemical theory (Sect. 4.2) is not valid for high pressures. In case no information is available, one can estimate the normal boiling point (Sect. 3.3) and critical point (Sect. 3.1). Then, a vapor pressure curve could be estimated with the Hoffmann-Florin equation. The acentric factor can also be determined by its definition (Eq. 8). Thus, all information for the application of the Clausius-Clapeyron equation is available. Example 9: Estimate the enthalpy of vaporization of acetone at t = 0 C. The following values are given: rliq = 812.9 kg/m3, Tc = 508.1 K, pc = 46.924 bar, o = 0.3064, M = 58.08 g/mol Wagner-coefficients A = 7.67033, B = 1.96469, C = 2.4438, D = 2.90162 (Eq. (42c)) The vapor pressure at t = 0 C can be determined with the Wagner equation to be ps = 0.093 bar. The specific volumes are: v 0 = 7.145 · 105 m3/mol v 00 = 0.2431 m3/mol (from Peng-Robinson equation) The derivative of the modified Wagner Equation (42c) is: dps ps ps ¼ ln þ A þ 1:5 B ð1 Tr Þ0:5 þ 2:5 C ð1 Tr Þ1:5 dT T pc þ5 D ð1 Tr Þ4 ð48Þ At t = 0 C, the result is dps/dT = 492.84 Pa/K. Thus, one gets: Dhv ¼ 273:15 K ð0:2453 7:145 105 Þ m3 =mol 492:84 Pa=K ¼ 32721 J=mol ¼ 563:4 J=g The value listed in > Subchap. D3.1 is 558.9 J/g. The deviation is 0.8%. For mixtures, an enthalpy of vaporization is not a useful quantity, as during the vaporization temperatures, the compositions of both vapor and liquid vary. For reasonable calculations, it is recommended that the calculation of the energy balance be performed by determining the exact enthalpy differences according to Sect. 6.4. For an isothermal evaporation, a linear mixing rule can be applied as an approximation: Dhv;Gem ¼ X i e xi Dhvi ð49Þ For the isobaric evaporation, Eq. (49) is not appropriate at all, as the enthalpies of vaporization would then have to be evaluated at their particular boiling temperatures, and the temperature increase of the liquid is not taken into account. 6.2 Specific Heat Capacity of Ideal Gases The specific heat capacity of ideal gases is a measure of the capability of a molecule to store energy. cpid is defined as the heat a molecule must be exposed to at constant pressure to achieve a certain change in temperature. It must be strongly distinguished between the isobaric specific heat capacity cpid at constant pressure and the isochoric specific heat capacity cvid at constant volume. Both quantities are related by cvid ¼ cpid R ð50Þ The following considerations are focusing on the specific isobaric heat capacity. It depends only on temperature and increases in a strictly monotonic way. In general, there are two contributions to cpid: the temperatureindependent one describing the kinetic energy and the rotational energy of the molecules, and a vibration contribution, which is only activated at high temperatures and that causes the temperature-dependence of the molecule [21, 22]. If a molecule consists only of 1 atom (He, Ne, Ar, Kr, Xe), the vibration and the rotational contributions are zero, and cpid is constant. Typical curvatures of cpid as a function of temperature are depicted in Fig. 6. On the left hand side, only the constant contributions for the kinetic and for the rotational contributions are active. Then, the function increases monotonically until all the vibration options in the molecules are fully active. Then, the function becomes constant again. The curvature can be well represented with the Aly-Lee equation [23], which is based on statistical thermodynamics: 2 2 C=T E=T ecpid ¼ A þ B þD ð51Þ sinhðC=T Þ coshðE=T Þ During the recent years, a PPDS equation 2 cPid T ¼ B þ ðC BÞ R AþT " 2 3 ! # A T T T 1 þG DþE þF AþT AþT AþT AþT ð51aÞ has been widely applied and proved to yield good results. Its disadvantage is the increased number of adjustable parameters. Equation (51a) has been used in > Subchap. D3.1 for 275 substances. Acceptable results can also be obtained with a simpler equation like cpid J=kg K ¼AþB 2 3 T T T E þD þ þC K K K ðT =K Þ2 ð52Þ although the extrapolation capability is weak, especially toward low temperatures. However, for most of the process engineering applications the quality of Eq. (52) should be sufficient. The last term is often omitted, leaving a polynomial of degree 3. Calculation Methods for Thermophysical Properties D1 D1. Fig. 6. Typical curvatures of the specific isobaric heat capacity of ideal gases. X D1. Fig. 7. Structural formula of ethyl acetate. X DC ¼ 2 ð1:53 104 Þ þ 1 ð5:44 105 Þ þ 1 ð4:02 105 Þ ¼ 2:918 104 DD ¼ 2 ð9:67 108 Þ þ 1 ð1:19 108 Þ þ 1 ð4:52 108 Þ ¼ 2:267 107 The estimation of the specific isobaric heat capacity of ideal gases can be performed with Joback’s group contribution method. The particular group contributions form the coefficients of a 3rd degree polynomial: X X ¼ DA 37:93 þ DB þ 0:21 ðT =K Þ J=mol K X þ DC 3:91 104 ðT =K Þ2 X þ DD þ 2:06 107 ðT =K Þ3 ð53Þ ecpid The corresponding coefficients for the group contributions are listed in Table 6. Relatively small deviation of approximately 1%. . .2% can be expected. The deviations become larger with increasing complexity of the molecule. Example 10: Determine the specific isobaric heat capacity of ethyl acetate in the ideal gas state at t = 25 C. The molecular weight of ethyl acetate is M = 88.11 g/mol. The group assignment of ethyl acetate is: 2 CH3 1 CH2 1 COO The group contributions are: X DA ¼ 2 ð19:5Þ þ 1 ð0:909Þ þ 1 ð24:5Þ ¼ 62:591 X DB ¼ 2 ð8:08 103 Þ þ 1 ð9:5 102 Þ þ 1 ð4:02 102 Þ ¼ 0:11904 The result for cpid is ecpid ¼ ð62:591 37:93Þ þ ð0:11904 þ 0:21Þ ð298:15Þ J=mol K þ 2:918 104 3:91 104 ð298:15Þ2 þ 2:267 107 þ 2:06 107 ð298:15Þ3 ¼ 113:397 or cpid = 1.287 J/gK, respectively. The true value is considered to be 1.290 J/gK. The thermodynamically exact mixing rule for mixtures of ideal gases is X id id ¼ e xi ecp;i ð54Þ ecp;mix i 6.3 Real Gas Corrections With increasing pressure, intermolecular forces play a more and more important role in the calculation of the enthalpy of gases. Usually, these forces are attractive so that energy is needed to increase the distance between the molecules. If this energy is not supplied, the substance cools down during the expansion. A famous example is the liquefaction of air by adiabatic throttling. To take these effects into account, the ideal gas heat capacity on its own is not sufficient. The difference of enthalpies between the ideal gas state at p = 0 and a state at an arbitrary pressure is called the residual part of the enthalpy. It can be evaluated for nonassociating 137 138 D1 Calculation Methods for Thermophysical Properties D1. Table 6. Group contribution for cpid according to Joback Structural group –CH3 Soave-Redlich-Kwong equation: DA DB x 102 DC x 104 DD x 108 19.500 –0.808 1.5300 –9.670 >CH2 –0.909 9.500 –0.5440 1.190 >CH– –23.000 20.400 –2.6500 12.000 >C< –66.200 42.700 –6.4100 30.100 =CH2 23.600 –3.810 1.7200 –10.300 =CH– –8.000 10.500 –0.9630 3.560 =C< –28.100 20.800 –3.0600 14.600 =C= 27.400 –5.570 1.0100 –5.020 CH 24.500 –2.710 1.1100 –6.780 C– 7.870 2.010 –0.0833 0.139 –CH2– (ring) –6.030 8.540 –0.0800 –1.800 >CH– (ring) –20.500 16.200 –1.6000 6.240 >C< (ring) –90.900 55.700 –9.0000 46.900 =CH– (ring) –2.140 5.740 –0.0164 –1.590 =C< (ring) –8.250 10.100 –1.4200 6.780 –F 26.500 –9.130 1.9100 –10.300 –Cl 33.300 –9.630 1.8700 –9.960 –Br 28.600 –6.490 1.3600 –7.450 –I 32.100 –6.410 1.2600 –6.870 –OH (alcohols) 25.700 –6.910 1.7700 –9.880 –OH (phenols) –2.810 11.100 –1.1600 4.940 –O– 25.500 –6.320 1.1100 –5.480 –O– (ring) 12.200 –1.260 0.6030 –3.860 6.450 6.700 –0.3570 0.286 >C=O (ring) 30.400 –8.290 2.3600 –13.100 –CH=O 30.900 –3.360 1.6000 –9.880 –COOH 24.100 4.270 0.8040 –6.870 –COO– 24.500 4.020 0.4020 –4.520 6.820 1.960 0.1270 –1.780 26.900 –4.120 1.6400 –9.760 >C=O =O –NH2 >NH –1.210 7.620 –0.4860 1.050 >NH (ring) 11.800 –2.300 1.0700 –6.280 –31.100 22.700 –3.2000 14.600 –N= (ring) 8.830 –0.384 0.4350 –2.600 =NH 5.690 –0.412 1.2800 –8.880 –CN 36.500 –7.330 1.8400 –10.300 –NO2 25.900 –0.374 1.2900 –8.880 –SH 35.300 –7.580 1.8500 –10.300 –S– 19.600 –0.561 0.4020 –2.760 –S– (ring) 16.700 0.481 0.2770 –2.110 >N– –N= substances by cubic equations of state. The corresponding expressions are: real ¼e hðT ; pÞ e hðT ; p ¼ 0Þ DhGas e ðZ 1Þ 1 a T @a ln v þ b ¼ RT b @T v The residual part of the specific heat capacity of gases can be calculated by the derivatives of Eqs. (55) and (56): real @DhGas real ¼ ð57Þ Dcp;Gas @T p As it yields a very complicated expression, it is recommended to perform the differentiation in Eq. (57) numerically. Taking into account the residual part of the enthalpy is important especially for associating substances. Considering only the dimerization of molecules of the same kind, the residual part can be evaluated with the association model described in Sect. 4.2: real ¼ DhGas;Ass: real ¼e hðT ; pÞ e hðT ; p ¼ 0Þ DhGas pﬃﬃﬃ e ðZ 1Þ p1ﬃﬃﬃ a T @a ln v þ ð1 þ p2ﬃﬃﬃÞb ¼ RT @T 8b v þ ð1 2Þb ð55Þ e zD DhD e zD zM þ 2 e ð58Þ with e f 0B DhD ¼ R ð59Þ where B is the coefficient in Eq. (34). This calculation is quite complicated, as first the true concentrations must be evaluated via Eqs. (36) and (38). The residual part of the specific heat capacity must again be determined by numerical differentiation. For illustration, Fig. 8 shows the specific isobaric heat capacities of acetic acid vapor with and without consideration of the residual part. 6.4 Specific Heat Capacity of Liquids The specific isobaric heat capacity of liquids (cpliq) is a function of temperature. The pressure dependence is usually negligible. Isobaric and isochoric heat capacity differ significantly, as in the isobaric case work has to be spent to increase the distance between the molecules. At low temperatures (approximately up to the normal boiling point), cpliq is an almost linear function of temperature. At higher temperatures, the slope increases. In many cases, a flat minimum is formed (Fig. 9). At the critical point, the specific heat capacity of a liquid becomes infinity. For a boiling liquid, as it often occurs in process engineering, the specific isobaric heat capacity is not a useful quantity, as the heating at constant pressure would result in evaporation and not in temperature increase. For practical applications, a ‘‘specific heat capacity along the saturation line’’ (cs) is used, without distinguishing these quantities in the colloquial language. The relationship is " Peng-Robinson equation: ð56Þ @v ecs ¼ ecp þ v T @T # p dps dT ð60Þ The difference between both heat capacities is only relevant for high temperatures. As a rule of thumb, it can be neglected Calculation Methods for Thermophysical Properties D1 D1. Fig. 8. Specific isobaric heat capacity of acetic acid vapor at various pressures. D1. Fig. 9. Specific heat capacity of liquid water as a function of temperature. for T < 0.8 Tc. The difference can be estimated with the equation e expð20:1 Tr 17:9Þ ecs ¼ ecpliq R ð61Þ The liquid heat capacity can be correlated with an extended polynomial 2 3 cpliq T T T E ¼AþB þC þD þ ð62Þ J=kgK K K K ðT =K Þ2 For more precise calculations, the PPDS equation can be used A cPliq ¼ R þ B þ Ct þ Dt2 þ Et3 þ Ft4 ð62aÞ t not considered to be important, as the quantity becomes more and more difficult to handle due to the increasing difference between cp and cs. For many substances, no data exist above the normal boiling point. Often only a linear temperaturedependence is justified, which leads to an underestimation of cp when it is extrapolated to high temperatures. To overcome this difficulty, artificial data points can be generated with an estimation method and fitted together with the data available. For the estimation of cpliq the method of Rowlinson-Bondi can be used, which is based on the specific heat capacity of ideal gases and the 3-parameter principle of corresponding states: e þ 0:45 R e ð1 Tr Þ1 ecpf l ¼ ecpid þ 1:45 R h i e 17:11 þ 25:2 ð1 Tr Þ1=3 Tr1 þ 1:742 ð1 Tr Þ1 þ 0:25 o R ð63Þ with T t¼1 Tc ð62bÞ Eq. (62a) is used in > Subchap. D3.1 for the correlation of heat capacities of approximately 275 substances. There are few substances where all coefficients have to be fitted. In most cases, a quadratic temperature-dependence is sufficient; in case Eq. (62a) is used, the coefficients B, C and D are active. The extrapolation towards the critical point is often The deviation to be expected should be approximately 5%. Example 11: Estimate the specific heat capacity of liquid methyl ethyl ketone at t = 100 C. The given data are: cpid (100 C) = 1.655 J/gK, e ¼ 72.11 g/mol. Tc = 535.55 K, o = 0.323, M id From cp (100 C) = 120.496 J/molK and Tr = 0.697 it can be calculated 139 140 D1 ec liq p J=molK Calculation Methods for Thermophysical Properties ¼ 119:342 þ 1:45 8:3143 0f e hiid ðT ; p ¼ 0Þ ¼ Dhi þ 1 þ 0:45 8:3143 ð1 0:697Þ 1=3 ½17:11 þ 25:2 ð1 0:697Þ 3. Transition to the mixture at p = 0 in the ideal gas state, that is, without an excess enthalpy X id e e ðT ; p ¼ 0; xi Þ ¼ xi e ð67Þ hiid ðT ; p ¼ 0Þ hmix 0:6971 þ 1:742 ð1 0:697Þ ¼ 175:4 ) cpliq ¼ 2:432 J=gK The value given in real 4. Addition of the residual part in the vapor phase DhGas D3.1 is 2.430 J/gK. For mixtures, the specific heat capacity of liquids can be calculated with a linear mixing rule X liq liq ¼ xi cp;i ð64Þ cp;mix real DhGas ðT ; p; e xi Þ ¼ e hðT ; p; e xi Þ e hid ðT ; p ¼ 0; e xi Þ neglecting the influence of the excess enthalpy. Routes for Enthalpy Calculation For process simulation it is necessary that the enthalpy is continuously described in the vapor as well as in the two-phase and in the liquid region. The problem occurs that the particular quantities contributing to the enthalpy are not independent from each other. Depending on the way the enthalpy is calculated (route), there is always one quantity that results from the summation of the other contributions. The most often used routes are described in the following section. A. Route: Vapor as starting phase I. Enthalpy of a vapor 1. Set the reference point to the standard condition (T0 = 298.15 K, p0 = 0, h0i = Dhi0f ) for all components. 0f e hiid ðT0 ; p ¼ 0Þ ¼ Dhi ð68Þ until the required state in the vapor phase is obtained: real id real e ðT ; p; e xi Þ ¼ hmix ðT ; p ¼ 0; e xi Þ þ DhGas ðT ; p; e xi Þ hmix ð69Þ i 6.5 ð66Þ T0 þ 0:25 0:323 8:3143 1 > Subchap. ZT ecpiid dT II. Enthalpy of a liquid If the enthalpy of a liquid is calculated (Fig. 10), the steps 1 and 2 are identical to the calculation of a vapor phase enthalpy. The transition to the mixture takes place in the liquid phase. In step 3, the residual part is determined for the pure components to reach the dew point curve at p = psi. 3. Calculation of the dew point curve state e hi 00 ðT Þ ¼ Dhi 0f þ ZT real ecpiid dT þ DhGas;i ðT ; psi Þ ð70Þ T0 4. Subtraction of the enthalpy of vaporization at the system temperature T to reach the bubble point curve 0f e hiliq ðT Þ ¼ Dhi þ ZT id real ecpi dT þ DhGas;i ðT ; psi Þ Dhvi ðT Þ T0 ð65Þ ð71Þ Therefore, the enthalpy is consistent regarding chemical reactions. 2. Calculation of the enthalpy of the ideal gas at p = 0 for id for all components: the system temperature T, using cpi In process simulation, liquids are in general treated as if they are at their bubble point at the system temperature. Enthalpy changes by compression of the liquid are neglected, which is at least at low pressures an acceptable approximation. D1. Fig. 10. Calculation of the enthalpy of a liquid with the route ‘‘vapor as starting phase’’. D1 Calculation Methods for Thermophysical Properties 5. Integration of the excess enthalpy The transition to the mixture takes place in the liquid phase via X liq e e ðT ; e xi Þ ¼ hE ðT ; e xi Þ ð72Þ xi e hmix hiliq ðT Þ þ e i The calculation of the excess enthalpy hE itself is explained in > Subchap. D5.1. The main disadvantage of this method is the error in the determination of the liquid heat capacity, which is calculated by deriving the enthalpy with respect to temperature. Even for well-known substances like water or methanol the deviations for cpliq are considerable [24], which can hardly be accepted if, for example, liquid–liquid heat exchangers are designed. A procedure has been developed [24] where cpliq can be reproduced using ‘‘vapor as starting phase.’’ I. Enthalpy of a liquid 1. Enthalpy of a pure liquid Starting from a reference state in the liquid phase href,i(Tref,i) the enthalpy of the liquid is evaluated by integration of the specific heat capacity of the liquid: ZT ecpiliq dT þ e href ;i ðTref ;i Þ i analogous to Eq. (72). A useful choice for TLG,i is the normal boiling point. 2. Transition to the vapor phase to reach the dew point curve: e hiliq ðTLG;i Þ þ Dhv ðTLG;i Þ hi 00 ðTLG;i Þ ¼ e ð76Þ 3. Transition to the ideal gas state real e hi 00 ðTLG;i Þ DhGas;i ðTLG;i ; psi ðTLG;i ÞÞ hiid ðTLG;i ; p ¼ 0Þ ¼ e ð77Þ e hiid ðTLG;i ; p ¼ 0Þ þ hiid ðT ; p ¼ 0Þ ¼ e ZT ecpiid dT ð78Þ TLG;i 5. Transition to the mixture at p = 0 in the ideal gas state, that is, without an excess enthalpy X id e e ðT ; p ¼ 0; e xi Þ ¼ ð79Þ xi e hmix hiid ðT ; p ¼ 0Þ i ð73Þ 6. Addition of the residual part to reach the required state in the vapor phase analogously to Eq. (69) Tref ;i 2. Transition to the mixture X liq e e hmix ðT ; e xi Þ ¼ xi Þ xi e hiliq ðT Þ þ hE ðT ; e Tref ;i 4. Integration to the system temperature B. Route: Liquid as starting phase e hiliq ðT Þ ¼ II. Enthalpy of a vapor 1. Integration of the specific heat capacity to the transition temperature TLG. ZTLG;i liq e ecpiliq dT þ e href ;i ðTref ;i Þ ð75Þ hi ðTLG;i Þ ¼ real id real e ðT ;p;e xi Þ ¼ e hmix ðT ;p ¼ 0;e xi Þ þ DhGas ðT ;p;e xi Þ ð80Þ hmix ð74Þ href,i(Tref,i) has to be chosen for each component in a way that the enthalpy for the standard state (t = 25 C, ideal gas state) results in the standard enthalpy of formation D0f hi . A useful choice for Tref,i is the melting point. The method is illustrated in Fig. 11. D1. Fig. 11. Calculation of the enthalpy of a saturated vapor with the route ‘‘liquid as starting phase’’. 141 142 D1 Calculation Methods for Thermophysical Properties The specific heat capacity of a liquid is reproduced with this route; nevertheless, it has also its disadvantages. The calculation of the enthalpy of vaporization is indirect and therefore not exact; it does not equal 0 at the critical point. The correlation for cpliq is often only verified in the temperature region below the normal boiling point and extrapolates poorly, giving large errors in the high-pressure region. Many arrangements (Tref, href, TLG for each component) have to be set up. 7 Viscosity The viscosity is a measure of the momentum transfer in a fluid perpendicular to the flow direction. It is needed especially for the calculation of pressure drops. Furthermore, it is a factor in the Reynolds and in the Grashof number for the determination of the heat transfer coefficient. It is distinguished between the dynamic viscosity and the kinematic viscosity n. They are related via ¼ nr ð81Þ In the following section, only the dynamic viscosity is regarded. 7.1 Dynamic Viscosity of Liquids Fig. 12 shows the typical curvature of the dynamic viscosity of liquids. In the temperature region above the melting point, it decreases with a large slope. The slope decreases with increasing temperatures, but remains negative. The dynamic viscosity can be roughly correlated with the simple approach ln B ¼Aþ Pas T ð82Þ This equation is appropriate to reproduce the curvature qualitatively. For a precise reproduction, further terms have to be added to Eq. (82), for example, 2 3 B T T T þE ln ¼Aþ þC þD Pas T =K K K K ð83Þ All of these equations have difficulties when they are extrapolated to high temperatures. It is necessary to check the equation in the temperature range of interest before it is applied. During the recent years, the PPDS equation " # C T 1=3 C T 4=3 ð84Þ þB ¼ E exp A Pas T D T D has been widely applied. Currently, this equation seems to be the most accurate correlation for liquid viscosities. Furthermore, it seems to extrapolate quite well. When it is programmed, it must be taken care that the term in brackets (C – T)/(T – D) sometimes turns out to be negative, so that it makes sense to write in these cases C T 1=3 T C 1=3 ¼ and T D T D C T 4=3 T C 1=3 C T ¼ T D T D T D One of the simplest options to estimate the dynamic viscosity of liquids is the group contribution method of Orrick/Erbar [2]. The calculation equation is ! P X e rð20 CÞ M DB ¼ ln ln þ DA þ ð85Þ 3 T =K mPas g=mol g=cm For substances that are not liquid at t = 20 C, the liquid density at the melting point has to be inserted. The group contributions for DA and DB can be taken from Table 7. Partially, the group contributions do not refer to molecular segments but to structural units. First, the molecule has to be checked for aromatic and nonaromatic 5-membered and 6-membered rings. Then, the remaining groups can be assigned. For carbon atoms not recorded so far, a contribution according to the first line in Table 7 is added. Finally, additional corrections for double bonds and the particular kinds of substitution on aromatic rings D1. Fig. 12. Dynamic viscosity of liquid water as a function of temperature. Calculation Methods for Thermophysical Properties D1. Table 7. Group contributions of the Orrick/Erbar method for the calculation of the dynamic viscosity of liquids DA DB Carbon atoms –6.95 – 0.21n 275 + 99n –CH with 3 radicals –0.15 35 C with 4 radicals –1.20 400 Double bond 0.24 –90 5-membered ring 0.10 32 6-membered ring –0.45 250 Structural groups Aromatic ring 0.00 20 –0.12 100 Meta substitution 0.05 –34 Para substitution –0.01 –5 –Cl –0.61 220 –Br –1.25 365 –I –1.75 400 –OH –3.00 1,600 Ortho substitution –COO –1.00 420 –O– –0.38 140 >C=O –0.50 350 –COOH –0.90 770 D1 The value listed in > Subchap. D3.1 is = 1.418 mPas. For T > 0.7 Tc Sastri [26] recommends the equation 1 T =Tc ln ðTNBP Þ 1 TNBP =Tc aðTNBP Þ ln ¼ ln ð85aÞ mPas ln½aðTNBP Þ mPas For alcohols, a = 0.1175, for other components, a = 0.248. Deviations of approximately 10% can be expected. Example 13: Determine the dynamic viscosity of n-butane on the saturation line at t = 100 C. TNBP = 272.65 K, Tc = 425.13 K, NBP = 0.202 mPas. 1 373:15=425:13 ln 0:202 1 272:65=425:13 lnð0:248 0:202Þ ln ¼ mPas ln½0:248 0:202 ¼ 2:4177 ) ¼ 0:089 mPas The actual value is 0.077 mPas. The liquid viscosity increases with increasing pressure. According to Lucas [29], the effect can be estimated via ðT ; pÞ ¼ ðT ; ps ðT ÞÞ 1 þ DðDpr =2:118ÞA 1 þ CoDpr ð86Þ with n: number of carbon atoms not belonging to the groups shown above Dpr ¼ p ps ðT Þ pc 4:674 104 1:0523 Tr0:03877 1:0513 0:3257 D¼ 0:2906 0:2086 1:0039 Tr2:573 A ¼ 0:9991 D1. Fig. 13. Structural formula of n-butanol. (ortho: neighbor C-atoms, para: opposite C-atoms, meta: C-atoms, where one non-substituted C-atom in the ring is between) are made. Components containing nitrogen or sulfur cannot be treated. Deviations of 15% and more should be expected. Better results can be obtained with the group contribution methods of Sastri/Rao [25, 26], van Velzen [27], and, especially, Nannoolal/Rarey [28], where, however, the explanation of the complicated increments would be beyond the scope of this chapter. C ¼ 0:07921 þ 2:1616 Tr 13:404 Tr2 þ 44:1706 Tr3 84:8291 Tr4 þ 96:1209 Tr5 59:8127 Tr6 þ 15:6719 Tr7 ð86aÞ Errors of approximately 10% should be expected. Example 12: Estimate the dynamic viscosity of n-butanol (C4H10O) at t = 50 C. e 74.12 g/mol. r(20 C) = 810.6 kg/m3, M= The group assignment of n-butanol (Fig. 13) is: 1 OH 4 carbon atoms The analysis of Table 7 yields the group contributions: X DA ¼ 1 ð3Þ þ ð6:95 0:21 4Þ ¼ 10:79 X DB ¼ 1 ð1;600Þ þ ð275 þ 99 4Þ ¼ 2;271 Example 14: Determine the dynamic viscosity of methyl cyclohexane at T = 300 K and p = 500 bar. (300 K, Siedelinie) = 0.661 mPas ps (300 K) = 67.56 mbar pc = 34.71 bar Tc = 572.15 K o = 0.235 The results for the particular terms are: Tr = 0.5243 Dpr = 14.403 A = 0.98221 D = 0.13717 C = 0.06191 Thus, one gets: giving a dynamic viscosity of ð300K; 500 barÞ ¼ 0:661 mPas ln 2271 ¼ lnð0:8106 74:12Þ þ 10:79 þ mPas 323:15 ¼ 0:3334 ) ¼ 1:3957 mPas 1 þ 0:13717 ð14:403=2:118Þ0:98221 1 þ 0:06191 0:235 14:403 ¼1:04 mPas The experimental value is reported to be 1.09 mPas. 143 144 D1 Calculation Methods for Thermophysical Properties For mixtures, the viscosity can be estimated via X e xi ln i ¼ ln Pas Pas i ð87Þ In fact, the prediction of the viscosity of a mixture is much more difficult and Eq. (87) is not very reliable. It can be expected to meet the correct order of magnitude, but hardly more. With the help of an experimental value or the application of group contribution methods, significant improvements can be achieved, however, with a high effort. A detailed compilation of methods of this kind can be found in [2]. Example 15: Determine the dynamic viscosity of a methanol/water mixture xMethanol = 0.5164. at t = 40 C for e Water ¼ 0:6652 mPas; Methanol ¼ 0:4421 mPas: ln ¼ 0:5164 ln 0:4421 þ 0:4836 ln 0:6652 mPas ¼ 0:6186 ) ¼ 0:5387 mPas The actual value is Z = 0.9345 mPas. It is higher than both pure component values, which cannot be reproduced with the mathematical structure of Eq. (87). 7.2 Dynamic Viscosity of Gases According to the kinetic gas theory, the viscosity of an ideal gas does not depend on the density [22]. This can be explained as follows: There are fewer particles available for the momentum transfer at low densities, but on the other hand they have a larger mean free path so that more momentum can be transferred across the flow direction. Both effects compensate for the ideal gas. For the real gas the viscosity slightly increases with density. There is a strong dependence on temperature, as the mean kinetic energy of the molecules increases with temperature, giving more momentum to be transferred in a collision. The dynamic viscosity of gases at low pressures can be estimated according to Lucas [30]: id 107 Pas ¼ FPid 0:807 Tr0:618 0:357 expð0:449 Tr Þ x þ0:34 expð4:058 Tr Þ þ 0:018 ð88Þ where the correction factor FPid takes into account the influence of the polarity, which is characterized by the reduced dipole moment mr 2 m pc Tc 2 mr ¼ 52:46 ð89Þ debye bar K For a given mr, FPid can be evaluated by FPid ¼ 1 FPid FPid for 0 mr 0:022 1:72 ¼ 1 þ 30:55 ð0:292 Zc Þ for 0:022 mr 0:075 ð90Þ ¼ 1 þ 30:55 ð0:292 Zc Þ1:72 j0:96 þ 0:1 ðTr 0:7Þj for mr 0:075 x is the reduced inverse viscosity and can be determined by !1=2 1=6 p 2=3 e Tc M c x ¼ 0:176 ð91Þ K bar g=mol For the so-called quantum gases H2, D2, and He, there is another correction factor [2]. The average error of the method is reported to be 1%. . .4% [2]; therefore, this quantity is usually not measured. The typical curvature of the dynamic viscosity of gases is depicted in Fig. 14. For process simulation, it is sufficient to reproduce it by a simple polynomial 2 3 4 id T T T T ¼AþB þC þD þE ð92Þ Pas K K K K Coefficients for Eq. (92) are given in > Subchap. D3.1. The DIPPR equation id ¼ AT B 1 þ CT 1 þ DT 2 ð92aÞ shows a better extrapolation behavior but is less flexible. Example 16: Estimate the dynamic viscosity of ammonia at t = 300 C and p = 1 bar. The following data are given: Tc = 405.5 K pc = 113.59 bar D1. Fig. 14. Dynamic viscosity of gaseous water as a function of temperature at low pressures. Calculation Methods for Thermophysical Properties Zc = 0.255 m = 1.5 debye e ¼ 17:03 g=mol M We obtain: Tr ¼ 573:15=405:5 ¼ 1:4134 mr ¼ 52:46 1:52 113:59 405:52 ¼ 0:0815 x ¼ 0:176 ð405:5Þ1=6 ð17:03Þ1=2 ð113:59Þ2=3 ¼ 0:004947 FPid ¼ 1 þ 30:55 ð0:292 0:255Þ1:72 j0:96 þ 0:1 ð1:4134 0:7Þj ¼ 1:1086 Thus, the viscosity is: id 1:1086 0:807 1:41340:618 0:357 expð0:449 1:4134Þ ¼ 107 Pas 0:004947 þ 0:34 expð4:058 1:4134Þ þ 0:018 ¼ 185:83 ) id ¼ 18:58mPas The value from > Subchap. D3.1 is id = 20.1 mPas. The pressure-dependence of the viscosity of gases can be determined according to Lucas [30] for 1 Tr 40 and 0 pr 100: ¼ id Z2 Fp ð93Þ with id from Eq. (88) or (92) and Z2 via Z2 ¼ 1 þ B prF A prE þ ð1 þ CprD Þ1 ð94Þ Example 17: Determine the dynamic viscosity of ammonia at T = 420 K and p = 300 bar. The following data are given: Tc = 405.5 K pc = 113.59 bar Zc = 0.255 m = 1.5 debye e ¼ 17:03g=mol M id (420 K, 1 bar) = 14.57 mPas x = 0.004947 mr = 0.0815 With Tr = 1.0358 and pr = 2.6411 one gets: A = 0.1998 B = 0.08834 C = 0.9764 D = 9.2349 E = 1.3088 F = 0.7808 and Z2 ¼ 1 þ FPid ¼ 1 þ 30:55 ð0:292 0:255Þ1:72 j0:96 þ 0:1 ð1:0358 0:7Þj ¼ 1:1046 with C D E ¼ 14:57 mPas 4:77398 0:9062 ¼ 63:03 mPas The reference value [31] is Z = 56.6 mPas. ð94aÞ For the calculation of the viscosity of gas mixtures the Wilke mixing rule [32] can be applied at low pressures: Gem ¼ F ¼ 0:9425 expð0:1853 Tr0:4489 Þ The correction factor Fp is Fp ¼ 1þ 1 þ ð1:1046 1Þ 4:773983 ¼ 0:9062 1:1046 The result for the dynamic viscosity is: A¼ B A prE ¼ 4:77398 B prF þ ð1 þ CprD Þ1 Furthermore, one obtains: Fp ¼ 0:001245 expð5:1726 Tr0:3286 Þ Tr ¼ A ð1:6553 Tr 1:2723Þ 0:4489 expð3:0578 Tr37:7332 Þ ¼ Tr 1:7368 expð2:231 Tr7:6351 Þ ¼ Tr ¼ 1:3088 D1 X e y Pi i yi Fij je i ð98Þ with ðFpid 1Þ Z23 h i2 e j =M e i Þ1=4 1 þ ði =j Þ1=2 ðM qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Fij ¼ e jÞ e i =M 8 ð1 þ M ð95Þ Fpid For Tr < 1 and p < ps(Tr) Lucas [30] gives the function Fp ¼ Z2 7 x 10 Pas ð96Þ with ð98aÞ At high pressures, mixing rules based on the correspondingstates principle are available [2]. Z2 ¼ 0:6 þ 0:76 prA þ ð6:99 prB 0:6Þð1 Tr Þ ð96aÞ A ¼ 3:262 þ 14:98 pr5:508 B ¼ 1:39 þ 5:746 pr and the correction factor Fp ¼ 1þ ðFpid 1Þ ½Z2 =ðx =10 id Fpid 7 PasÞ 3 ð97Þ As a rule of thumb, an error of approximately 10% should be expected [30] except for the quantum gases, where again additional correction factors are necessary. 8 Thermal Conductivity The thermal conductivity is often the decisive quantity in heat transfer processes. Its order of magnitude is l = 0.1. . . 0.2 W/Km for most liquids. Exceptions are water (l 0.6. . . 0.7 W/Km) and some oligoethers. For gases, an order of magnitude of l 0.01. . . 0.03 W/Km can be expected. The quantum gases hydrogen (l 0.2 W/Km) and helium (l 0.14 W/Km) behave differently. 145 146 D1 Calculation Methods for Thermophysical Properties D1. Fig. 15. Curvatures of the liquid thermal conductivity as a function of temperature for water and toluene. 8.1 D1. Table 8. Values for Q in Eq. (101) Thermal Conductivity of Liquids The thermal conductivity of liquids can be described with a 4th degree polynomial 2 3 4 lfl T T T T ¼AþB þC þD þE ð99Þ W=Km K K K K or with the Jamieson [33] equation lL ¼ A ð1 þ Bt1=3 þ Ct2=3 þ DtÞ ð99aÞ with T t¼1 Tc ð99bÞ Values for the coefficients of Eq. (99) are given in > Subchap. D3.1. The thermal conductivity decreases almost linearly with the temperature over a wide range, so that a polynomial of the 1st degree is often sufficient, especially if only data below the normal boiling point are available. The other coefficients are also necessary, if either data at higher temperatures are given or if a maximum has to be described, as is the case for water. The curvatures for the liquid thermal conductivity for water and toluene as a typical organic substance are depicted in Fig. 15. As the thermal conductivities are in the same order of magnitude for most substances, the estimation is comparably simple. The method of Sato-Riedel [34] is well established: !1=2 e lfl 3 þ 20 ð1 Tr Þ2=3 M ¼ 1:11 ð100Þ 2=3 W=Km g=mol 3 þ 20 1 TNBP;r Example 18: Determine the thermal conductivity of liquid acetone at t = –50 C. The given values are: tc = 234.95 C tNBP = 56.08 C e 58:08g=mol M¼ lf l 3 þ 20 ð1 223:15=508:1Þ2=3 ¼ 0:1864 ¼ 1:11ð58:08Þ1=2 W=Km 3 þ 20 ð1 329:23=508:1Þ2=3 The value given in > Subchap. D3.1 is l = 0.193 W/Km. pr Tr 1 5 10 50 100 200 0.8 0.036 0.038 0.038 0.038 0.038 0.038 0.7 0.018 0.025 0.027 0.031 0.032 0.032 0.6 0.015 0.02 0.022 0.024 0.025 0.025 0.5 0.012 0.0165 0.017 0.019 0.02 0.02 The pressure dependence of thermal conductivity for liquids is almost negligible. At very high pressures, it has a certain influence, which can be estimated with the Missenard method lðpr ; T Þ ¼ 1 þ Q pr0:7 ð101Þ lðps ; T Þ Values for Q are listed in Table 8. Example 19: Determine the thermal conductivity of toluene at T = 304 K and p = 6,330 bar. The given values are: l (304 K, 1 bar) = 0.1309 W/Km pc = 41.26 bar Tc = 591.75 K With Tr = 0.5137 and pr = 153.42 one gets Q = 0.0207 from Table 8 by interpolation. Thus, it is lðpr ; T Þ ¼ lðps ; T Þ 1 þ Q pr0:7 ¼ 0:1309 W=Km: 1 þ 0:0207 153:420:7 ¼ 0:2227 W=Km The experimental value [2] is 0.228 W/Km. As a mixing rule for the thermal conductivity of liquids, the method of Li [35] is appropriate, as it can also be extended to multicomponent mixtures: n X n X 2Fi Fj ð102Þ lmix ¼ 1 1 i¼1 j¼1 li þ lj with e xi vliq;i Fi ¼ P n e xj vliq;j j¼1 ð102aÞ Calculation Methods for Thermophysical Properties Example 20: Determine the thermal conductivity of a liquid mixture of benzene and methanol with xbenzene = 0.381 at T = 273 K. The following data at T = 273 K are given: lbenzene = 0.151 W/Km (extrapolated below melting point) lmethanol = 0.207 W/Km e benzene ¼ 78:11g=mol M e methanol ¼ 32:04g=mol M 0:381 8:702 105 ¼ 0:5754 0:381 8:702 105 þ 0:619 3:952 105 ¼ 1 Fbenzene ¼ 0:4246 Fbenzene ¼ Fmethanol lmix 2 0:57542 2 0:5754 0:4246 2 0:42462 ¼ þ 2 þ W=Km 2 0:1511 0:1511 þ 0:2071 2 0:2071 ¼ 0:1726 The experimental value [2] is l = 0.17 W/Km. 8.2 with C¼1þa and 0:215 þ 0:28288 a 1:061 b þ 0:26665 g 0:6366 þ bg þ 1:061 ab Thermal Conductivity of Gases b ¼ 0:7862 0:7109 o þ 1:3168 o2 id ð103Þ The typical, almost linear curvature is depicted in Fig. 16. The thermal conductivity of gases at low pressures can be estimated according to Chung [36] via l¼ e 3:75CR e M ð104bÞ Tr2 For nonpolar substances, deviations of about 5%. . .10% might be expected. For polar compounds, the error is often higher. In these cases, the group contribution method of Roy/Thodos [2] is recommended. Example 21: Determine the thermal conductivity of 2-methylpentane at t = 100 C and 1 bar. The given data are: e ¼ 86:16 g=mol M o = 0.280 Tc = 497.7 K cp = 2.008 J/gK = 8.2 mPas One gets: 2:016 86:16 2:5 ¼ 18:308 8:3143 b ¼ 0:7862 0:7109 0:280 þ 1:3168 0:2802 ¼ 0:6904 a¼ The thermal conductivity of gases can be derived from the kinetic gas theory analogously to the viscosity. Instead of the momentum transfer, the transfer of kinetic energy has to be regarded [22]. Similar to viscosity, the thermal conductivity increases with increasing temperature. At low to moderate pressures (approximately 0.1. . .10 bar), it does not depend on the pressure. The thermal conductivity of gases can be correlated with a 4th degree polynomial: 2 3 4 l T T T T ¼AþB þC þD þE W=Km K K K K ð104aÞ e 2:5 a ¼ ecp =R g ¼ 2 þ 10:5 rbenzene = 897.6 kg/m3 = > vbenzene = 8.702 ˙ 10–5 m3/mol (extrapolated below melting point) rmethanol = 810.7 kg/m3 = > vmethanol = 3.952 ˙ 10–5 m3/mol D1 ð104Þ g ¼ 2 þ 10:5 ð373:15=497:7Þ2 ¼ 7:9023 0:215 þ 0:28288 a 1:061 b þ 0:26665 g C¼1þa ¼ 7:3538 0:6366 þ bg þ 1:061 ab 3:75 7:3538 8:2 106 8:3143 W l¼ ¼ 0:0218 W=Km 86:16 103 Km The value listed in > Subchap. D3.1 is 0.0206 W/Km. The thermal conductivity of gases depends on the pressure in an unusual way. At very low pressures (p < 10–3 mbar), when the mean free path is large in comparison with the vessel dimensions, the thermal conductivity is proportional to the pressure and to the distance d between the limiting walls in the direction of the heat flux: sﬃﬃﬃﬃﬃﬃﬃﬃﬃ e 3 3R l ¼ pd ð105Þ e 8 MT D1. Fig. 16. Thermal conductivity of gaseous water as a function of temperature. 147 148 D1 Calculation Methods for Thermophysical Properties At normal pressures (p = 0.001 bar . . . 10 bar), it is almost independent of the pressure. At high pressures, the thermal conductivity can be estimated according to Stiel and Thodos [37]: l ¼ lid þ 0:0122 G1 Zc5 ½expð0:535 r=rc Þ 1 l ¼ lid þ 0:0114 G1 Zc5 ½expð0:67 r=rc Þ 1:069 l ¼ lid þ 0:0026 G1 Zc5 ½expð1:155 r=rc Þ þ 2:016 The following values are given: e benzene ¼ 78:11 g=mol M e argon ¼ 39:95 g=mol M benzene = 9.465 mPas argon = 27.05 mPas lbenzene = 0.01694 W/Km largon = 0.02089 W/Km We get: h i2 1 þ ð9:465=27:05Þ1=2 ð39:95=78:11Þ1=4 pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 0:4629 F12 ¼ 8 ð1 þ 78:11=39:95Þ h i2 1 þ ð27:05=9:465Þ1=2 ð78:11=39:95Þ1=4 pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 2:58655 F21 ¼ 8 ð1 þ 39:95=78:11Þ for r=rc < 0:5 for 0:5 < r=rc < 2 ð106Þ for 2 < r=rc < 2:8 G is given by !1=2 1=6 p 2=3 e G Tc M c ¼ 210 1 K bar g=mol ðW=KmÞ ð107Þ The method is not considered to be very accurate, deviations of 10%. . .20% are usual. For polar compounds, this method is not appropriate. There are other, more difficult methods available [2], which are more accurate. However, none of them can really handle polar compounds. Example 22: Determine the thermal conductivity of nitrous oxide at t = 105 C and p = 138 bar. The given values are: lid = 0.02375 W/Km pc = 72.45 bar Tc = 309.52 K rc = 454 kg/m3 r (105 C, 138 bar) = 303.978 kg/m3 e 44:01g=mol M¼ For G, one gets: G ¼ 210 309:521=6 44:011=2 72:452=3 ¼ 208:49 ðW=KmÞ1 r=rc ¼ 0:66956 72:45 105 44:01 103 Zc ¼ ¼ 0:2729 454 8:3143 309:52 which yields l ¼ 0:02375 þ 0:0114 208:491 0:27295 W=Km ½expð0:67 0:66956Þ 1:069 ¼ 0:0417 The experimental value is 0.039 W/Km. For the calculation of the thermal conductivity of gaseous mixtures, the mixing rule of Wassiljeva, Mason, and Saxena [2] can be applied analogously to the mixing rule of Wilke for viscosity: X e yl Pi i ð108Þ lmix ¼ j yj Fij i with h i2 e j =M e i Þ1=4 1 þ ði =j Þ1=2 ðM qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Fij ¼ e jÞ e i =M 8 ð1 þ M ð108aÞ Example 23: Determine the thermal conductivity of a gaseous mixture consisting of 25 mol% benzene and 75 mol% argon at t = 100.6 C and p = 1 bar. F11 ¼ F22 ¼ 1 The thermal conductivity of the mixture is calculated to be: lmix 0:25 0:01694 0:75 0:02089 ¼ þ W=Km 0:25 1 þ 0:75 0:4629 0:25 2:58655 þ 0:75 1 ¼ 0:0183 The experimental value is l = 0.0192 W/Km. 9 Surface Tension The surface tension is a quantity which decides whether a liquid is prone to form droplets or not. For pure substances, it decreases with increasing temperature and becomes 0 at the critical point (Fig. 17), where vapor and liquid are identical. It is essentially determined by intermolecular forces, especially by the differences of the attractive forces acting on the molecules located in the surface, one from the vapor side and one from the liquid side. The surface tension can be correlated by 2 3 s ð109Þ ¼ A ð1 Tr ÞBþCTr þDTr þETr N=m where the coefficients C, D, and E can either be set to 0 or be fitted according to demand. Coefficients for Eq. (109) are given in > Subchap. D3.1. The surface tension can be estimated according to Brock/ Bird/Miller [2], based on the 3-parameter corresponding states principle: p 2=3 T 1=3 s c c Q ð1 Tr Þ11=9 ð110Þ ¼ bar K mN=m with " Q ¼ 0:1196 1 þ TNBP Tc pc ln 1:01325 bar 1 TNBP =Tc # 0:279 ð110aÞ For substances which are not strongly polar, the deviations are usually less than 5%. Example 24: Estimate the surface tension of bromobenzene at t = 50 C. The given data are: TNBP = 429.15 K Calculation Methods for Thermophysical Properties D1 D1. Fig. 17. Surface tension of water as a function of temperature. Tc = 670.20 K pc = 45.19 bar With Q ¼ 0:1196 1 þ 429:15 45:19 670:20 ln 1:01325 r1 = 707.8 kg/m3 = 0.009549 mol/cm3 r2 = 872.80 kg/m3 = 0.011174 mol/cm3 One gets: 1 429:15=670:20 0:279 ¼ 0:6492 we get s ¼ 45:192=3 670:201=3 0:6492 ð1 323:15=670:2Þ11=9 mN=m ¼ 32:25 The value listed in > Subchap. D3.1 is 33 mN/m. liq Pmix e rmix liq mol=cm3 vap Pmix e rmix vap mol=cm3 smix ¼ ð208:20 0:0104237Þ4 mN=m ¼ 22:18 mN=m !4 ð111Þ is suggested, where the terms for the gas phase can be neglected at low pressures. P is the parachor !1 1=4 e s r P¼ ð112Þ mN=m mol=cm3 which can be averaged via XX Pi þ Pj e Pmix ¼ xi e xj 2 i j ð113Þ More accurate methods, especially for aqueous systems, are listed in Poling/Prausnitz/O’Connell [2]. Example 25: Estimate the surface tension of a mixture of diethyl ether (1) and benzene (2) with a mole fraction x1 = 0.423 at T = 298 K. The influence of the vapor in Eq. (107) can be neglected due to the low pressure. The given data are: e 1 ¼ 74:12g=mol M e M2 ¼ 78:11g=mol s1 = 16.429 mN/m s2 = 28.214 mN/m P2 ¼ 0:0111741 28:2141=4 ¼ 206:26 210:84 þ 206:26 Pmix ¼ 0:4232 210:84 þ 2 0:423 0:577 2 þ 0:5772 206:26 ¼ 208:20 1 0:423 0:577 1 mol mix 1 1 rliq ¼ e x1 e x2 e ¼ rliq;1 þ e rliq;2 þ 0:009549 0:011174 cm3 ¼ 0:0104237 mol=cm3 As a mixing rule, the equation smix ¼ mN=m P1 ¼ 0:0095491 16:4291=4 ¼ 210:84 The experimental value [34] is 21.81 mN/m. 10 Diffusion Coefficient The binary diffusion coefficient D12 is needed for all calculations where mass transfer is involved. In this chapter, it is defined as dx ð114Þ j12 ¼ rmix D12 dz with j12 as mass flux density and z as coordinate direction. The diffusion coefficient is symmetric, that is, D12 = D21. It is essentially determined by intermolecular forces. For its evaluation, experimental values are difficult to measure and hardly available. In almost all cases, it has to be relied on estimation methods. 10.1 Diffusion Coefficients in Gases In addition for its role in viscosity and thermal conductivity, the kinetic gas theory [22] is the basis for the estimation methods for diffusion coefficients in the gas phase. It depends not only on temperature but also on pressure. At pressures up to p = 10 bar, 149 150 D1 Calculation Methods for Thermophysical Properties it is inversely proportional to the pressure. It is almost independent from the concentration. At low pressures, the binary diffusion coefficient for gases can be estimated according to Fuller [38] with a remarkable accuracy. The calculation equation is given by: " 1 1 #1=2 T 1:75 e1 e2 M M 0:00143 K þ g=mol g=mol D12 ¼ ð115Þ i2 pﬃﬃﬃh P P cm2 =s 1=3 1=3 p ð Þ þ ð D Þ 2 D v v 1 2 bar The influence of the pressure can be evaluated with the equation of Riazi and Whitson [2]: BþC p=pc ðrD12 Þ ¼ 1:07 ð116Þ id ðrD12 Þid B ¼ 0:27 0:38 o ð116aÞ Dv is the so-called diffusion volume, which can be determined with the group contributions from Table 9. The accuracy of the Fuller method is approximately 4% [2]. C ¼ 0:05 þ 0:1 o ð116bÞ Example 26: Determine the binary diffusion coefficient of a mixture of ammonia (NH3) and diethyl ether (C4H10O) at T = 288 K and p = 2 bar. The molecular weights are MNH3 = 17.03 g/mol and MC4H10O = 74.12 g/mol. The diffusion volumes for both components can be evaluated as: X Dv1 ¼ 20:7 X Dv2 ¼ 4 15:9 þ 10 2:31 þ 6:11 ¼ 92:81 After inserting the diffusion volumes into Eq. (115), one gets: D12 ¼ 0:00143ð288Þ1:75 ð17:03Þ1 þ ð74:12Þ1 i2 pﬃﬃﬃh 2 2 ð20:7Þ1=3 þð92:81Þ1=3 cm2 =s The value taken from the literature [2] is D12 = 0.0505 cm2/s. D1. Table 9. Group contributions for the diffusion volumes in the Fuller method Atom and structure contributions 15.9 Br 21.9 H 2.31 I 29.8 O 6.11 S N 4.54 Aromatic ring –18.3 Heterocyclic ring –18.3 F 14.7 Cl 21 and For mixtures, o and pc can be calculated with a linear mixing rule: X e yi oi ð117Þ o¼ i pc ¼ X e yi pci ð118Þ i The disadvantage of this relationship is that it requires the dynamic viscosity of the vapor mixture, which has to be estimated itself. Therefore, approximately 15% deviation for the estimation of vapor diffusion coefficients at high pressures should be expected. 10.2 Diffusion Coefficients in Liquids 1=2 ¼ 0:0517 cm2 =s C with 22.9 Simple molecules He 2.67 CO 18.0 Ne 5.98 CO2 26.9 Ar 16.2 N2O 35.9 Kr 24.5 NH3 20.7 Xe 32.7 H2O 13.1 H2 6.12 SF6 71.3 D2 6.84 Cl2 38.4 N2 18.5 Br2 69.0 O2 16.3 SO2 41.8 Air 19.7 The binary diffusion coefficient in liquid mixtures is a complicated function of the concentration and furthermore depends on temperature and pressure. A reliable estimation method is not available. For most of the related engineering problems it is sufficient to meet the correct order of magnitude. It is distinguished between the limiting case of the ideally diluted solution and the case with arbitrary concentrations. For the limiting case of infinite dilution of the solute A in the solvent B the diffusion coefficient can be estimated using several methods [2]. They are all characterized by individual rules for special components, limited ranges of applicability, or input parameters which are difficult to access. A reasonable compromise between accuracy and applicability is the simplified version of the method of Tyn/Calus [2]: 1=3 1 DAB vA ðTNBP Þ 1=6 8 vB ðTNBP Þ ¼ 8:93 10 cm2 =s cm3 =mol cm3 =mol ð119Þ 0:6 PB T B 1 PA K mPas with P as the parachor, which can be estimated to be 0:25 vi ðT Þ si Pi ¼ cm3 =mol mN=m ð120Þ There is also a group contribution method available [2], which, however, only covers a small part of all possible applications. The special rules of the Tyn/Calus equation are: ● The dynamic viscosity of the solvent should be less than 20. . .30 mPas. ● If the solute is water, vA and PA should be set to vA = 37.4 cm3/mol and PA = 105.2. Calculation Methods for Thermophysical Properties ● If the solute is an organic acid, the values for vA and PA should be doubled. Exceptions are made if the solvent is water, methanol, or n-butanol. ● If the solvent is an alcohol and the solute is nonpolar, the values for vA and PA should be multiplied with a factor corresponding to 8B/mPas. The deviations of the Tyn/Calus equation that should be expected are approximately 10%. The temperature dependence of Eq. (119) is only an approximation. The actual functional relationship is not finally clarified. Moreover, the pressure dependence is not well defined. It is only known that the liquid diffusion coefficient decreases with increasing pressure at very high pressures. The model of the ideally diluted solution is applicable if the concentration of the solute does not exceed 5%. . .10%. For the transition of the ideally diluted solution to the general case with arbitrary concentrations the Vignes correlation can be used: xA gA Þ xB xA @ lnðe 1 e 1 e ¼ ðD Þ ðD Þ ð121Þ DAB AB BA @ ln e xA T;p where g is the activity coefficient (see > Subchap. D5.1). Because of the validity of the Gibbs-Duhem equation it does not matter which component is used for the differential quotient. Example 27: Determine the binary diffusion coefficient in a liquid mixture of benzene (A) and toluene (B) at T = 298 K for xA = 0.4. Approximately, it is an ideal mixture so that the activity coefficients can be regarded to be unity. The given values are: vA(TNBP) = 95.84 cm3/mol vB(TNBP) = 118.31 cm3/mol vA(T) = 89.49 cm3/mol vB(T) = 106.79 cm3/mol sA(T) = 28.21 mN/m sB(T) = 27.94 mN/m A(T) = 0.601 mPas B(T) = 0.553 mPas The parachors can be determined to be: PA = 206.24 PB = 245.52 Thus, the diffusion coefficients in the ideally diluted state are: 245:52 0:6 1 DAB ¼ 8:93 108 ð118:31Þ1=3 ð95:84Þ1=6 206:24 298 ð0:553Þ1 cm2 =s ¼ 2:33 105 cm2 =s 1 DBA ¼ 8:93 108 ð95:84Þ1=3 ð118:31Þ1=6 206:24 0:6 245:52 298 ð0:601Þ1 cm2 =s ¼ 1:93 105 cm2 =s There is only one experimental value available [2] 1 (DBA = 1.85·10–5 cm2/s), which is met very well. For the actual concentration, the diffusion coefficient is determined with the Vignes correlation DAB ¼ ð2:33 105 Þ0:6 ð1:93 105 Þ0:4 cm2 =s ¼ 2:16 105 cm2 =s 10.3 D1 Diffusion in Multicomponent Mixtures In multicomponent mixtures, the diffusion flow depends not only on its own but also on the interaction of all concentration gradients. In extreme cases, a component can even diffuse in the opposite direction of its own concentration gradient [39]. The calculation of such processes is very complex and beyond the scope of this chapter. 11 Symbols a b A, B, C, D, E, F cs D f Fij Fp j kij K n nA P q r t v z e z Z Z2 a g DG DH DT Dp DNBP Dv Dg0f Dh0f real DhGas Dhin Dhm Dhv m n x parameter in RKS and PR equation of state (Pa m6 mol–2) parameter in RKS and PR equation of state (m3 mol–1) coefficients specific heat capacity along the saturation line (J kg–1 K–1) diffusion coefficient (m2 s–1) fugacity (Pa) weighting factor factor for pressure correction mole flux density (mol m–2 s–1) interaction parameter in cubic equations of state equilibrium constant (Pa–1) degree of association number of atoms in a molecule parachor electric charge (C) distance (m) Celsius temperature ( C) specific volume (m3 mol–1) coordinate (m) true concentration (association) (mol mol–1) compressibility factor correction factor coefficient activity coefficient group contribution for standard Gibbs energy of formation group contribution for standard enthalpy of formation group contribution for critical temperature group contribution for critical pressure group contribution for normal boiling point group contribution for critical volume standard Gibbs energy of formation (J mol–1) standard enthalpy of formation (J mol–1) residual part of vapor enthalpy (J mol–1) enthalpy of association (J mol–1) (component i, degree of association n) enthalpy of fusion (J mol–1) enthalpy of vaporization (J mol–1) dipole moment (debye) kinematic viscosity (m2s–1) reduced inverse viscosity 151 152 D1 SDv j F o Indices D E Gas id LG liq m M mix NBP ref s SRK 0 00 1 12 Calculation Methods for Thermophysical Properties diffusion volume fugacity coefficient parameter in thermal conductivity mixing rule acentric factor dimer excess quantity Gas ideal gas transition liquid–gas liquid melting point monomer mixture normal boiling point reference state saturation state Soave-Redlich-Kwong boiling liquid saturated vapor state of infinite dilution Bibliography 1. 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Hans-Joachim Kretzschmar 2 1 2 Ruhr-Universität Bochum, Bochum, Germany Hochschule Zittau/Görlitz, University of Applied Sciences, Zittau, Germany 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 2 Tables of Thermophysical Properties. . . . . . . . . . . . . . . . . . . 153 1 Introduction The International Association for the Properties of Water and Steam (IAPWS) adopted two international standards for the thermodynamic properties of water substance. The scientific equation of state was adopted in 1995 and is called ‘‘The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use’’ [1] or just IAPWS-95 for short. The formulation is valid in the entire stable fluid region of H2O from the melting curve to 1,000 C at pressures up to 10,000 bar; the lowest temperature on the melting curve is t = 21.985 C (at 2099 bar). In this entire region, IAPWS-95 represents the most accurate experimental data within their uncertainties. This formulation can be reasonably extrapolated far beyond its range of validity. A comprehensive article [2] describes all details about this formulation. The industrial standard for the thermodynamic properties of water and steam was adopted in 1997 and is called ‘‘IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam’’ [3] or ‘‘IAPWS-IF97’’ for short. IAPWSIF97 consists of a set of equations for different regions that covers the following range of validity: p 1000 bar 0 C t 800 C 800 C < t 2000 C p 500 bar This industrial standard has been coupled to the scientific standard IAPWS-95 by fitting the basic equations of IAPWSIF97 to values of several thermodynamic properties calculated from IAPWS-95. The Industrial Formulation IAPWS-IF97 is comprehensively described in the book ‘‘International Steam Tables’’ [4]. 2 Tables of Thermophysical Properties The values of the thermophysical properties listed in the following tables were calculated from the Industrial Formulation IAPWS-IF97 [3, 4], except for the temperature range t < 0 C of Table 1. The tabulated values of the transport properties were calculated from the current IAPWS equations for the thermal conductivity [5] and the dynamic viscosity [6], each in the version for industrial use. These equations are VDI-GVC (ed.), VDI Heat Atlas, DOI 10.1007/978-3-540-77877-6_11, # Springer-Verlag Berlin Heidelberg 2010 3 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 also given in the latest International Steam Tables [4]. Apart from the basic equations of IAPWS-IF97, this book contains all backward equations that have been developed in the past years. These backward equations allow quick calculations of properties for input values other than (p,T), for example, (p,h), (p,s), and (h,s) without iterations. The book also contains the representation of 25 properties in pressure-temperature diagrams. The property values in Tables 1–14 were calculated with the CD providing the interactive program ‘‘IAPWS-IF97 Electronic Steam Tables’’ that accompanies the International Steam Tables [4]. This software allows the calculation of ‘‘personal’’ steam tables for arbitrary values of pressure and temperature. Tables 1–14 cover the following properties: t – Celsius temperature T – Thermodynamic temperature p – Pressure r – Density v – Specific volume Z – Compression factor, Z = p/(rRT) h – Specific enthalpy s – Specific entropy cp – Specific isobaric heat capacity av – Isobaric cubic expansion coefficient, av= (1/v)(∂v/∂T )p l – Thermal conductivity – Dynamic viscosity n – Kinematic viscosity, n = /r a – Thermal diffusivity, a = l/(cp r) Pr – Prandtl number, Pr = cp/l s – Surface tension b – Laplace coefficient, b = {s/[g(r0 r00 )]}0.5, where g is the acceleration of gravity, g = 9.80655 m s2 Further properties are tabulated in the International Steam Tables [4]. The characteristic properties of water are: e = 18.015 275 Molar mass M 1 g mol Specific gas constant R = 0.461 526 kJ kg1 K1 Critical point: Tc = 647.096 K or tc = 373.946 C pc = 220.64 bar rc = 322 kg m3 Triple point: Tt = 273.16 K or tt = 0.01 C pt = 6.116 57 mbar Normal boiling point (p = 1.013 25 bar): Tb = 373.124 K or tb = 99.974 C (Continued on page 171) 154 D2 Properties of Selected Important Pure Substances D2.1. Table 1. Properties of water at the pressure p = 1 bara t r kg m3 C h kJ kg1 n s cp av l h a kJ kg1 K1 kJ kg1 K1 103 K1 103 W m1 K1 106 Pa s 106 m2 s1 106 m2 s1 20 993.57 85.624 0.32600 4.401 0.6604 4392.1 4.421 15 996.30 63.836 0.24076 4.321 0.4488 3348.5 3.361 14 996.73 59.521 0.22408 4.309 0.4137 3186.5 3.197 13 997.13 55.217 0.20751 4.299 0.3806 3036.6 3.045 12 997.49 50.924 0.19103 4.289 0.3492 2897.4 2.905 11 997.82 46.639 0.17466 4.280 0.3194 2768.1 2.774 10 998.13 42.363 0.15838 4.272 0.2911 2647.7 2.653 9 998.40 38.095 0.14219 4.265 0.2641 2535.3 2.539 8 998.66 33.833 0.12609 4.258 0.2384 2430.4 2.434 7 998.88 29.579 0.11007 4.252 0.2139 2332.1 2.335 6 999.08 25.330 0.09414 4.246 0.1904 2240.1 2.242 5 999.26 21.087 0.07828 4.241 0.1679 2153.7 2.155 Pr 4 999.42 16.849 0.06251 4.236 0.1463 2072.4 2.074 3 999.55 12.616 0.04681 4.231 0.1255 1996.0 1.997 2 999.67 8.3865 0.03118 4.227 0.1055 1924.0 1.925 1 999.77 4.1616 0.01563 4.223 0.0863 1856.0 1.856 0 999.84 0.05966 0.00015 4.219 0.0677 562.0 1791.8 1.792 0.1332 13.45 1 999.90 4.2774 0.01526 4.216 0.0497 564.1 1731.0 1.731 0.1338 12.94 2 999.94 8.4918 0.03061 4.213 0.0324 566.2 1673.5 1.674 0.1344 12.45 3 999.97 12.703 0.04589 4.210 0.0156 568.3 1619.0 1.619 0.1350 11.99 4 999.97 16.912 0.06110 4.207 0.0006 570.3 1567.3 1.567 0.1356 11.56 5 999.97 21.118 0.07625 4.205 0.0163 572.3 1518.2 1.518 0.1361 11.15 6 999.94 25.322 0.09134 4.203 0.0315 574.3 1471.5 1.472 0.1367 10.77 7 999.90 29.524 0.10636 4.201 0.0463 576.3 1427.0 1.427 0.1372 10.40 8 999.85 33.723 0.12133 4.199 0.0606 578.2 1384.7 1.385 0.1377 10.06 9 999.78 37.921 0.13623 4.197 0.0746 580.1 1344.4 1.345 0.1382 9.727 10 999.70 42.117 0.15108 4.195 0.0881 582.0 1305.9 1.306 0.1388 9.414 11 999.61 46.312 0.16586 4.194 0.1013 583.8 1269.2 1.270 0.1393 9.117 12 999.50 50.505 0.18060 4.193 0.1142 585.7 1234.0 1.235 0.1398 8.834 13 999.38 54.697 0.19527 4.191 0.1267 587.5 1200.5 1.201 0.1403 8.565 14 999.25 58.888 0.20989 4.190 0.1389 589.3 1168.3 1.169 0.1407 8.308 15 999.10 63.078 0.22446 4.189 0.1509 591.0 1137.6 1.139 0.1412 8.063 20 998.21 84.012 0.29648 4.185 0.2066 599.5 1001.6 1.003 0.1435 6.991 25 997.05 104.93 0.36723 4.182 0.2569 607.5 890.0 0.893 0.1457 6.127 30 995.65 125.83 0.43676 4.180 0.3029 615.0 797.2 0.801 0.1478 5.419 35 994.04 146.73 0.50513 4.179 0.3453 622.0 719.1 0.723 0.1497 4.831 40 992.22 167.62 0.57239 4.179 0.3849 628.6 652.7 0.658 0.1516 4.339 45 990.22 188.52 0.63859 4.179 0.4222 634.8 595.8 0.602 0.1534 3.922 50 988.05 209.41 0.70375 4.180 0.4574 640.5 546.5 0.553 0.1551 3.566 55 985.71 230.31 0.76794 4.181 0.4910 645.8 503.6 0.511 0.1567 3.260 60 983.21 251.22 0.83117 4.183 0.5231 650.8 466.0 0.474 0.1582 2.995 65 980.57 272.14 0.89350 4.185 0.5541 655.4 432.9 0.441 0.1597 2.764 70 977.78 293.07 0.95495 4.188 0.5841 659.6 403.6 0.413 0.1611 2.562 75 974.86 314.02 1.0156 4.192 0.6132 663.5 377.4 0.387 0.1624 2.384 80 971.80 334.99 1.0754 4.196 0.6417 667.0 354.1 0.364 0.1636 2.227 85 968.62 355.98 1.1344 4.200 0.6695 670.2 333.1 0.344 0.1647 2.087 Properties of Water and Steam D2.1 D2.1. Table 1. (continued) t r kg m3 C n s cp av l h a kJ kg1 K1 kJ kg1 K1 103 K1 103 W m1 K1 106 Pa s 106 m2 s1 106 m2 s1 h kJ kg1 Pr 90 965.32 376.99 1.1926 4.205 0.6970 673.0 314.2 0.325 0.1658 1.963 95 961.89 398.03 1.2502 4.211 0.7241 675.5 297.1 0.309 0.1668 1.852 958.64 417.44 1.3026 4.216 0.7489 677.6 282.7 0.295 0.1676 1.759 99.606 b The values for the properties at t 0 C and p = 1 bar correspond to the (metastable) subcooled liquid; in the stable state at these t-p values, water is in the solid phase (ice). The values were calculated with the scientific standard equation of state IAPWS-95 [1, 2] that can be extrapolated up to these for t < 0 C temperatures. The equation for l [4, 5] cannot be extrapolated to temperatures t < 0 C; thus, the properties a and Pr cannot be calculated, either. b Temperature at the saturated-liquid line. t, Temperature; r, Density; h, Specific enthalpy; s, Specific entropy; cp, Specific isobaric heat capacity; av, Isobaric cubic expansion coefficient; l, Thermal conductivity; , Dynamic viscosity; n, Kinematic viscosity; a, Thermal diffusivity; Pr, Prandtl number. a D2.1. Table 2. Thermodynamic properties of water in the saturation state from the triple point to the critical point t ps C bar r0 r00 kg m3 h0 kJ h00 kg1 s0 kJ s00 kg1 K 1 cp0 kJ cp00 kg1 1 K av0 103 av00 1 K a 0.006112 999.79 0.004851 0.041588 2500.9 0.000155 9.1558 4.220 1.888 0.06807 3.681 0.01b 0.006117 999.79 0.004854 0.000612 2500.9 0.000000 9.1555 4.220 1.888 0.06789 3.681 0.00 5.00 0.008726 999.92 0.006802 21.019 2510.1 0.076252 9.0249 4.205 1.892 0.01599 3.618 10.00 0.012282 999.65 0.009407 42.021 2519.2 0.15109 8.8998 4.196 1.896 0.08789 3.559 15.00 0.017057 999.05 0.01284 62.984 2528.4 0.22447 8.7804 4.189 1.900 0.1507 3.501 20.00 0.023392 998.16 0.01731 83.920 2537.5 0.29650 8.6661 4.185 1.906 0.2065 3.447 25.00 0.031697 997.00 0.02307 104.84 2546.5 0.36726 8.5568 4.182 1.912 0.2568 3.395 30.00 0.042467 995.61 0.03041 125.75 2555.6 0.43679 8.4521 4.180 1.918 0.3028 3.346 35.00 0.056286 994.00 0.03967 146.64 2564.6 0.50517 8.3518 4.179 1.925 0.3453 3.298 40.00 0.073844 992.18 0.05124 167.54 2573.5 0.57243 8.2557 4.179 1.932 0.3849 3.254 45.00 0.095944 990.18 0.06556 188.44 2582.5 0.63862 8.1634 4.179 1.940 0.4222 3.211 50.00 0.12351 988.01 0.08314 209.34 2591.3 0.70379 8.0749 4.180 1.948 0.4574 3.171 55.00 0.15761 985.67 0.10455 230.24 2600.1 0.76798 7.9899 4.181 1.957 0.4910 3.133 60.00 0.19946 983.18 0.13042 251.15 2608.8 0.83122 7.9082 4.183 1.966 0.5232 3.098 65.00 0.25041 980.53 0.16145 272.08 2617.5 0.89354 7.8296 4.185 1.976 0.5542 3.064 70.00 0.31201 977.75 0.19842 293.02 2626.1 0.95499 7.7540 4.188 1.987 0.5841 3.033 75.00 0.38595 974.83 0.24218 313.97 2634.6 1.0156 7.6812 4.192 1.999 0.6133 3.005 80.00 0.47415 971.78 0.29366 334.95 2643.0 1.0754 7.6110 4.196 2.012 0.6417 2.979 85.00 0.57867 968.60 0.35387 355.95 2651.3 1.1344 7.5434 4.200 2.026 0.6696 2.955 90.00 0.70182 965.30 0.42388 376.97 2659.5 1.1927 7.4781 4.205 2.042 0.6970 2.934 95.00 0.84609 961.89 0.50489 398.02 2667.6 1.2502 7.4150 4.211 2.059 0.7241 2.916 100.00 1.0142 958.35 0.59814 419.10 2675.6 1.3070 7.3541 4.217 2.077 0.7510 2.901 110.00 1.4338 950.95 0.82686 461.36 2691.1 1.4187 7.2380 4.230 2.121 0.8044 2.880 120.00 1.9867 943.11 1.1220 503.78 2705.9 1.5278 7.1291 4.246 2.174 0.8580 2.871 130.00 2.7026 934.83 1.4968 546.39 2720.1 1.6346 7.0264 4.265 2.237 0.9124 2.876 140.00 3.6150 926.13 1.9665 589.20 2733.4 1.7393 6.9293 4.286 2.311 0.9683 2.894 150.00 4.7610 917.01 2.5478 632.25 2745.9 1.8420 6.8370 4.310 2.396 1.026 2.927 160.00 6.1814 907.45 3.2593 675.57 2757.4 1.9428 6.7491 4.338 2.492 1.087 2.975 170.00 7.9205 897.45 4.1217 719.21 2767.9 2.0419 6.6649 4.369 2.599 1.152 3.038 180.00 10.026 887.01 5.1583 763.19 2777.2 2.1395 6.5841 4.406 2.716 1.222 3.117 190.00 12.550 876.08 6.3948 807.57 2785.3 2.2358 6.5060 4.447 2.846 1.297 3.214 200.00 15.547 864.67 7.8603 852.39 2792.1 2.3308 6.4303 4.494 2.990 1.379 3.332 210.00 19.074 852.73 9.5875 897.73 2797.4 2.4248 6.3565 4.548 3.150 1.469 3.474 155 156 D2 Properties of Selected Important Pure Substances D2.1. Table 2. (continued) t ps C r0 r00 bar kg h0 m3 kJ h00 s0 kg1 kJ s00 kg1 cp0 1 kJ K cp00 kg1 av0 1 103 K av00 K 1 220.00 23.193 840.23 11.614 943.64 2801.1 2.5178 6.2842 4.611 3.328 1.570 3.643 230.00 27.968 827.12 13.984 990.21 2803.0 2.6102 6.2131 4.683 3.528 1.683 3.845 240.00 33.467 813.36 16.748 1037.5 2803.1 2.7019 6.1425 4.767 3.755 1.811 4.085 250.00 39.759 798.89 19.965 1085.7 2801.0 2.7934 6.0722 4.865 4.012 1.958 4.372 260.00 46.921 783.62 23.710 1134.8 2796.6 2.8847 6.0017 4.981 4.308 2.130 4.717 270.00 55.028 767.46 28.072 1185.1 2789.7 2.9762 5.9304 5.119 4.655 2.334 5.137 280.00 64.165 750.27 33.163 1236.7 2779.8 3.0681 5.8578 5.286 5.070 2.580 5.658 290.00 74.416 731.91 39.128 1289.8 2766.6 3.1608 5.7832 5.492 5.581 2.886 6.316 300.00 85.877 712.14 46.162 1344.8 2749.6 3.2547 5.7058 5.752 6.223 3.274 7.167 310.00 98.647 690.67 54.529 1402.0 2727.9 3.3506 5.6243 6.088 7.051 3.785 8.297 8.157 4.483 9.858 9.738 5.504 12.16 7.186 15.89 320.00 112.84 667.08 64.616 1462.1 2700.7 3.4491 5.5373 6.541 330.00 128.58 640.78 77.018 1525.7 2666.2 3.5516 5.4425 7.189 340.00 146.00 610.68 92.731 1594.4 2622.1 3.6599 5.3359 8.217 350.00 165.29 574.69 113.62 1670.9 2563.6 3.7783 5.2109 10.10 16.64 10.36 360.00 186.66 527.84 143.99 1761.5 2481.0 3.9164 5.0527 14.87 27.57 18.81 370.00 210.43 450.03 202.18 1892.6 2333.5 4.1142 4.7996 47.10 93.40 79.65 148.0 373.00 218.13 395.81 248.68 1974.1 2227.6 4.2377 4.6299 231.91 401.13 435.72 679.1 373.946c 220.64 322.00 2087.5 12.24 1d 4.4120 22.66 39.74 1d The values at t = 0 C were determined by extrapolating the saturation curves from t = 0.01 C (triple-point temperature) to t = 0 C. Triple-point temperature. c Critical temperature. d At the critical point, IAPWS-IF97 does not yield accurate values for cp and av. t, Temperature; ps, Saturation pressure; r, Density; h, Specific enthalpy; s, Specific entropy; cp, Specific isobaric heat capacity; av, Isobaric cubic expansion coefficient; 0 , Saturated liquid; 00 , Saturated vapor. a b D2.1. Table 3. Transport properties of water in the saturation state from the triple point to the critical point ps t bar C l0 l00 103 W m1 K1 h0 h00 106 Pa s n0 n00 Pr0 106 m2 s1 Pr00 s b 103 N m1 103 m 0.00a 0.006112 562.0 16.49 1792.0 8.945 1.792 1844.0 13.46 1.024 75.65 2.778 0.01b 0.006117 562.0 16.49 1791.4 8.946 1.792 1842.8 13.45 1.024 75.65 2.778 5.00 0.008726 572.3 16.85 1518.3 9.090 1.518 1336.4 11.16 1.020 74.94 2.765 10.00 0.012282 581.9 17.21 1306.0 9.238 1.306 982.1 9.417 1.017 74.22 2.752 15.00 0.017057 591.0 17.58 1137.6 9.390 1.139 731.3 8.065 1.015 73.49 2.739 20.00 0.023392 599.5 17.95 1001.6 9.544 1.003 551.3 6.993 1.013 72.74 2.726 25.00 0.031697 607.5 18.33 890.0 9.701 0.8927 420.5 6.128 1.012 71.97 2.713 30.00 0.042467 615.0 18.71 797.2 9.860 0.8007 324.2 5.419 1.011 71.19 2.700 35.00 0.056286 622.0 19.09 719.1 10.02 0.7235 252.6 4.832 1.010 70.40 2.688 40.00 0.073844 628.6 19.48 652.7 10.18 0.6579 198.8 4.339 1.010 69.60 2.675 45.00 0.095944 634.7 19.88 595.8 10.35 0.6017 157.9 3.922 1.010 68.78 2.661 50.00 0.12351 640.5 20.28 546.5 10.52 0.5531 126.5 3.567 1.010 67.94 2.648 55.00 0.15761 645.8 20.69 503.6 10.68 0.5109 102.2 3.260 1.011 67.10 2.635 60.00 0.19946 650.8 21.10 466.0 10.85 0.4740 83.22 2.995 1.011 66.24 2.621 65.00 0.25041 655.3 21.53 432.9 11.02 0.4415 68.28 2.765 1.012 65.37 2.607 70.00 0.31201 659.6 21.96 403.5 11.19 0.4127 56.42 2.562 1.013 64.48 2.593 75.00 0.38595 663.4 22.41 377.4 11.37 0.3872 46.93 2.385 1.014 63.58 2.579 80.00 0.47415 667.0 22.86 354.0 11.54 0.3643 39.29 2.227 1.016 62.67 2.565 85.00 0.57867 670.1 23.32 333.1 11.71 0.3439 33.10 2.087 1.017 61.75 2.550 90.00 0.70182 673.0 23.80 314.2 11.89 0.3255 28.04 1.963 1.019 60.82 2.535 Properties of Water and Steam D2.1 D2.1. Table 3. (continued) l0 ps t h0 W m1 K1 bar C l00 103 h00 n0 106 Pa s n00 Pr0 106 m2 s1 Pr00 s b 103 N m1 103 m 95.00 0.84609 675.5 24.29 297.1 12.06 0.3089 23.88 1.852 1.022 59.87 2.520 100.00 1.0142 677.8 24.79 281.6 12.23 0.2938 20.45 1.752 1.025 58.91 2.504 110.00 1.4338 681.3 25.85 254.6 12.58 0.2677 15.21 1.581 1.032 56.96 2.473 120.00 1.9867 683.6 26.96 232.0 12.93 0.2460 11.52 1.441 1.042 54.97 2.439 130.00 2.7026 684.8 28.15 212.9 13.27 0.2278 8.867 1.326 1.055 52.93 2.405 140.00 3.6150 684.9 29.42 196.6 13.62 0.2123 6.925 1.231 1.070 50.86 2.369 150.00 4.7610 683.9 30.77 182.6 13.96 0.1991 5.480 1.151 1.087 48.74 2.331 160.00 6.1814 681.8 32.22 170.4 14.30 0.1878 4.389 1.084 1.106 46.59 2.292 170.00 7.9205 678.7 33.77 159.8 14.64 0.1780 3.553 1.029 1.127 44.41 2.251 180.00 10.026 674.6 35.42 150.4 14.99 0.1695 2.905 0.9821 1.149 42.19 2.209 190.00 12.550 669.5 37.19 142.0 15.33 0.1621 2.397 0.9435 1.173 39.95 2.164 200.00 15.547 663.4 39.10 134.6 15.67 0.1557 1.993 0.9118 1.198 37.67 2.117 210.00 19.074 656.3 41.14 127.9 16.01 0.1500 1.670 0.8862 1.226 35.38 2.069 220.00 23.193 648.2 43.34 121.8 16.35 0.1449 1.408 0.8662 1.256 33.07 2.017 230.00 27.968 639.1 45.72 116.2 16.70 0.1405 1.195 0.8514 1.289 30.74 1.963 240.00 33.467 629.0 48.32 111.1 17.06 0.1365 1.019 0.8417 1.326 28.39 1.906 250.00 39.759 617.8 51.16 106.3 17.43 0.1330 0.8730 0.8369 1.367 26.04 1.846 260.00 46.921 605.6 54.30 101.8 17.81 0.1299 0.7511 0.8374 1.413 23.69 1.783 270.00 55.028 592.2 57.81 97.58 18.21 0.1272 0.6486 0.8434 1.466 21.34 1.715 280.00 64.165 577.7 61.79 93.55 18.63 0.1247 0.5618 0.8559 1.529 18.99 1.643 290.00 74.416 562.0 66.37 89.66 19.08 0.1225 0.4877 0.8761 1.605 16.66 1.566 300.00 85.877 545.0 71.75 85.86 19.58 0.1206 0.4242 0.9061 1.698 14.36 1.483 98.647 12.09 1.392 310.00 526.5 78.24 82.09 20.13 0.1189 0.3693 0.9493 1.815 320.00 112.84 506.5 86.35 78.31 20.77 0.1174 0.3215 1.011 1.962 9.864 1.292 330.00 128.58 484.8 96.96 74.43 21.53 0.1162 0.2796 1.104 2.163 7.703 1.180 340.00 146.00 461.4 111.7 70.33 22.48 0.1152 0.2424 1.252 2.462 5.625 1.052 350.00 165.29 436.5 134.5 65.80 23.74 0.1145 0.2089 1.523 2.936 3.665 0.9004 360.00 186.66 411.9 176.6 60.32 25.64 0.1143 0.1781 2.178 4.002 1.877 0.7062 370.00 210.43 418.1 309.5 51.90 29.60 0.1153 0.1464 8.933 0.3882 0.3997 373.00 218.13 535.0 507.0 46.38 33.11 0.1172 0.1331 0.0648 0.2118 373.946c 220.64 –d 0 0 39.33 5.846 20.11 26.19 1e 0.1221 The values at t = 0 C were determined by extrapolating the saturation curves from t = 0.01 C (triple-point temperature) to t = 0 C. Triple-point temperature. c Critical temperature. d The industrial equations for l [4, 5] and [4, 6] do not represent the critical enhancement in the near-critical region. If more accurate values are needed in this region, the scientific equations for l [5] and [6] should be used. e In the near-critical region, the use of IAPWS-IF97 for cp and the use of the industrial equations for l [4, 5] and [4, 6] do not yield accurate values for Pr. t, Temperature; ps; Saturation pressure; l, Thermal conductivity; , Dynamic viscosity; n, Kinematic viscosity; Pr, Prandtl number; s, Surface tension; b, Laplace coefficient; 0 , Saturated liquid; 00 , Saturated vapor. a b D2.1. Table 4. Density r/(kg m3) of water for given values of pressure and temperaturea Pressure p bar 1 Temperature t / C 0 999.84 b 25 50 75 100 0.5896 125 0.5503 150 200 250 300 0.5163 0.4603 0.4156 0.3790 2.3528 2.1078 1.9135 4.8543 4.2967 3.8763 997.05 988.05 974.86 5 1000.0 997.23 988.22 975.03 958.54 939.16 917.02 10 1000.3 997.45 988.44 975.25 958.77 939.41 917.30 20 1000.8 997.90 988.87 975.70 959.24 939.92 917.87 865.01 30 1001.3 998.35 989.30 976.14 959.71 940.43 918.43 865.77 40 1001.8 998.80 989.74 976.58 960.17 940.93 919.00 866.52 8.9699 14.160 798.92 7.9681 12.319 16.987 157 158 D2 Properties of Selected Important Pure Substances D2.1. Table 4. (continued) Pressure p bar 0 25 50 75 100 125 150 200 250 300 50 1002.3 999.24 990.17 977.02 960.64 941.43 919.56 867.27 800.08 22.052 60 1002.8 999.69 990.60 977.45 961.10 941.93 920.11 868.02 801.23 27.631 70 1003.3 1000.1 991.03 977.89 961.56 942.43 920.67 868.75 802.37 33.905 80 1003.8 1000.6 991.46 978.33 962.02 942.93 921.22 869.49 803.49 90 1004.3 1001.0 991.88 978.76 962.47 943.43 921.77 870.22 804.60 713.07 100 1004.8 1001.5 992.31 979.19 962.93 943.92 922.32 870.95 805.70 715.29 150 1007.3 1003.7 994.43 981.35 965.20 946.37 925.03 874.51 811.02 725.55 200 1009.7 1005.8 996.53 983.48 967.43 948.78 927.69 877.97 816.09 734.71 250 1012.2 1008.0 998.60 985.58 969.64 951.16 930.30 881.34 820.92 743.01 300 1014.5 1010.1 1000.7 987.66 971.82 953.50 932.86 884.62 825.55 750.64 350 1016.9 1012.2 1002.7 989.72 973.97 955.80 935.38 887.82 830.00 757.72 400 1019.2 1014.3 1004.7 991.76 976.10 958.07 937.86 890.94 834.28 764.34 450 1021.5 1016.4 1006.7 993.77 978.19 960.31 940.30 893.99 838.41 770.57 500 1023.8 1018.4 1008.7 995.77 980.27 962.52 942.70 896.98 842.40 776.46 600 1028.3 1022.5 1012.6 999.69 984.34 966.85 947.39 902.75 850.02 787.38 700 1032.7 1026.4 1016.4 1003.5 988.32 971.07 951.94 908.29 857.20 797.36 800 1037.0 1030.3 1020.1 1007.3 992.22 975.18 956.36 913.62 864.00 806.58 900 1041.2 1034.1 1023.8 1011.0 996.02 979.19 960.66 918.77 870.47 815.15 1000 1045.3 1037.9 1027.4 1014.6 999.75 983.12 964.85 923.74 876.65 823.18 Pressure p bar a Temperature t / C 41.186 Temperature t / C 350 400 450 500 550 600 650 700 750 800 1 0.3483 0.3223 0.2999 0.2805 0.2634 0.2483 0.2348 0.2227 0.2118 0.2019 5 1.7540 1.6200 1.5056 1.4066 1.3200 1.2436 1.1757 1.1149 1.0601 1.0104 10 3.5399 3.2616 3.0263 2.8240 2.6479 2.4931 2.3557 2.2330 2.1226 2.0227 20 7.2153 6.6134 6.1148 5.6922 5.3278 5.0097 4.7289 4.4791 4.2551 4.0529 9.2692 8.6064 8.0407 7.5503 7.1199 6.7384 6.3975 6.0905 30 11.043 10.063 40 15.043 13.618 12.493 11.569 10.788 10.116 50 19.241 17.289 15.792 14.581 13.570 12.706 11.956 11.298 10.712 10.188 60 23.667 21.087 19.169 17.646 16.388 15.322 14.403 13.598 12.885 12.249 70 28.357 25.024 22.630 20.765 19.243 17.965 16.868 15.912 15.068 14.317 80 33.358 29.114 26.180 23.941 22.138 20.634 19.352 18.240 17.261 16.392 9.5290 9.0112 8.5499 8.1357 90 38.732 33.374 29.826 27.177 25.071 23.332 21.857 20.582 19.465 18.475 100 44.559 37.822 33.574 30.476 28.046 26.057 24.381 22.939 21.679 20.566 150 87.103 63.812 54.118 48.011 43.582 40.127 37.309 34.941 32.909 31.135 78.615 67.600 60.348 54.992 50.776 47.320 44.405 41.896 89.750 78.522 70.723 64.810 60.084 56.171 52.847 98.285 87.380 79.430 73.238 68.203 63.984 86.778 80.495 75.300 93.037 86.784 200 600.65 100.51 250 625.47 166.53 108.99 300 643.95 357.60 148.41 115.07 350 659.00 474.92 201.66 144.23 119.79 105.01 400 671.86 523.37 270.80 177.78 143.16 123.62 110.45 100.69 450 683.16 554.46 343.02 215.78 168.40 143.21 126.83 114.97 105.81 500 693.27 577.74 402.02 257.11 195.37 163.70 143.73 129.57 118.80 110.20 600 710.89 612.39 479.69 338.80 252.86 206.89 178.86 159.61 145.31 134.11 700 726.04 638.41 528.52 406.02 310.25 251.58 215.13 190.41 172.31 158.31 800 739.40 659.49 563.73 457.03 362.31 295.54 251.57 221.43 199.47 182.61 900 751.40 677.35 591.36 496.46 406.89 336.75 287.17 252.12 226.46 206.78 1000 762.33 692.92 614.19 528.20 444.48 374.22 321.08 282.00 252.96 230.65 94.645 98.424 The bold horizontal lines in the columns indicate the transition from the liquid phase to the gas phase. The values for the properties at t = 0 C and p = 1 bar correspond to the (metastable) subcooled liquid; in the stable state at these t-p values, water is in the solid phase (ice). b Properties of Water and Steam D2.1 D2.1. Table 5. Compression factor Z of water for given values of pressure and temperaturea Pressure p bar Temperature t / C 0 1 0.000793 b 25 50 75 100 125 150 200 0.000729 0.000679 250 300 0.000638 0.9848 0.9890 0.9917 0.9949 0.9966 0.9976 5 0.003966 0.003644 0.003392 0.003191 0.003029 0.002897 0.002792 0.9878 0.007930 0.007286 0.006783 0.006381 0.006056 0.005793 0.005582 0.9732 0.9434 0.9825 10 0.9639 0.9753 20 0.01585 0.01457 0.01356 0.01276 0.01211 0.01158 0.01116 0.01059 0.9489 0.9206 30 0.02377 0.02184 0.02033 0.01913 0.01815 0.01736 0.01673 0.01587 0.9235 0.8775 40 0.03167 0.02910 0.02710 0.02549 0.02419 0.02313 0.02229 0.02114 0.02074 0.8902 50 0.03957 0.03636 0.03386 0.03185 0.03022 0.02890 0.02784 0.02640 0.02588 0.8571 60 0.04746 0.04362 0.04061 0.03820 0.03625 0.03466 0.03339 0.03165 0.03101 0.8209 70 0.05534 0.05086 0.04736 0.04455 0.04227 0.04042 0.03893 0.03690 0.03613 80 0.06322 0.05810 0.05410 0.05089 0.04829 0.04617 0.04447 0.04213 0.04124 0.7805 0.7343 90 0.07108 0.06534 0.06084 0.05723 0.05430 0.05191 0.05000 0.04736 0.04633 0.04771 100 0.07894 0.07257 0.06757 0.06356 0.06030 0.05765 0.05552 0.05258 0.05140 0.05285 150 0.1181 0.1086 0.1011 0.09513 0.09024 0.08626 0.08303 0.07855 0.07660 0.07816 200 0.1571 0.1445 0.1346 0.1266 0.1200 0.1147 0.1104 0.1043 0.1015 0.1029 250 0.1959 0.1802 0.1679 0.1579 0.1497 0.1430 0.1376 0.1299 0.1261 0.1272 300 0.2346 0.2158 0.2010 0.1890 0.1792 0.1712 0.1647 0.1553 0.1505 0.1511 350 0.2730 0.2513 0.2340 0.2201 0.2087 0.1993 0.1916 0.1805 0.1746 0.1746 400 0.3113 0.2866 0.2669 0.2510 0.2380 0.2272 0.2184 0.2056 0.1986 0.1978 450 0.3494 0.3218 0.2997 0.2818 0.2671 0.2550 0.2451 0.2305 0.2223 0.2208 500 0.3874 0.3568 0.3324 0.3125 0.2962 0.2827 0.2716 0.2553 0.2458 0.2434 600 0.4628 0.4264 0.3973 0.3735 0.3539 0.3377 0.3243 0.3044 0.2923 0.2881 700 0.5377 0.4956 0.4618 0.4341 0.4113 0.3923 0.3765 0.3529 0.3382 0.3319 800 0.6120 0.5643 0.5258 0.4943 0.4682 0.4464 0.4283 0.4010 0.3835 0.3750 900 0.6857 0.6325 0.5894 0.5540 0.5247 0.5002 0.4797 0.4486 0.4282 0.4174 1000 0.7589 0.7002 0.6526 0.6134 0.5808 0.5535 0.5307 0.4957 0.4724 0.4592 Pressure p bar Temperature t / C 350 400 450 500 550 600 650 700 750 800 0.9998 1 0.9983 0.9987 0.9990 0.9992 0.9994 0.9995 0.9996 0.9997 0.9998 5 0.9912 0.9935 0.9951 0.9962 0.9970 0.9977 0.9982 0.9985 0.9988 0.9991 10 0.9822 0.9869 0.9901 0.9924 0.9941 0.9954 0.9963 0.9971 0.9977 0.9982 20 0.9638 0.9734 0.9800 0.9847 0.9881 0.9907 0.9927 0.9942 0.9954 0.9963 30 0.9446 0.9596 0.9697 0.9769 0.9821 0.9860 0.9890 0.9913 0.9931 0.9945 40 0.9245 0.9454 0.9593 0.9690 0.9760 0.9813 0.9852 0.9883 0.9908 0.9927 50 0.9035 0.9309 0.9487 0.9610 0.9699 0.9765 0.9815 0.9854 0.9884 0.9909 60 0.8815 0.9159 0.9379 0.9529 0.9637 0.9717 0.9778 0.9824 0.9861 0.9890 70 0.8583 0.9004 0.9268 0.9447 0.9575 0.9669 0.9740 0.9795 0.9838 0.9872 80 0.8339 0.8845 0.9156 0.9365 0.9512 0.9621 0.9703 0.9765 0.9815 0.9854 90 0.8079 0.8680 0.9041 0.9281 0.9449 0.9572 0.9665 0.9736 0.9791 0.9836 100 0.7803 0.5988 0.8510 0.8924 0.9196 0.9385 0.9523 0.9627 0.9706 0.9768 0.9817 150 0.7566 0.8305 0.8756 0.9060 0.9276 0.9436 0.9558 0.9653 0.9727 200 0.1158 0.6405 0.7623 0.8291 0.8724 0.9025 0.9245 0.9410 0.9538 0.9638 250 0.1390 0.4832 0.6873 0.7806 0.8381 0.8772 0.9054 0.9264 0.9425 0.9551 300 0.1620 0.2700 0.6057 0.7306 0.8035 0.8520 0.8865 0.9120 0.9315 0.9467 350 0.1847 0.2372 0.5200 0.6801 0.7691 0.8271 0.8680 0.8980 0.9208 0.9385 400 0.2070 0.2460 0.4426 0.6305 0.7355 0.8029 0.8500 0.8845 0.9105 0.9306 450 0.2290 0.2612 0.3931 0.5844 0.7034 0.7798 0.8328 0.8715 0.9006 0.9231 500 0.2508 0.2786 0.3726 0.5450 0.6737 0.7579 0.8165 0.8592 0.8913 0.9160 600 0.2935 0.3154 0.3748 0.4963 0.6246 0.7197 0.7873 0.8370 0.8744 0.9033 159 160 D2 Properties of Selected Important Pure Substances D2.1. Table 5. (continued) Pressure p bar Temperature t / C 350 400 450 500 550 600 650 700 750 800 700 0.3352 0.3529 0.3968 0.4832 0.5939 0.6905 0.7637 0.8185 0.8603 0.8928 800 0.3762 0.3905 0.4252 0.4905 0.5812 0.6717 0.7464 0.8044 0.8493 0.8845 900 0.4165 0.4277 0.4560 0.5080 0.5822 0.6632 0.7356 0.7948 0.8416 0.8788 1000 0.4561 0.4645 0.4878 0.5306 0.5922 0.6631 0.7310 0.7896 0.8372 0.8754 a The bold horizontal lines in the columns indicate the transition from the liquid phase to the gas phase. The values for the properties at t = 0 C and p = 1 bar correspond to the (metastable) subcooled liquid; in the stable state at these t-p values, water is in the solid phase (ice). b D2.1. Table 6. Specific enthalpy h/(kJ kg1) of water for given values of pressure and temperaturea Pressure p bar Temperature t / C 0 b 25 50 75 100 125 150 200 250 300 1 0.05966 104.93 209.41 314.02 2675.8 2726.7 2776.6 2875.5 2974.5 3074.5 5 0.46700 105.30 209.76 314.35 419.40 525.25 632.27 2961.1 3064.6 10 0.97582 105.76 210.19 314.75 419.77 525.59 632.57 2855.9 2828.3 2943.2 3051.7 20 1.9923 106.69 211.05 315.56 420.53 526.28 633.19 852.57 3024.3 30 3.0072 107.61 211.91 316.36 421.28 526.97 633.81 852.98 2903.2 2856.5 40 4.0206 108.53 212.77 317.17 422.03 527.67 634.43 853.39 1085.7 2961.7 50 5.0325 109.46 213.63 317.98 422.78 528.36 635.06 853.80 1085.7 2925.6 60 6.0429 110.38 214.49 318.78 423.53 529.05 635.68 854.22 1085.7 2885.5 70 7.0517 111.30 215.36 319.59 424.29 529.75 636.30 854.64 1085.6 80 8.0591 112.22 216.22 320.40 425.04 530.44 636.93 855.06 1085.7 2839.8 2786.4 2994.3 90 9.0649 113.14 217.07 321.20 425.79 531.14 637.56 855.49 1085.7 1344.3 100 10.069 114.06 217.93 322.01 426.55 531.83 638.18 855.92 1085.7 1343.1 150 15.069 118.64 222.23 326.04 430.32 535.32 641.34 858.12 1086.0 1338.1 200 20.034 123.21 226.51 330.07 434.10 538.82 644.52 860.39 1086.6 1334.1 250 24.964 127.76 230.78 334.10 437.88 542.34 647.73 862.73 1087.3 1331.1 300 29.860 132.29 235.05 338.13 441.67 545.87 650.96 865.14 1088.3 1328.7 350 34.724 136.81 239.31 342.16 445.47 549.42 654.22 867.61 1089.4 1326.8 400 39.556 141.30 243.56 346.18 449.27 552.97 657.49 870.12 1090.6 1325.4 450 44.357 145.78 247.80 350.20 453.07 556.53 660.78 872.69 1092.0 1324.4 500 49.129 150.25 252.03 354.22 456.87 560.11 664.10 875.31 1093.4 1323.7 600 58.586 159.14 260.47 362.25 464.49 567.28 670.77 880.67 1096.7 1323.3 700 67.935 167.96 268.88 370.28 472.12 574.49 677.50 886.19 1100.4 1323.7 800 77.180 176.73 277.26 378.28 479.75 581.72 684.29 891.85 1104.3 1324.9 900 86.329 185.44 285.60 386.28 487.39 588.98 691.13 897.63 1108.6 1326.6 1000 95.386 194.10 293.92 394.26 495.04 596.27 698.01 903.51 1113.0 1328.9 Pressure p bar Temperature t / C 350 400 450 500 550 600 650 700 750 800 1 3175.8 3278.5 3382.8 3488.7 3596.3 3705.6 3816.6 3929.4 4043.9 4160.2 5 3168.1 3272.3 3377.7 3484.4 3592.6 3702.5 3813.9 3927.0 4041.9 4158.4 10 3158.2 3264.4 3371.2 3479.0 3588.1 3698.6 3810.5 3924.1 4039.3 4156.1 20 3137.6 3248.2 3358.1 3468.1 3578.9 3690.7 3803.8 3918.2 4034.2 4151.6 30 3116.1 3231.6 3344.7 3457.0 3569.6 3682.8 3797.0 3912.3 4029.0 4147.0 40 3093.3 3214.4 3331.0 3445.8 3560.2 3674.8 3790.2 3906.4 4023.8 4142.5 50 3069.3 3196.6 3317.0 3434.5 3550.8 3666.8 3783.3 3900.5 4018.6 4137.9 Properties of Water and Steam D2.1 D2.1. Table 6. (continued) Pressure p bar Temperature t / C 350 400 450 500 550 600 650 700 750 800 60 3043.9 3178.2 3302.8 3422.9 3541.2 3658.8 3776.4 3894.5 4013.4 4133.3 70 3016.8 3159.1 3288.2 3411.3 3531.5 3650.6 3769.4 3888.5 4008.1 4128.7 80 2988.1 3139.3 3273.2 3399.4 3521.8 3642.4 3762.4 3882.4 4002.9 4124.0 90 2957.2 3118.8 3257.9 3387.3 3511.9 3634.2 3755.4 3876.4 3997.6 4119.4 100 3097.4 3242.3 3375.1 3501.9 3625.8 3748.3 3870.3 3992.3 4114.7 150 2924.0 2693.0 2975.5 3157.8 3310.8 3450.5 3583.3 3712.4 3839.5 3965.6 4091.3 200 1646.0 2816.8 3061.5 3241.2 3396.2 3539.2 3675.6 3808.2 3938.5 4067.7 250 1623.9 2578.6 2950.4 3165.9 3339.3 3493.7 3638.0 3776.4 3911.2 4044.0 300 1608.8 2152.4 2820.9 3084.8 3279.8 3446.9 3599.7 3744.2 3883.8 4020.2 350 1597.5 1988.4 2671.0 2998.0 3218.1 3399.0 3560.9 3711.9 3856.3 3996.5 400 1588.7 1931.1 2511.8 2906.7 3154.6 3350.4 3521.8 3679.4 3828.8 3972.8 450 1581.7 1897.6 2377.3 2813.4 3090.2 3301.5 3482.5 3647.0 3801.3 3949.3 500 1576.0 1874.3 2284.4 2722.5 3025.7 3252.6 3443.5 3614.8 3774.1 3926.0 600 1567.4 1843.1 2179.8 2570.4 2902.1 3157.0 3366.8 3551.4 3720.6 3880.2 700 1561.6 1822.9 2123.4 2466.2 2795.0 3067.5 3293.6 3490.5 3669.0 3835.8 800 1557.7 1808.8 2087.6 2397.6 2709.9 2988.1 3225.7 3432.9 3619.7 3793.3 900 1555.2 1798.6 2062.7 2350.3 2645.2 2920.8 3164.4 3379.5 3573.5 3753.0 1000 1553.9 1791.1 2044.5 2316.2 2596.1 2865.1 3110.6 3330.8 3530.7 3715.2 a The bold horizontal lines in the columns indicate the transition from the liquid phase to the gas phase. The values for the properties at t = 0 C and p = 1 bar correspond to the (metastable) subcooled liquid; in the stable state at these t-p values, water is in the solid phase (ice). b D2.1. Table 7. Specific entropy s/(kJ kg1 K1) of water for given values of pressure and temperaturea Pressure p bar Temperature t / C 0 25 50 75 100 125 150 200 250 300 1 0.00015 0.36723 0.70375 1.0156 7.3610 7.4931 7.6147 7.8356 8.0346 8.2171 5 0.00012 0.36713 0.70357 1.0153 1.3067 1.5813 1.8419 7.0611 7.2726 7.4614 10 0.00009 0.36700 0.70334 1.0150 1.3063 1.5808 1.8414 6.6955 6.9266 7.1247 20 0.00003 0.36674 0.70287 1.0144 1.3055 1.5798 1.8403 2.3301 6.5474 6.7685 30 0.00003 0.36648 0.70241 1.0137 1.3048 1.5789 1.8391 2.3285 6.2893 6.5412 40 0.00009 0.36622 0.70195 1.0131 1.3040 1.5780 1.8380 2.3269 2.7933 6.3638 50 0.00014 0.36596 0.70149 1.0125 1.3032 1.5770 1.8369 2.3254 2.7909 6.2109 60 0.00019 0.36569 0.70103 1.0119 1.3024 1.5761 1.8358 2.3238 2.7885 6.0702 70 0.00023 0.36543 0.70057 1.0112 1.3017 1.5752 1.8347 2.3223 2.7861 80 0.00027 0.36516 0.70011 1.0106 1.3009 1.5743 1.8337 2.3207 2.7837 5.9335 5.7935 90 0.00031 0.36490 0.69965 1.0100 1.3001 1.5734 1.8326 2.3192 2.7814 3.2529 100 0.00034 0.36463 0.69919 1.0094 1.2994 1.5724 1.8315 2.3177 2.7791 3.2484 150 0.00045 0.36328 0.69689 1.0063 1.2956 1.5679 1.8262 2.3102 2.7679 3.2275 200 0.00047 0.36190 0.69460 1.0033 1.2918 1.5635 1.8209 2.3030 2.7572 3.2087 250 0.00041 0.36051 0.69232 1.0003 1.2881 1.5591 1.8158 2.2959 2.7469 3.1915 300 0.00028 0.35908 0.69004 0.99729 1.2845 1.5548 1.8107 2.2890 2.7371 3.1756 350 0.00006 0.35764 0.68777 0.99433 1.2809 1.5505 1.8058 2.2823 2.7276 3.1608 400 0.00023 0.35618 0.68551 0.99139 1.2773 1.5463 1.8009 2.2758 2.7185 3.1469 450 0.00059 0.35469 0.68325 0.98848 1.2738 1.5422 1.7961 2.2693 2.7097 3.1338 500 0.00102 0.35319 0.68099 0.98558 1.2703 1.5381 1.7914 2.2631 2.7012 3.1214 600 0.00208 0.35012 0.67649 0.97987 1.2634 1.5301 1.7822 2.2509 2.6848 3.0982 b 161 162 D2 Properties of Selected Important Pure Substances D2.1. Table 7. (continued) Pressure p bar Temperature t / C 0 25 50 75 100 125 150 200 250 300 700 0.00338 0.34698 0.67201 0.97423 1.2567 1.5223 1.7732 2.2392 2.6694 3.0769 800 0.00491 0.34377 0.66754 0.96866 1.2501 1.5146 1.7645 2.2280 2.6548 3.0572 900 0.00665 0.34049 0.66309 0.96317 1.2436 1.5071 1.7560 2.2171 2.6408 3.0388 1000 0.00858 0.33716 0.65864 0.95774 1.2373 1.4998 1.7477 2.2066 2.6275 3.0215 Pressure p bar 1 Temperature t / C 350 400 450 500 550 600 650 700 750 800 8.3865 8.5451 8.6945 8.8361 8.9709 9.0998 9.2234 9.3424 9.4571 9.5681 5 7.6345 7.7954 7.9464 8.0891 8.2247 8.3543 8.4784 8.5977 8.7128 8.8240 10 7.3028 7.4668 7.6198 7.7640 7.9007 8.0309 8.1557 8.2755 8.3909 8.5024 20 6.9582 7.1290 7.2863 7.4335 7.5723 7.7042 7.8301 7.9509 8.0670 8.1791 30 6.7449 6.9233 7.0853 7.2356 7.3767 7.5102 7.6373 7.7590 7.8759 7.9885 40 6.5843 6.7712 6.9383 7.0919 7.2353 7.3704 7.4989 7.6215 7.7391 7.8523 50 6.4515 6.6481 6.8208 6.9778 7.1235 7.2604 7.3901 7.5137 7.6321 7.7459 60 6.3356 6.5431 6.7216 6.8824 7.0306 7.1692 7.3002 7.4248 7.5439 7.6583 70 6.2303 6.4501 6.6351 6.7997 6.9505 7.0909 7.2232 7.3488 7.4687 7.5837 80 6.1319 6.3657 6.5577 6.7264 6.8798 7.0221 7.1557 7.2823 7.4030 7.5186 90 6.0378 6.2875 6.4871 6.6601 6.8163 6.9605 7.0955 7.2231 7.3446 7.4608 100 6.2139 6.4217 6.5993 6.7584 6.9045 7.0409 7.1696 7.2918 7.4087 150 5.9458 5.4435 5.8817 6.1433 6.3479 6.5230 6.6797 6.8235 6.9576 7.0839 7.2039 200 3.7288 5.5525 5.9041 6.1445 6.3390 6.5077 6.6596 6.7994 6.9301 7.0534 250 3.6803 5.1399 5.6755 5.9642 6.1816 6.3638 6.5246 6.6706 6.8057 6.9324 300 3.6435 4.4750 5.4419 5.7956 6.0403 6.2374 6.4077 6.5602 6.7000 6.8303 350 3.6131 4.2140 5.1945 5.6331 5.9093 6.1229 6.3032 6.4625 6.6072 6.7411 400 3.5870 4.1141 4.9447 5.4746 5.7859 6.0170 6.2079 6.3743 6.5239 6.6614 450 3.5638 4.0505 4.7362 5.3209 5.6685 5.9179 6.1197 6.2932 6.4479 6.5891 500 3.5430 4.0028 4.5892 5.1759 5.5566 5.8245 6.0372 6.2180 6.3777 6.5226 600 3.5064 3.9316 4.4134 4.9356 5.3519 5.6528 5.8867 6.0815 6.2512 6.4034 700 3.4747 3.8778 4.3080 4.7662 5.1786 5.5003 5.7522 5.9600 6.1390 6.2982 800 3.4465 3.8339 4.2331 4.6474 5.0391 5.3674 5.6321 5.8509 6.0382 6.2039 900 3.4211 3.7965 4.1747 4.5593 4.9288 5.2540 5.5255 5.7526 5.9470 6.1184 1000 3.3978 3.7638 4.1267 4.4899 4.8407 5.1580 5.4316 5.6640 5.8644 6.0405 a The bold horizontal lines in the columns indicate the transition from the liquid phase to the gas phase. The values for the properties at t = 0 C and p = 1 bar correspond to the (metastable) subcooled liquid; in the stable state at these t-p values, water is in the solid phase (ice). b D2.1. Table 8. Specific isobaric heat capacity cp/(kJ kg1 K1) of water for given values of pressure and temperaturea Pressure p bar Temperature t / C 0 1 4.219 b 25 50 75 100 125 150 200 250 300 4.182 4.180 4.192 2.074 2.011 1.986 1.976 1.989 2.012 5 4.217 4.181 4.179 4.191 4.216 4.255 4.310 2.145 2.078 2.066 10 4.215 4.179 4.177 4.190 4.215 4.253 4.309 2.429 2.212 2.141 20 4.210 4.176 4.175 4.187 4.212 4.251 4.305 4.491 2.560 2.320 30 4.205 4.174 4.173 4.185 4.210 4.248 4.302 4.486 3.077 2.543 40 4.200 4.171 4.171 4.183 4.208 4.245 4.299 4.480 4.865 2.820 50 4.196 4.168 4.168 4.181 4.206 4.243 4.296 4.474 4.851 3.171 60 4.191 4.165 4.166 4.179 4.203 4.240 4.293 4.469 4.838 3.638 Properties of Water and Steam D2.1 D2.1. Table 8. (continued) Pressure p bar 0 25 50 75 100 125 150 200 250 300 70 4.186 4.162 4.164 4.177 4.201 4.238 4.290 4.463 4.825 4.292 80 4.181 4.160 4.162 4.175 4.199 4.235 4.287 4.458 4.812 5.287 90 4.177 4.157 4.159 4.173 4.197 4.233 4.284 4.452 4.800 5.730 100 4.172 4.154 4.157 4.170 4.194 4.230 4.281 4.447 4.788 5.682 150 4.150 4.141 4.147 4.160 4.184 4.218 4.266 4.422 4.732 5.476 200 4.129 4.128 4.136 4.150 4.173 4.206 4.252 4.398 4.682 5.317 250 4.109 4.116 4.126 4.141 4.163 4.195 4.238 4.376 4.637 5.188 300 4.090 4.104 4.116 4.131 4.153 4.184 4.225 4.355 4.596 5.081 350 4.072 4.093 4.107 4.122 4.144 4.173 4.213 4.335 4.558 4.991 400 4.054 4.082 4.097 4.113 4.135 4.163 4.200 4.316 4.523 4.912 450 4.038 4.072 4.088 4.105 4.126 4.153 4.189 4.298 4.491 4.843 500 4.022 4.061 4.080 4.096 4.117 4.143 4.177 4.281 4.461 4.782 600 3.994 4.042 4.063 4.080 4.100 4.125 4.156 4.249 4.407 4.677 700 3.968 4.024 4.047 4.064 4.084 4.107 4.136 4.219 4.360 4.591 800 3.945 4.008 4.032 4.050 4.068 4.090 4.116 4.192 4.317 4.518 900 3.924 3.992 4.018 4.036 4.054 4.074 4.098 4.167 4.279 4.455 1000 3.906 3.978 4.005 4.023 4.040 4.059 4.081 4.144 4.245 4.400 Pressure p bar a Temperature t / C Temperature t / C 350 400 450 500 550 600 650 700 750 800 1 2.040 2.070 2.101 2.135 2.169 2.203 2.238 2.273 2.308 2.343 5 2.075 2.095 2.121 2.149 2.180 2.213 2.246 2.280 2.314 2.348 10 2.123 2.128 2.145 2.168 2.195 2.224 2.255 2.287 2.320 2.353 20 2.230 2.200 2.196 2.207 2.225 2.249 2.275 2.303 2.333 2.364 30 2.354 2.278 2.251 2.247 2.256 2.273 2.295 2.320 2.347 2.375 40 2.497 2.364 2.309 2.289 2.288 2.298 2.315 2.336 2.360 2.387 50 2.661 2.459 2.371 2.333 2.321 2.324 2.335 2.353 2.374 2.398 60 2.850 2.563 2.436 2.379 2.355 2.350 2.356 2.369 2.387 2.409 70 3.070 2.678 2.507 2.426 2.390 2.377 2.377 2.386 2.401 2.421 80 3.329 2.804 2.582 2.476 2.426 2.404 2.398 2.403 2.415 2.432 90 3.637 2.943 2.662 2.529 2.463 2.432 2.420 2.421 2.429 2.444 100 4.012 3.096 2.747 2.583 2.501 2.460 2.442 2.438 2.443 2.456 150 8.789 4.178 3.269 2.896 2.711 2.612 2.557 2.529 2.517 2.515 200 8.106 6.360 4.007 3.284 2.955 2.781 2.682 2.625 2.593 2.578 250 6.980 13.00 5.086 3.766 3.235 2.968 2.817 2.727 2.673 2.642 300 6.393 25.80 6.691 4.360 3.553 3.171 2.960 2.833 2.755 2.707 350 6.015 11.65 8.976 5.071 3.907 3.389 3.110 2.944 2.840 2.774 400 5.742 8.701 10.95 5.875 4.294 3.619 3.267 3.057 2.926 2.843 450 5.534 7.472 10.86 6.688 4.700 3.857 3.426 3.172 3.013 2.912 500 5.370 6.778 9.567 7.309 5.103 4.097 3.587 3.288 3.101 2.981 600 5.124 5.997 7.540 7.522 5.753 4.556 3.901 3.515 3.273 3.119 700 4.946 5.555 6.510 6.969 6.037 4.923 4.182 3.727 3.436 3.253 800 4.808 5.262 5.918 6.375 5.982 5.137 4.408 3.914 3.583 3.377 900 4.697 5.052 5.532 5.916 5.778 5.206 4.558 4.069 3.713 3.486 1000 4.605 4.892 5.258 5.576 5.549 5.171 4.628 4.191 3.823 3.576 The bold horizontal lines in the columns indicate the transition from the liquid phase to the gas phase. The values for the properties at t = 0 C and p = 1 bar correspond to the (metastable) subcooled liquid; in the stable state at these t-p values, water is in the solid phase (ice). b 163 164 D2 Properties of Selected Important Pure Substances D2.1. Table 9. Isobaric cubic expansion coefficient av/(103 K1) of water for given values of pressure and temperaturea Pressure p bar Temperature t / C 0 1 0.06769 b 25 50 75 100 125 150 200 250 300 0.2569 0.4574 0.6132 2.897 2.646 2.452 2.159 1.937 1.761 5 0.06617 0.2574 0.4574 0.6128 0.7503 0.8843 1.026 2.370 2.051 1.829 10 0.06427 0.2579 0.4573 0.6123 0.7494 0.8830 1.024 2.720 2.217 1.923 20 0.06049 0.2591 0.4572 0.6113 0.7477 0.8805 1.021 1.375 2.649 2.143 30 0.05674 0.2602 0.4570 0.6104 0.7460 0.8779 1.017 1.368 3.289 2.416 40 0.05300 0.2614 0.4569 0.6094 0.7443 0.8754 1.014 1.360 1.958 2.760 50 0.04930 0.2625 0.4568 0.6085 0.7426 0.8729 1.010 1.353 1.939 3.203 60 0.04561 0.2637 0.4567 0.6075 0.7409 0.8705 1.007 1.346 1.921 3.800 70 0.04195 0.2648 0.4566 0.6066 0.7393 0.8680 1.003 1.339 1.903 4.647 80 0.03831 0.2659 0.4565 0.6056 0.7376 0.8656 0.9999 1.332 1.885 5.953 90 0.03469 0.2670 0.4564 0.6047 0.7360 0.8632 0.9965 1.325 1.869 3.243 100 0.03110 0.2681 0.4563 0.6038 0.7344 0.8609 0.9932 1.318 1.852 3.170 150 0.01348 0.2736 0.4559 0.5994 0.7265 0.8493 0.9771 1.286 1.776 2.865 200 0.00358 0.2790 0.4555 0.5952 0.7190 0.8383 0.9618 1.256 1.708 2.633 250 0.02009 0.2842 0.4552 0.5912 0.7118 0.8278 0.9473 1.229 1.647 2.449 300 0.03606 0.2893 0.4550 0.5874 0.7049 0.8177 0.9334 1.203 1.592 2.298 350 0.05152 0.2943 0.4548 0.5837 0.6983 0.8081 0.9202 1.178 1.542 2.170 400 0.06647 0.2992 0.4547 0.5802 0.6919 0.7988 0.9075 1.155 1.496 2.062 450 0.08092 0.3040 0.4546 0.5769 0.6858 0.7899 0.8954 1.133 1.455 1.967 500 0.09491 0.3086 0.4546 0.5736 0.6799 0.7814 0.8839 1.113 1.416 1.884 600 0.1215 0.3176 0.4547 0.5676 0.6688 0.7652 0.8621 1.075 1.347 1.744 700 0.1464 0.3261 0.4549 0.5621 0.6585 0.7502 0.8419 1.040 1.287 1.630 800 0.1697 0.3341 0.4551 0.5569 0.6488 0.7363 0.8233 1.009 1.234 1.535 900 0.1916 0.3418 0.4555 0.5521 0.6398 0.7232 0.8060 0.9807 1.187 1.454 1000 0.2122 0.3490 0.4559 0.5477 0.6313 0.7109 0.7897 0.9545 1.144 1.384 Pressure p bar Temperature t / C 350 400 450 500 550 600 650 700 750 800 1 1.615 1.493 1.388 1.297 1.218 1.147 1.085 1.029 0.9784 0.9327 5 1.660 1.523 1.410 1.313 1.229 1.156 1.092 1.034 0.9827 0.9361 10 1.719 1.563 1.437 1.333 1.244 1.168 1.100 1.041 0.9880 0.9404 20 1.848 1.647 1.495 1.374 1.275 1.190 1.118 1.055 0.9988 0.9490 30 1.997 1.738 1.556 1.417 1.306 1.214 1.136 1.069 1.010 0.9578 40 2.169 1.839 1.621 1.462 1.338 1.238 1.154 1.083 1.021 0.9666 50 2.368 1.950 1.691 1.509 1.372 1.262 1.173 1.097 1.032 0.9755 60 2.600 2.072 1.765 1.558 1.406 1.288 1.191 1.111 1.043 0.9844 70 2.873 2.208 1.845 1.610 1.442 1.313 1.211 1.126 1.055 0.9935 80 3.198 2.358 1.930 1.664 1.479 1.340 1.230 1.141 1.066 1.003 90 3.593 2.525 2.021 1.721 1.517 1.367 1.250 1.156 1.078 1.012 100 4.080 2.711 2.119 1.780 1.556 1.394 1.270 1.171 1.090 1.021 4.079 2.729 2.124 1.774 1.543 1.377 1.251 1.150 1.068 7.052 150 10.85 200 6.982 3.626 2.559 2.030 1.710 1.493 1.335 1.213 1.117 250 5.171 17.05 4.992 3.109 2.327 1.894 1.617 1.422 1.278 1.166 300 4.260 37.84 7.117 3.795 2.664 2.094 1.747 1.513 1.344 1.215 350 3.694 12.91 10.24 4.627 3.039 2.306 1.883 1.606 1.411 1.265 400 3.293 7.963 12.82 5.566 3.444 2.528 2.021 1.699 1.477 1.314 450 2.990 5.984 12.13 6.487 3.861 2.752 2.160 1.792 1.543 1.362 500 2.754 4.899 7.108 4.257 2.971 2.295 1.883 1.606 1.408 9.692 D2.1 Properties of Water and Steam D2.1. Table 9. (continued) Pressure p bar Temperature t / C 350 400 450 500 550 600 650 700 750 800 600 2.408 3.717 6.227 6.878 4.809 3.355 2.542 2.050 1.726 1.496 700 2.161 3.069 4.579 5.685 4.843 3.594 2.734 2.190 1.829 1.573 800 1.973 2.652 3.676 4.611 4.481 3.632 2.848 2.292 1.909 1.637 900 1.825 2.357 3.106 3.840 3.988 3.510 2.875 2.352 1.964 1.685 1000 1.704 2.136 2.712 3.294 3.526 3.295 2.821 2.373 1.992 1.716 a The bold horizontal lines in the columns indicate the transition from the liquid phase to the gas phase. The values for the properties at t = 0 C and p = 1 bar correspond to the (metastable) subcooled liquid; in the stable state at these t-p values, water is in the solid phase (ice). b D2.1. Table 10. Thermal conductivity l/(103 W m1 K1) of water for given values of pressure and temperaturea,c Pressure p bar Temperature t / C 0 25 50 75 1 562.0b 607.5 640.5 663.5 24.78 26.69 28.80 33.37 38.28 43.49 5 562.3 607.7 640.7 663.7 678.0 684.5 683.9 34.24 38.81 43.90 10 562.6 608.0 641.0 663.9 678.3 684.8 684.2 36.06 39.70 44.49 20 563.2 608.5 641.5 664.5 678.8 685.4 684.9 663.8 42.22 45.95 30 563.7 609.1 642.0 665.0 679.4 686.0 685.6 664.7 45.95 47.81 40 564.3 609.6 642.5 665.5 679.9 686.6 686.2 665.5 617.8 50.14 50 564.9 610.1 643.0 666.0 680.5 687.2 686.9 666.4 619.1 53.03 60 565.5 610.6 643.5 666.6 681.0 687.8 687.5 667.3 620.4 56.65 70 566.1 611.2 644.1 667.1 681.6 688.4 688.2 668.1 621.7 61.24 80 566.7 611.7 644.6 667.6 682.1 689.0 688.8 669.0 623.0 67.24 90 567.3 612.2 645.1 668.1 682.7 689.6 689.5 669.8 624.2 545.9 100 567.8 612.7 645.6 668.6 683.2 690.2 690.2 670.7 625.5 548.1 150 570.8 615.4 648.1 671.2 685.9 693.1 693.4 674.9 631.5 558.7 200 573.6 617.9 650.6 673.8 688.6 696.0 696.5 678.9 637.2 568.3 250 576.5 620.5 653.1 676.3 691.2 698.8 699.6 682.9 642.7 577.2 300 579.3 623.1 655.6 678.8 693.8 701.6 702.7 686.7 648.0 585.5 350 582.1 625.6 658.0 681.3 696.4 704.4 705.7 690.5 653.2 593.2 400 584.9 628.1 660.4 683.7 699.0 707.1 708.6 694.2 658.1 600.5 450 587.6 630.6 662.8 686.1 701.5 709.8 711.6 697.8 662.9 607.4 500 590.3 633.0 665.2 688.5 704.0 712.4 714.4 701.3 667.5 614.0 600 595.7 637.9 669.9 693.2 708.9 717.6 720.0 708.1 676.4 626.3 700 600.9 642.6 674.5 697.9 713.7 722.7 725.5 714.7 684.8 637.7 800 606.1 647.3 679.0 702.4 718.4 727.6 730.8 721.1 692.8 648.2 900 611.1 651.9 683.5 706.9 723.0 732.5 736.0 727.2 700.4 658.1 1000 616.0 656.4 687.8 711.3 727.5 737.2 741.0 733.2 707.7 667.4 Pressure p bar 100 125 150 200 250 300 Temperature t / C 350 400 450 500 550 600 650 700 750 800 1 48.97 54.71 60.69 66.90 73.30 79.90 86.66 93.57 100.6 107.7 5 49.32 55.03 60.98 67.16 73.55 80.13 86.88 93.78 100.8 107.9 10 49.80 55.44 61.35 67.51 73.87 80.43 87.16 94.04 101.0 108.2 20 50.87 56.32 62.13 68.22 74.53 81.05 87.74 94.59 101.6 108.6 30 52.11 57.30 62.97 68.97 75.22 81.68 88.33 95.15 102.1 109.1 40 53.55 58.36 63.86 69.75 75.93 82.34 88.95 95.72 102.6 109.7 50 55.22 59.53 64.81 70.58 76.67 83.02 89.58 96.31 103.2 110.2 165 166 D2 Properties of Selected Important Pure Substances D2.1. Table 10. (continued) Pressure p bar Temperature t / C 350 400 450 500 550 600 650 700 60 57.14 60.80 65.82 71.44 77.44 83.72 90.22 70 59.36 62.20 66.90 72.35 78.24 84.44 90.89 80 61.95 63.72 68.04 73.30 79.07 85.19 90 64.97 65.40 69.26 74.29 79.93 85.96 100 68.55 67.25 70.56 75.34 80.83 86.76 78.50 81.38 85.85 91.13 89.76 89.10 91.91 96.22 79.94 750 800 96.91 103.8 110.7 97.53 104.3 111.3 91.57 98.16 104.9 111.8 92.27 98.81 105.5 112.4 93.00 99.47 106.1 113.0 103.0 109.4 116.0 107.0 113.0 119.3 150 104.1 200 454.1 103.4 250 474.1 160.0 106.3 102.1 106.4 111.5 117.0 123.0 300 490.6 328.1 131.5 111.9 108.0 109.0 112.1 116.4 121.4 126.9 350 504.7 373.0 170.8 128.5 118.6 116.9 118.5 121.8 126.2 131.2 99.02 99.22 96.91 101.4 400 517.3 398.5 225.0 149.7 131.2 125.9 450 528.7 419.9 277.9 175.7 145.9 136.2 125.7 133.6 134.3 136.9 140.7 500 539.1 438.3 315.7 205.5 162.9 147.7 142.3 141.4 143.0 145.9 600 557.7 468.8 365.2 174.1 162.1 157.2 156.2 157.4 574.0 493.7 401.3 264.6 311.7 201.8 700 175.0 171.0 170.0 800 588.7 514.9 430.9 348.2 280.2 234.6 208.5 194.3 187.0 183.7 900 602.0 533.5 456.0 378.5 312.7 264.2 233.1 214.5 203.9 198.2 1000 614.3 550.0 477.9 404.8 341.0 291.7 257.3 235.0 221.3 213.2 127.8 131.4 135.8 --------------------------------- 242.7 203.8 184.4 --------------------------------- a The bold horizontal lines in the columns indicate the transition from the liquid phase to the gas phase. The values for the properties at t = 0 C and p = 1 bar correspond to the (metastable) subcooled liquid; in the stable state at these t-p values, water is in the solid phase (ice). c The l values below the dashed lines are beyond the range of validity of the l equation for industrial use [4, 5]; for details of this extrapolation, see [4]. If more accurate l values are needed in this range, the l equation for scientific use [5] should be used. b D2.1. Table 11. Dynamic viscosity /(106 Pa s) of water for given values of pressure and temperaturea Pressure p bar Temperature t / C 0 b 25 50 75 100 12.23 125 13.21 150 200 250 300 1 1791.8 890.0 546.5 377.4 14.19 16.20 18.25 20.31 5 1790.9 890.0 546.6 377.5 281.7 222.2 182.6 16.06 18.16 20.26 10 1789.7 889.9 546.7 377.7 281.8 222.3 182.7 15.88 18.06 20.21 20 1787.5 889.8 546.9 377.9 282.1 222.6 183.0 134.7 17.85 20.09 30 1785.3 889.6 547.1 378.2 282.4 222.8 183.3 135.0 17.64 19.98 40 1783.2 889.5 547.3 378.5 282.6 223.1 183.5 135.2 106.3 19.89 50 1781.0 889.4 547.5 378.7 282.9 223.3 183.8 135.5 106.6 19.79 60 1778.9 889.3 547.7 379.0 283.2 223.6 184.0 135.7 106.9 19.71 70 1776.8 889.1 547.9 379.2 283.4 223.9 184.3 136.0 107.1 19.65 80 1774.7 889.0 548.1 379.5 283.7 224.1 184.5 136.2 107.4 19.60 90 1772.6 888.9 548.3 379.8 284.0 224.4 184.8 136.5 107.7 86.03 100 1770.6 888.8 548.5 380.0 284.2 224.6 185.0 136.7 108.0 86.43 150 1760.7 888.3 549.6 381.4 285.6 225.9 186.3 137.9 109.3 88.35 200 1751.2 887.9 550.6 382.7 286.9 227.2 187.5 139.1 110.7 90.10 250 1742.3 887.6 551.7 384.0 288.2 228.5 188.7 140.3 111.9 91.72 300 1733.9 887.4 552.8 385.3 289.6 229.8 189.9 141.5 113.2 93.25 350 1725.9 887.2 553.9 386.7 290.9 231.0 191.1 142.6 114.4 94.70 400 1718.4 887.1 555.1 388.0 292.2 232.3 192.3 143.8 115.5 96.08 450 1711.3 887.1 556.2 389.3 293.5 233.5 193.5 144.9 116.7 97.40 500 1704.7 887.2 557.4 390.7 294.8 234.8 194.7 146.0 117.8 98.67 Properties of Water and Steam D2.1 D2.1. Table 11. (continued) Pressure p bar Temperature t / C 0 25 50 75 100 125 150 200 250 300 600 1692.8 887.6 559.8 393.3 297.4 237.2 197.0 148.2 120.0 101.1 700 1682.5 888.4 562.2 396.0 300.0 239.7 199.4 150.3 122.1 103.4 800 1673.7 889.4 564.8 398.7 302.6 242.1 201.6 152.4 124.2 105.5 900 1666.4 890.7 567.4 401.4 305.1 244.5 203.9 154.5 126.2 107.6 1000 1660.6 892.4 570.1 404.1 307.7 246.9 206.2 156.5 128.1 109.6 Temperature t / C Pressure p bar 350 400 450 500 550 600 650 700 750 800 1 22.38 24.45 26.51 28.56 30.60 32.61 34.60 36.57 38.51 40.43 5 22.36 24.44 26.52 28.57 30.61 32.62 34.62 36.59 38.53 40.45 10 22.33 24.43 26.52 28.58 30.62 32.64 34.64 36.61 38.55 40.47 20 22.28 24.42 26.53 28.60 30.66 32.68 34.68 36.65 38.60 40.52 30 22.23 24.41 26.54 28.63 30.69 32.73 34.73 36.70 38.65 40.57 40 22.19 24.40 26.56 28.67 30.74 32.77 34.78 36.75 38.70 40.62 50 22.16 24.41 26.58 28.70 30.78 32.82 34.83 36.80 38.75 40.67 60 22.14 24.42 26.61 28.75 30.83 32.87 34.88 36.86 38.80 40.72 70 22.12 24.44 26.65 28.79 30.88 32.93 34.94 36.92 38.86 40.78 80 22.13 24.46 26.69 28.84 30.94 32.99 35.00 36.97 38.92 40.83 90 22.14 24.50 26.74 28.90 31.00 33.05 35.06 37.04 38.98 40.89 100 22.18 24.55 26.80 28.97 31.07 33.12 35.13 37.10 39.04 40.95 150 22.91 25.02 27.23 29.38 31.46 33.50 35.49 37.45 39.37 41.26 200 69.27 26.14 27.95 29.97 31.99 33.97 35.93 37.85 39.74 41.61 250 72.74 29.29 29.14 30.80 32.66 34.55 36.44 38.31 40.16 41.99 300 75.44 44.20 31.09 31.92 33.49 35.24 37.03 38.83 40.63 42.41 350 77.72 56.08 34.35 33.43 34.52 36.04 37.69 39.40 41.13 42.86 400 79.73 61.50 39.44 35.41 35.76 36.96 38.44 40.03 41.68 43.34 450 81.55 65.18 45.54 37.92 37.23 38.01 39.26 40.72 42.26 43.85 500 83.22 68.07 50.97 40.92 38.92 39.18 40.17 41.45 42.88 44.39 600 86.24 72.61 58.74 47.51 42.91 41.88 42.19 43.07 44.23 45.54 700 88.95 76.24 64.07 53.48 47.29 44.92 44.45 44.85 45.69 46.77 800 91.43 79.35 68.20 58.36 51.56 48.12 46.86 46.75 47.24 48.07 900 93.74 82.11 71.64 62.39 55.44 51.30 49.35 48.71 48.84 49.41 1000 95.92 84.62 74.64 65.83 58.91 54.34 51.83 50.71 50.48 50.78 a The bold horizontal lines in the columns indicate the transition from the liquid phase to the gas phase. The values for the properties at t = 0 C and p = 1 bar correspond to the (metastable) subcooled liquid; in the stable state at these t-p values, water is in the solid phase (ice). b D2.1. Table 12. Kinematic viscosity n / (106 m2 s1) of water for given values of pressure and temperaturea Pressure p bar Temperature t / C 0 1 1.792 b 25 50 75 0.8927 0.5531 0.3872 100 20.75 125 24.00 150 27.49 200 250 300 35.20 43.91 53.60 5 1.791 0.8924 0.5531 0.3872 0.2939 0.2366 0.1991 6.826 8.618 10 1.789 0.8922 0.5531 0.3872 0.2939 0.2366 0.1992 3.271 4.203 10.59 5.213 20 1.786 0.8916 0.5531 0.3873 0.2941 0.2368 0.1994 0.1557 1.990 2.522 30 1.783 0.8911 0.5530 0.3874 0.2942 0.2369 0.1995 0.1559 1.246 1.622 40 1.780 0.8906 0.5530 0.3875 0.2944 0.2371 0.1997 0.1560 0.1330 1.171 50 1.777 0.8901 0.5529 0.3876 0.2945 0.2372 0.1998 0.1562 0.1332 0.8976 167 168 D2 Properties of Selected Important Pure Substances D2.1. Table 12. (continued) Pressure p bar 0 25 50 75 100 125 150 200 250 300 60 1.774 0.8895 0.5529 0.3877 0.2946 0.2374 0.2000 0.1563 0.1334 0.7134 70 1.771 0.8890 0.5529 0.3878 0.2948 0.2375 0.2001 0.1565 0.1335 0.5794 80 1.768 0.8885 0.5529 0.3879 0.2949 0.2377 0.2003 0.1567 0.1337 0.4758 90 1.765 0.8880 0.5528 0.3880 0.2951 0.2378 0.2005 0.1568 0.1339 0.1206 100 1.762 0.8875 0.5528 0.3881 0.2952 0.2380 0.2006 0.1570 0.1340 0.1208 150 1.748 0.8851 0.5527 0.3886 0.2959 0.2387 0.2014 0.1577 0.1348 0.1218 200 1.734 0.8828 0.5526 0.3891 0.2966 0.2395 0.2021 0.1585 0.1356 0.1226 250 1.721 0.8806 0.5525 0.3896 0.2973 0.2402 0.2029 0.1592 0.1363 0.1234 300 1.709 0.8785 0.5524 0.3901 0.2980 0.2410 0.2036 0.1599 0.1371 0.1242 350 1.697 0.8765 0.5524 0.3907 0.2986 0.2417 0.2044 0.1607 0.1378 0.1250 400 1.686 0.8746 0.5525 0.3912 0.2993 0.2424 0.2051 0.1614 0.1385 0.1257 450 1.675 0.8728 0.5525 0.3918 0.3000 0.2432 0.2058 0.1621 0.1392 0.1264 500 1.665 0.8711 0.5526 0.3923 0.3007 0.2439 0.2065 0.1628 0.1399 0.1271 600 1.646 0.8681 0.5528 0.3934 0.3021 0.2454 0.2080 0.1641 0.1412 0.1284 700 1.629 0.8655 0.5532 0.3946 0.3035 0.2468 0.2094 0.1655 0.1425 0.1296 800 1.614 0.8632 0.5536 0.3958 0.3049 0.2483 0.2108 0.1668 0.1437 0.1308 900 1.601 0.8613 0.5542 0.3970 0.3064 0.2497 0.2123 0.1681 0.1449 0.1320 1000 1.589 0.8598 0.5548 0.3983 0.3078 0.2511 0.2137 0.1694 0.1461 0.1332 700 750 800 Pressure p bar a Temperature t / C Temperature t / C 350 400 450 1 64.26 75.87 88.41 5 12.75 15.09 17.61 500 101.8 550 116.2 600 131.3 650 147.4 164.2 181.8 20.31 23.19 26.23 29.44 32.82 36.35 10.12 11.56 13.09 14.70 16.39 18.16 200.2 40.03 10 6.308 7.491 8.762 20 3.087 3.692 4.338 5.025 5.754 6.524 7.334 8.183 9.072 20.01 30 2.013 2.425 2.863 3.327 3.817 4.334 4.878 5.447 6.041 6.661 40 1.475 1.792 2.126 2.478 2.849 3.240 3.650 4.078 4.526 4.993 50 1.152 1.412 1.683 1.969 2.268 2.583 2.913 3.258 3.617 3.992 60 0.9353 1.158 1.388 1.629 1.881 2.145 2.422 2.711 3.012 3.325 70 0.7802 0.9765 1.178 1.387 1.605 1.833 2.071 2.320 2.579 2.848 80 0.6633 0.8403 1.020 1.205 1.398 1.599 1.809 2.027 2.255 2.491 2.213 10.00 90 0.5717 0.7342 0.8967 1.063 1.237 1.417 1.604 1.799 2.002 100 0.4977 0.6492 0.7983 0.950 1.108 1.271 1.441 1.617 1.801 1.991 150 0.2630 0.3921 0.5031 0.6119 0.7219 0.8348 0.951 1.072 1.196 1.325 200 0.1153 0.2601 0.3556 0.4434 0.5301 0.6178 0.7076 0.7999 0.8950 0.9932 250 0.1163 0.1759 0.2674 0.3431 0.4159 0.4885 0.5622 0.6376 0.7150 0.7946 300 0.1172 0.1236 0.2095 0.2774 0.3408 0.4032 0.4662 0.5302 0.5957 0.6629 350 0.1179 0.1181 0.1704 0.2318 0.2882 0.3432 0.3983 0.4541 0.5110 0.5692 400 0.1187 0.1175 0.1457 0.1992 0.2498 0.2990 0.3480 0.3976 0.4480 0.4994 450 0.1194 0.1176 0.1327 0.1757 0.2211 0.2654 0.3096 0.3541 0.3994 0.4456 500 0.1200 0.1178 0.1268 0.1592 0.1992 0.2394 0.2795 0.3199 0.3610 0.4028 600 0.1213 0.1186 0.1225 0.1402 0.1697 0.2024 0.2359 0.2698 0.3044 0.3396 700 0.1225 0.1194 0.1212 0.1317 0.1524 0.1785 0.2066 0.2355 0.2652 0.2955 800 0.1237 0.1203 0.1210 0.1277 0.1423 0.1628 0.1863 0.2111 0.2368 0.2632 900 0.1248 0.1212 0.1211 0.1257 0.1363 0.1523 0.1718 0.1932 0.2157 0.2390 1000 0.1258 0.1221 0.1215 0.1246 0.1325 0.1452 0.1614 0.1798 0.1995 0.2202 The bold horizontal lines in the columns indicate the transition from the liquid phase to the gas phase. The values for the properties at t = 0 C and p = 1 bar correspond to the (metastable) subcooled liquid; in the stable state at these t-p values, water is in the solid phase (ice). b Properties of Water and Steam D2.1 D2.1. Table 13. Thermal diffusivity a / (106 m2 s1) of water for given values of pressure and temperaturea,c Pressure p bar Temperature t / C 0 1 0.1332 b 25 50 75 100 125 0.1457 0.1551 0.1624 20.26 24.12 150 28.09 200 250 300 36.69 46.31 57.04 5 0.1333 0.1458 0.1552 0.1624 0.1678 0.1713 0.1730 6.786 8.860 10 0.1334 0.1458 0.1552 0.1625 0.1679 0.1714 0.1731 3.058 4.177 11.11 20 0.1337 0.1460 0.1554 0.1626 0.1680 0.1716 0.1733 0.1709 1.839 2.486 30 0.1339 0.1462 0.1555 0.1628 0.1681 0.1717 0.1735 0.1711 1.054 1.526 40 0.1341 0.1463 0.1557 0.1629 0.1683 0.1719 0.1737 0.1714 0.1590 1.047 50 0.1343 0.1465 0.1558 0.1631 0.1684 0.1720 0.1739 0.1717 0.1595 0.7583 60 0.1346 0.1467 0.1559 0.1632 0.1686 0.1722 0.1741 0.1720 0.1601 0.5636 70 0.1348 0.1468 0.1561 0.1633 0.1687 0.1724 0.1743 0.1723 0.1606 0.4208 80 0.1350 0.1470 0.1562 0.1635 0.1689 0.1725 0.1744 0.1726 0.1611 0.3088 5.361 90 0.1352 0.1471 0.1564 0.1636 0.1690 0.1727 0.1746 0.1729 0.1616 0.1336 100 0.1354 0.1473 0.1565 0.1637 0.1692 0.1728 0.1748 0.1732 0.1621 0.1349 150 0.1365 0.1481 0.1572 0.1644 0.1699 0.1736 0.1757 0.1745 0.1645 0.1406 200 0.1376 0.1488 0.1579 0.1651 0.1706 0.1744 0.1766 0.1758 0.1668 0.1455 250 0.1386 0.1496 0.1585 0.1657 0.1712 0.1751 0.1774 0.1771 0.1688 0.1497 300 0.1396 0.1503 0.1592 0.1664 0.1719 0.1759 0.1783 0.1783 0.1708 0.1535 350 0.1406 0.1510 0.1598 0.1670 0.1726 0.1766 0.1791 0.1794 0.1726 0.1569 400 0.1415 0.1517 0.1604 0.1676 0.1732 0.1773 0.1799 0.1805 0.1744 0.1599 450 0.1425 0.1524 0.1610 0.1682 0.1738 0.1780 0.1807 0.1816 0.1760 0.1628 500 0.1433 0.1530 0.1617 0.1688 0.1745 0.1786 0.1814 0.1826 0.1776 0.1654 600 0.1451 0.1543 0.1628 0.1700 0.1757 0.1800 0.1829 0.1846 0.1805 0.1701 700 0.1467 0.1556 0.1640 0.1711 0.1768 0.1812 0.1843 0.1865 0.1832 0.1742 800 0.1482 0.1568 0.1651 0.1722 0.1780 0.1824 0.1856 0.1883 0.1857 0.1779 900 0.1496 0.1579 0.1661 0.1732 0.1791 0.1836 0.1869 0.1899 0.1880 0.1812 1000 0.1509 0.1590 0.1672 0.1743 0.1801 0.1847 0.1882 0.1915 0.1902 0.1843 Pressure p bar Temperature t / C 350 400 450 1 68.94 82.02 96.29 5 13.55 16.21 19.10 500 111.7 550 600 650 700 750 800 227.6 128.3 146.1 164.9 184.8 205.7 22.22 25.56 29.12 32.91 36.90 41.10 45.49 11.02 12.71 14.50 16.40 18.41 20.52 22.72 11.34 10 6.626 7.986 9.451 20 3.161 3.872 4.626 5.430 6.286 7.195 8.156 9.168 10.23 30 2.005 2.499 3.018 3.566 4.146 4.759 5.406 6.087 6.800 7.545 40 1.426 1.813 2.214 2.634 3.076 3.542 4.032 4.547 5.086 5.648 50 1.078 1.400 1.731 2.075 2.434 2.812 3.208 3.624 4.058 4.510 60 0.8470 1.125 1.409 1.702 2.007 2.325 2.659 3.008 3.373 3.752 70 0.6818 0.9282 1.179 1.436 1.701 1.978 2.267 2.569 2.883 3.210 80 0.5579 0.7807 1.007 1.236 1.472 1.718 1.973 2.239 2.517 2.805 90 0.4612 0.6660 0.8724 1.081 1.295 1.515 1.745 1.983 2.232 2.489 100 0.3834 0.5743 0.7651 0.9569 1.152 1.353 1.562 1.779 2.004 2.237 150 0.1359 0.2999 0.4438 0.5853 0.7266 0.8694 1.016 1.166 1.321 1.481 200 0.0933 0.1617 0.2849 0.4013 0.5154 0.6291 0.7442 0.8615 0.9818 1.105 250 0.1086 0.0739 0.1917 0.2929 0.3906 0.4866 0.5829 0.6804 0.7796 0.8810 300 0.1192 0.0356 0.1325 0.2230 0.3094 0.3933 0.4769 0.5609 0.6462 0.7327 350 0.1273 0.0674 0.0943 0.1756 0.2534 0.3285 0.4026 400 0.1341 0.0875 0.0759 0.1433 0.2134 0.2815 0.4770 0.4152 0.5520 0.4825 0.6279 0.5503 450 0.1398 0.1014 0.0746 0.1218 0.1844 0.2466 0.3483 0.3074 0.3683 0.4295 0.4909 500 0.1448 0.1119 0.0821 0.1093 0.1634 0.2202 0.2760 0.3320 0.3881 0.4442 -------------------------------- 169 170 D2 Properties of Selected Important Pure Substances D2.1. Table 13. (continued) Pressure p bar Temperature t / C 350 400 450 500 550 600 650 700 750 800 600 0.1531 0.1276 0.1010 0.1038 700 0.1599 0.1392 0.1167 0.1101 0.1387 0.1847 0.1645 0.2323 0.2050 0.2803 0.2467 0.3284 0.3762 0.2888 800 0.1656 0.1484 0.1291 0.1195 0.1296 0.1293 0.3302 900 0.1706 0.1559 0.1394 0.1289 0.1330 0.1545 0.1880 0.2242 0.2616 0.2979 0.1507 0.1781 0.2091 0.2425 1000 0.1750 0.1623 0.1480 0.1375 0.1383 0.2749 0.1508 0.1732 0.1988 0.2288 0.2585 ------------------------------ a The bold horizontal lines in the columns indicate the transition from the liquid phase to the gas phase. The values for the properties at t = 0 C and p = 1 bar correspond to the (metastable) subcooled liquid; in the stable state at these t-p values, water is in the solid phase (ice). c The a values below the dashed lines were calculated with l values from the l equation for industrial use [4, 5] beyond its range of validity; for details of this extrapolation, see [4]. If more accurate a values are needed in this range, the l equation for scientific use [5] should be used. b D2.1. Table 14. Prandtl number Pr of water for given values of pressure and temperaturea,c Pressure p bar Temperature t / C 0 1 13.45 5 13.43 25 b 50 75 100 125 150 200 250 300 6.127 3.566 2.384 1.024 0.9947 0.9785 0.9594 0.9482 0.9398 6.122 3.565 2.384 1.752 1.381 1.151 1.0059 0.9727 0.9536 10 13.41 6.117 3.563 2.383 1.751 1.381 1.151 1.069 1.0061 0.9723 20 13.36 6.107 3.560 2.382 1.751 1.380 1.150 0.9114 1.082 1.0144 30 13.32 6.096 3.556 2.380 1.750 1.380 1.150 0.9108 1.181 1.063 40 13.27 6.086 3.553 2.379 1.749 1.379 1.150 0.9101 0.8369 1.118 50 13.23 6.076 3.549 2.377 1.748 1.379 1.149 0.9095 0.8351 1.184 60 13.18 6.066 3.546 2.376 1.748 1.379 1.149 0.9089 0.8333 1.266 70 13.14 6.056 3.542 2.375 1.747 1.378 1.149 0.9083 0.8316 1.377 80 13.10 6.046 3.539 2.373 1.746 1.378 1.148 0.9077 0.8299 1.541 90 13.05 6.036 3.536 2.372 1.746 1.377 1.148 0.9071 0.8283 0.9030 100 13.01 6.026 3.532 2.370 1.745 1.377 1.148 0.9065 0.8267 0.8959 150 12.80 5.978 3.516 2.364 1.742 1.375 1.146 0.9038 0.8195 0.8659 200 12.61 5.932 3.501 2.357 1.739 1.373 1.145 0.9014 0.8131 0.8429 250 12.42 5.888 3.485 2.351 1.736 1.372 1.143 0.8992 0.8075 0.8245 300 12.24 5.845 3.471 2.345 1.733 1.370 1.142 0.8972 0.8025 0.8094 350 12.07 5.805 3.457 2.340 1.731 1.369 1.141 0.8954 0.7981 0.7967 400 11.91 5.766 3.444 2.334 1.728 1.368 1.140 0.8939 0.7942 0.7859 450 11.76 5.728 3.431 2.329 1.726 1.366 1.139 0.8924 0.7906 0.7766 500 11.62 5.692 3.418 2.324 1.724 1.365 1.139 0.8912 0.7874 0.7685 600 11.35 5.625 3.395 2.315 1.720 1.363 1.137 0.8890 0.7820 0.7550 700 11.11 5.563 3.373 2.306 1.716 1.362 1.136 0.8873 0.7775 0.7443 800 10.89 5.506 3.354 2.299 1.713 1.361 1.136 0.8861 0.7739 0.7356 900 10.70 5.454 3.336 2.292 1.711 1.360 1.135 0.8852 0.7709 0.7285 1000 10.53 5.407 3.319 2.286 1.709 1.359 1.135 0.8846 0.7685 0.7226 Pressure p bar 1 Temperature t / C 350 400 450 500 550 600 650 700 750 800 0.9322 0.9250 0.9181 0.9114 0.9051 0.8991 0.8936 0.8884 0.8837 0.8795 5 0.9408 0.9307 0.9221 0.9143 0.9073 0.9008 0.8948 0.8893 0.8844 0.8800 10 0.9520 0.9381 0.9272 0.9180 0.9100 0.9028 0.8963 0.8904 0.8852 0.8806 20 0.9766 0.9536 0.9376 0.9254 0.9154 0.9067 0.8992 0.8926 0.8868 0.8817 30 1.0040 0.9704 0.9486 0.9330 0.9208 0.9107 0.9022 0.8948 0.8884 0.8829 Properties of Water and Steam D2.1 D2.1. Table 14. (continued) Pressure p bar Temperature t / C 350 400 450 500 550 600 650 700 750 800 40 1.034 0.9886 0.9601 0.9408 0.9263 0.9147 0.9051 0.8969 0.8899 0.8840 50 1.068 1.0082 0.9723 0.9488 0.9319 0.9187 0.9080 0.8990 0.8914 0.8851 60 1.104 1.029 0.9851 0.9571 0.9376 0.9227 0.9109 0.9011 0.8929 0.8861 70 1.144 1.052 0.9986 0.9657 0.9433 0.9268 0.9138 0.9032 0.8944 0.8871 80 1.189 1.076 1.013 0.9746 0.9492 0.9308 0.9166 0.9052 0.8959 0.8882 90 1.240 1.102 1.028 0.9838 0.9552 0.9349 0.9195 0.9072 0.8973 0.8892 100 1.298 1.130 1.043 0.9932 0.9613 0.9390 0.9224 0.9093 0.8987 0.8901 150 1.935 1.308 1.134 1.045 0.9936 0.9602 0.9367 0.9191 0.9054 0.8947 200 1.236 1.608 1.248 1.105 1.029 0.9820 0.9508 0.9285 0.9116 0.8987 250 1.071 2.381 1.394 1.171 1.065 1.0039 0.9646 0.9372 0.9171 0.9020 300 0.9832 3.475 1.581 1.244 1.102 1.025 0.9776 0.9451 0.9218 0.9046 350 0.9262 1.751 1.806 1.320 1.137 1.045 0.9893 400 0.8850 1.343 1.920 1.390 1.171 1.062 0.9256 0.9284 0.9065 0.9075 450 0.8536 1.160 1.781 1.443 1.199 1.076 0.9992 1.0070 0.9520 0.9575 0.9614 0.9299 0.9076 500 0.8290 1.053 1.544 1.456 1.220 1.087 1.0124 0.9637 0.9302 0.9069 600 0.7924 0.9289 1.213 1.351 1.039 1.196 1.0154 1.0080 0.9027 0.8578 1.096 1.085 0.9268 0.7664 1.223 1.176 0.9627 700 0.9549 0.9182 0.8949 800 0.7467 0.8109 0.9367 1.069 1.101 1.054 0.9909 0.9415 0.9054 0.8837 900 0.7313 0.7775 0.8691 0.9753 1.024 1.011 0.9651 0.9242 0.8895 0.8693 1000 0.7190 0.7525 0.8211 0.9067 0.9586 0.9632 0.9322 0.9045 0.8722 0.8517 ---------------------------------- -------------------------------- a The bold horizontal lines in the columns indicate the transition from the liquid phase to the gas phase. The values for the properties at t = 0 C and p = 1 bar correspond to the (metastable) subcooled liquid; in the stable state at these t-p values, water is in the solid phase (ice). c The Pr values below the dashed lines were calculated with l values from the l equation for industrial use [4, 5] beyond its range of validity; for details of this extrapolation, see [4]. If more accurate Pr values are needed in this range, the l equation for scientific use [5] should be used. b As usual for water, the reference state for the caloric properties was set by choosing the specific internal energy and the specific entropy of the saturated liquid to be zero at the triple point, i.e., ut0 (Tt) = 0 and st0 (Tt) = 0. As a consequence of this zero-point setting, the specific enthalpy of the saturated liquid at the triple point is given by ht0 (Tt) = 0.000 611 783 kJ kg1. 2. 3. 4. 5. 3 Bibliography 6. 1. IAPWS Revised Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use (September 2009). Available at http://www.iapws.org Wagner W, Pruß A (2002) The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J Phys Chem Ref Data 31, 387–535 IAPWS Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (August 2009). Available at http://www.iapws.org Wagner W, Kretzschmar H-J (2008) International steam tables – Properties of water and steam based on the industrial formulation IAPWS-IF97. Springer-Verlag, Berlin IAPWS Revised Release on the IAPS Formulation 1985 for the Thermal Conductivity of Ordinary Water Substance (September 2008). Available at http://www.iapws.org IAPWS Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance (September 2008). Available at http://www.iapws.org 171 172 D2 Properties of Selected Important Pure Substances D2.2 Properties of Dry Air Roland Span Ruhr-Universität Bochum, Bochum, Germany 1 Composition of Dry Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 2.1 Reference States of Enthalpy and Entropy . . . . . . . . . . . . . 172 2 Critical Parameters of Dry Air . . . . . . . . . . . . . . . . . . . . . . . 172 3 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 1 Composition of Dry Air p r Mole fraction Molecular mass g/mol Mass fraction N2 0.7812 28.013 0.75570 Ar 0.0092 39.948 0.01269 O2 0.2096 31.999 0.23161 Substance e = 28.9583 g/mol Molecular mass of the mixture: M Specific gas constant of the mixture: R = 0.28712 kJ/(kg K) Deviations caused by neglecting the CO2 fraction in air always remain smaller than the uncertainty of the equations used to calculate the tabulated properties. The impact of all other trace components is smaller than the impact of CO2. Humidity has to be considered separately. To calculate the properties tabulated in the following pages, the ‘‘pseudo pure-component’’ equations from the cited references were used. According to the authors, these equations are slightly more accurate than the mixture models published in the same articles. Z Compression factor b Z = p/(rRT) Pr Prandtl number Pr = Z cp/l Isobaric expansion coefficient in 103/K b = v1 (@ v/@T)p cp Specific isobaric heat capacity in kJ/(kg K) ws Isentropic speed of sound in m/s v Specific volume in m3/kg 3 l Thermal conductivity in mW/(m K) n Kinematic viscosity n in 107 m2/s Pressure in bar Density in kg/m # Temperature in C h Specific enthalpy in kJ/kg Dynamic viscosity in 106 Pa·s s Specific entropy in kJ/(kg K) Thermal diffusivity in 107 m2/s 2 a Critical Parameters of Dry Air Critical Temperatures Pressures 132.531 K 3.7860 MPa 11.8308 mol/ dm3 140.619 C 37.860 bar 342.599 kg/m3 3.7850 MPa 10.4477 mol/ dm3 140.519 C 37.850 bar 302.547 kg/m3 132.604 K 3.7891 MPa 11.0948 mol/ dm3 140.547 C 37.891 bar 321.286 kg/m3 Maxcondentherm 132.631 K Maxcondenbar 2.1 Densities Reference States of Enthalpy and Entropy h = 0 kJ/kg, s = 0 kJ/(kg K) at T = 298.15 K (W) = 25 C), p = 1.01325 bar for the pure components D2.2 Properties of Dry Air D2.2. Table 1. Properties of dry air at p = 1 bar q C r kg/m3 h kJ/kg s kJ/(kg K) cp kJ/(kg K) b 103/K l mW/(m K) h m Pa*s n 107 m2/s a 107 m2/s Pr – ws m/s 200 900.81 435.60 4.0270 1.9145 4.8833 149.590 206.790 2.296 0.867 2.6466 917.9 194.36 875.52 424.76 3.8842 1.9329 5.2331 140.180 167.360 1.912 0.828 2.3076 866.7 191.54 4.4419 219.76 1.3183 1.0891 13.8730 7.673 5.811 13.08 15.86 0.8248 177.1 190 4.3492 218.09 1.2980 1.0818 13.5040 7.824 5.921 13.62 16.63 0.8187 179.0 180 3.8383 207.44 1.1770 1.0517 11.6120 8.803 6.630 17.28 21.81 0.7921 190.8 170 3.4418 197.01 1.0707 1.0359 10.2600 9.774 7.323 21.28 27.41 0.7762 201.6 160 3.1230 186.70 0.9753 1.0266 9.2236 10.733 8.001 25.62 33.48 0.7653 211.7 150 2.8600 176.47 0.8886 1.0206 8.3947 11.679 8.664 30.29 40.01 0.7571 221.3 140 2.6390 166.28 0.8091 1.0165 7.7122 12.611 9.313 35.29 47.01 0.7507 230.4 130 2.4503 156.13 0.7356 1.0137 7.1381 13.529 9.948 40.60 54.47 0.7454 239.2 120 2.2873 146.01 0.6672 1.0116 6.6471 14.434 10.571 46.22 62.38 0.7409 247.6 110 2.1448 135.90 0.6033 1.0101 6.2217 15.326 11.182 52.13 70.74 0.7370 255.7 100 2.0193 125.80 0.5432 1.0090 5.8490 16.205 11.780 58.34 79.54 0.7335 263.5 90 1.9078 115.72 0.4866 1.0081 5.5196 17.071 12.368 64.83 88.76 0.7304 271.1 80 1.8080 105.64 0.4330 1.0074 5.2260 17.924 12.944 71.59 98.41 0.7275 278.5 70 1.7183 95.57 0.3822 1.0068 4.9627 18.766 13.511 78.63 108.5 0.7249 285.7 60 1.6371 85.51 0.3338 1.0064 4.7250 19.596 14.067 85.93 118.9 0.7224 292.7 50 1.5632 75.44 0.2877 1.0061 4.5094 20.416 14.614 129.8 0.7202 299.5 40 1.4958 65.38 0.2436 1.0059 4.3128 21.224 15.152 101.3 141.1 0.7181 306.2 30 1.4340 55.33 0.2013 1.0058 4.1329 22.023 15.680 109.4 152.7 0.7161 312.7 20 1.3771 45.27 0.1608 1.0057 3.9675 22.811 16.201 117.7 164.7 0.7143 319.1 10 1.3245 35.21 0.1218 1.0058 3.8149 23.590 16.714 126.2 177.1 0.7126 325.4 0 1.2758 25.15 0.0843 1.0059 3.6738 24.360 17.218 135.0 189.8 0.7110 331.5 10 1.2306 15.09 0.0481 1.0061 3.5428 25.121 17.715 144.0 202.9 0.7095 337.5 20 1.1885 5.03 0.0132 1.0064 3.4209 25.873 18.205 153.2 216.3 0.7081 343.4 30 1.1492 5.04 0.0205 1.0067 3.3071 26.618 18.689 162.6 230.1 0.7068 349.2 40 1.1124 15.11 0.0532 1.0071 3.2007 27.354 19.165 172.3 244.2 0.7056 354.9 50 1.0779 25.18 0.0849 1.0077 3.1010 28.082 19.635 182.2 258.5 0.7045 360.5 60 1.0455 35.26 0.1156 1.0082 3.0073 28.804 20.099 192.2 273.2 0.7035 365.9 70 1.0150 45.34 0.1454 1.0089 2.9192 29.518 20.557 202.5 288.2 0.7026 371.3 80 0.9862 55.44 0.1744 1.0097 2.8361 30.225 21.009 213.0 303.5 0.7018 376.7 93.49 90 0.9590 65.54 0.2026 1.0105 2.7576 30.925 21.455 223.7 319.1 0.7011 381.9 100 0.9333 75.65 0.2301 1.0115 2.6833 31.620 21.896 234.6 335.0 0.7004 387.0 120 0.8858 95.90 0.2830 1.0136 2.5463 32.989 22.763 257.0 367.5 0.6994 397.1 140 0.8428 116.19 0.3333 1.0160 2.4225 34.336 23.610 280.1 401.0 0.6986 406.9 160 0.8039 136.54 0.3814 1.0188 2.3103 35.660 24.439 304.0 435.4 0.6982 416.4 180 0.7684 156.95 0.4275 1.0218 2.2081 36.964 25.251 328.6 470.8 0.6980 425.7 200 0.7359 177.42 0.4717 1.0252 2.1145 38.248 26.046 353.9 507.0 0.6981 434.7 250 0.6655 228.91 0.5751 1.0347 1.9120 41.382 27.970 420.3 601.0 0.6993 456.2 300 0.6075 280.90 0.6700 1.0454 1.7450 44.417 29.811 490.7 699.5 0.7016 476.6 350 0.5587 333.46 0.7579 1.0568 1.6048 47.367 31.579 565.2 802.2 0.7046 495.9 400 0.5172 386.60 0.8399 1.0688 1.4855 50.240 33.284 643.5 908.9 0.7081 514.3 450 0.4815 440.33 0.9170 1.0808 1.3827 53.047 34.932 725.6 1019.5 0.7117 532.0 500 0.4503 494.67 0.9896 1.0927 1.2932 55.795 36.530 811.2 1133.9 0.7154 549.0 550 0.4230 549.60 1.0584 1.1043 1.2147 58.490 38.084 900.4 1252.3 0.7190 565.4 600 0.3988 605.09 1.1239 1.1154 1.1451 61.139 39.597 993.0 1374.6 0.7224 581.3 650 0.3772 661.13 1.1863 1.1260 1.0830 63.745 41.073 1089.0 1501.0 0.7255 596.7 173 174 D2 Properties of Selected Important Pure Substances D2.2. Table 1. (continued) r kg/m3 q C h kJ/kg s kJ/(kg K) cp kJ/(kg K) b 103/K l mW/(m K) h m Pa*s n 107 m2/s a 107 m2/s Pr – ws m/s 700 0.3578 717.68 1.2459 1.1361 1.0274 66.312 42.517 1188.3 1631.4 0.7284 611.7 750 0.3403 774.72 1.3031 1.1455 0.9772 68.846 43.931 1290.9 1766.0 0.7310 626.3 800 0.3245 832.22 1.3580 1.1544 0.9317 71.348 45.317 1396.7 1904.9 0.7333 640.6 850 0.3100 890.16 1.4107 1.1628 0.8902 73.822 46.679 1505.7 2047.9 0.7352 654.6 900 0.2968 948.49 1.4615 1.1706 0.8522 76.271 48.018 1617.8 2195.3 0.7370 668.3 950 0.2847 1007.20 1.5106 1.1778 0.8174 78.695 49.336 1733.1 2347.0 0.7384 681.7 1000 0.2735 1066.30 1.5579 1.1846 0.7853 81.099 50.635 1851.4 2503.1 0.7396 694.8 D2.2. Table 2. Properties of the saturated liquid q C p0 bar r0 kg/m3 h0 kJ/kg s0 kJ/(kg K) cP0 kJ/(kg K) b0 103/K l0 mW/(m K) h0 m Pa*s n0 107 m2/s a0 107 m2/s Pr0 Z0 w0 m/s s0 N/m 212 0.070027 951.78 458.54 4.3679 1.9013 4.3568 169.16 351.22 3.6902 0.93477 3.9477 0.000419 1019.0 13.81 210 0.10276 943.46 454.73 4.3067 1.9017 4.4305 165.92 318.80 3.3791 0.92475 3.6541 0.000601 1002.8 13.32 208 0.14697 935.07 450.92 4.2474 1.9027 4.5093 162.66 290.38 3.1055 0.91425 3.3968 0.000840 986.2 12.83 206 0.20536 926.60 447.11 4.1899 1.9045 4.5936 159.40 265.40 2.8642 0.90325 3.1710 0.001150 969.5 12.34 204 0.28095 918.06 443.30 4.1340 1.9071 4.6842 156.13 243.38 2.6510 0.89174 2.9728 0.001541 952.4 11.86 202 0.37705 909.43 439.47 4.0797 1.9105 4.7817 152.84 223.90 2.4620 0.87968 2.7987 0.002030 935.1 11.39 200 0.49727 900.71 435.64 4.0267 1.9149 4.8870 149.55 206.63 2.2941 0.86707 2.6458 0.002629 917.6 10.91 198 0.64543 891.88 431.79 3.9751 1.9202 5.0008 146.24 191.26 2.1444 0.85388 2.5114 0.003354 899.8 10.45 196 0.82562 882.94 427.93 3.9246 1.9267 5.1242 142.91 177.53 2.0107 0.84010 2.3934 0.004221 881.7 9.983 194 1.0421 873.87 424.06 3.8754 1.9344 5.2583 139.58 165.23 1.8908 0.82570 2.2899 0.005248 863.3 9.525 192 1.2993 864.67 420.16 3.8271 1.9434 5.4044 136.22 154.17 1.7830 0.81068 2.1993 0.006449 844.7 9.071 190 1.6019 855.32 416.25 3.7799 1.9538 5.5640 132.86 144.18 1.6857 0.79501 2.1204 0.007845 825.8 8.622 188 1.9545 845.81 412.31 3.7336 1.9659 5.7389 129.53 135.14 1.5977 0.77902 2.0509 0.009452 806.5 8.179 186 2.3620 836.12 408.34 3.688 1.9798 5.9310 126.19 126.90 1.5178 0.76228 1.9911 0.011290 787.0 7.741 184 2.8295 826.24 404.33 3.6433 1.9957 6.1428 122.82 119.39 1.4449 0.74482 1.9399 0.013379 767.1 7.308 182 3.3619 816.15 400.30 3.5992 2.0139 6.3772 119.44 112.49 1.3783 0.72666 1.8967 0.015740 746.9 6.880 180 3.9644 805.83 396.22 3.5558 2.0347 6.6374 116.05 106.13 1.3170 0.70779 1.8608 0.018394 726.4 6.458 178 4.6422 795.25 392.10 3.5129 2.0584 6.9277 112.65 100.25 1.2606 0.6882 1.8317 0.021367 705.5 6.043 176 5.4006 784.39 387.92 3.4705 2.0854 7.2530 109.25 94.782 1.2084 0.66789 1.8092 0.024683 684.2 5.633 174 6.2450 773.22 383.69 3.4285 2.1164 7.6195 105.85 89.677 1.1598 0.64686 1.7930 0.028371 662.6 5.230 172 7.1809 761.70 379.40 3.3868 2.1518 8.0348 102.45 84.887 1.1144 0.62508 1.7829 0.032462 640.6 4.833 170 8.2139 749.80 375.03 3.3454 2.1927 8.5085 99.062 80.373 1.0719 0.60255 1.7790 0.036989 618.2 4.444 168 9.3494 737.47 370.59 3.3042 2.2398 9.0531 95.680 76.099 1.0319 0.57924 1.7815 0.041992 595.3 4.062 166 10.593 724.66 366.05 3.2631 2.2947 9.6846 92.313 72.033 0.99402 0.55514 1.7906 0.047516 572.1 3.687 164 11.951 711.31 361.42 3.2220 2.3590 10.4250 88.966 68.146 0.95804 0.53019 1.8070 0.053613 548.4 3.321 162 13.429 697.34 356.67 3.1808 2.4352 11.3020 85.644 64.413 0.92369 0.50433 1.8315 0.060343 524.3 2.963 160 15.032 682.66 351.79 3.1393 2.5266 12.3600 82.353 60.809 0.89076 0.47745 1.8656 0.067781 499.6 2.615 158 16.767 667.17 346.75 3.0974 2.6382 13.6570 79.097 57.312 0.85903 0.44939 1.9116 0.076017 474.4 2.276 156 18.640 650.70 341.53 3.0550 2.7773 15.2870 75.879 53.898 0.82831 0.41987 1.9728 0.085165 448.5 1.949 154 20.656 633.06 336.10 3.0116 2.9560 17.4020 72.701 50.544 0.79840 0.38850 2.0551 0.095377 421.9 1.632 152 22.821 613.97 330.40 2.9671 3.1948 20.2620 69.564 47.220 0.76910 0.35464 2.1687 0.10686 394.2 1.329 150 25.140 592.99 324.35 2.9207 3.5324 24.3640 66.469 43.890 0.74016 0.31733 2.3325 0.11990 365.2 1.040 148 27.618 569.39 317.83 2.8716 4.0503 30.7800 63.433 40.496 0.71123 0.27506 2.5857 0.13499 334.3 0.768 146 30.259 541.83 310.60 2.8181 4.9562 42.2910 60.546 36.939 0.68176 0.22546 3.0238 0.15298 300.6 0.516 144 33.060 507.16 302.13 2.7562 6.9740 68.8600 58.297 32.997 0.65062 0.16482 3.9474 0.17580 262.3 0.289 142 35.992 454.16 290.48 2.6714 184.2900 60.168 27.911 0.61458 0.08684 7.0773 0.21046 215.0 0.097 15.256 0.16804 0.23499 0.32171 0.43200 0.56999 0.74008 0.9469 1.1953 1.4904 1.8374 2.2415 2.7085 3.2438 204 202 200 198 196 194 192 190 188 186 184 182 180 9.3976 19.175 21.323 23.642 26.144 28.843 31.764 34.964 154 152 150 148 146 144 142 15.354 17.188 158 156 12.115 13.666 162 160 10.694 166 164 7.1491 8.2181 170 168 5.3174 6.1843 174 172 3.8531 0.11739 206 4.5424 0.079916 208 178 0.052874 176 0.033892 210 p00 bar 212 q C 207.50 168.49 142.55 122.75 106.73 93.336 81.902 72.001 63.341 55.710 48.952 42.945 37.594 32.821 28.560 24.760 21.372 18.359 15.686 13.320 11.236 9.4081 7.8132 6.4304 5.2399 4.2233 3.3630 2.6425 2.0461 1.5587 1.1663 0.85556 0.61391 0.42988 0.29293 0.19366 r00 kg/m3 238.43 229.71 224.14 220.10 217.04 214.67 212.83 211.42 210.37 209.61 209.11 208.84 208.78 208.89 209.17 209.60 210.16 210.86 211.67 212.60 213.63 214.75 215.97 217.27 218.65 220.10 221.63 223.22 224.86 226.57 228.32 230.11 231.95 233.82 235.71 237.64 h00 kJ/kg D2.2. Table 3. Properties of the saturated vapor 2.2718 2.1916 2.1334 2.0852 2.0429 2.0045 1.9688 1.9350 1.9025 1.8710 1.8401 1.8095 1.7791 1.7485 1.7177 1.6864 1.6544 1.6217 1.5880 1.5531 1.5168 1.4790 1.4394 1.3977 1.3539 1.3074 1.2581 1.2057 1.1496 1.0895 1.0250 0.95552 0.88042 0.79906 0.71069 0.61444 s00 kJ/(kg K) 12.181 6.4725 4.5166 3.5294 2.9374 2.5446 2.2658 2.0581 1.8975 1.7698 1.6659 1.5796 1.5069 1.4448 1.3911 1.3443 1.3031 1.2668 1.2344 1.2056 1.1798 1.1566 1.1359 1.1173 1.1007 1.0859 1.0727 1.0611 1.0508 1.0419 1.0342 1.0276 1.0221 1.0175 1.0137 1.0106 kJ/(kg K) cP00 176.500 91.847 62.639 47.822 38.912 33.001 28.819 25.723 23.354 21.495 20.007 18.800 17.809 16.989 16.309 15.743 15.274 14.888 14.574 14.323 14.130 13.989 13.897 13.850 13.847 13.886 13.966 14.086 14.246 14.447 14.688 14.970 15.294 15.661 16.072 16.529 b00 103/K 38.048 28.812 24.144 21.152 19.021 17.404 16.124 15.079 14.205 13.458 12.809 12.238 11.729 11.269 10.851 10.466 10.109 9.7755 9.4618 9.165 8.8823 8.6118 8.3516 8.1002 7.8564 7.6190 7.3872 7.1600 6.9368 6.7169 6.4997 6.2848 6.0718 5.8602 5.6497 5.4401 l00 mW/(m K) 13.697 12.270 11.380 10.724 10.203 9.7708 9.4012 9.0779 8.7900 8.5299 8.2920 8.0719 7.8663 7.6727 7.4889 7.3132 7.1442 6.9806 6.8216 6.6662 6.5137 6.3636 6.2153 6.0684 5.9225 5.7773 5.6325 5.4879 5.3434 5.1987 5.0538 4.9085 4.7628 4.6167 4.4701 4.3230 h00 m Pa*s 0.6601 0.7282 0.7983 0.8737 0.9560 1.0468 1.1479 1.2608 1.3877 1.5311 1.6939 1.8796 2.0924 2.3378 2.6221 2.9537 3.3427 3.8022 4.3490 5.0045 5.7971 6.7640 7.9549 9.4371 11.303 13.680 16.749 20.768 26.115 33.352 43.330 57.372 77.581 107.400 152.600 223.230 v00 107 m2/s 0.1505 0.2642 0.3750 0.4883 0.6067 0.7328 0.8689 1.0176 1.1818 1.3649 1.5708 1.8041 2.0704 2.3766 2.7311 3.1444 3.6296 4.2032 4.8866 5.7072 6.7006 7.9140 9.4103 11.274 13.622 16.614 20.478 25.537 32.263 41.358 53.883 71.483 96.766 133.98 190.26 277.95 a00 107 m2/s 4.38490 2.75650 2.12880 1.78940 1.57570 1.42860 1.32110 1.23900 1.17420 1.12180 1.07840 1.04180 1.01060 0.98364 0.96008 0.93934 0.92096 0.90460 0.88997 0.87688 0.86516 0.85468 0.84533 0.83704 0.82974 0.82337 0.81789 0.81327 0.80945 0.80642 0.80415 0.80260 0.80174 0.80156 0.80202 0.80310 Pr00 – 0.44749 0.50839 0.55424 0.59274 0.62649 0.65677 0.68435 0.70971 0.73320 0.75506 0.77548 0.79460 0.81254 0.82938 0.84520 0.86004 0.87396 0.88700 0.89918 0.91053 0.92107 0.93082 0.93980 0.94803 0.95552 0.9623 0.96838 0.97378 0.97854 0.98269 0.98625 0.98927 0.99178 0.99384 0.9955 0.9968 Z00 – ws 170.61 172.82 174.77 176.55 178.19 179.67 180.98 182.13 183.10 183.91 184.55 185.04 185.36 185.54 185.56 185.43 185.17 184.76 184.21 183.53 182.72 181.77 180.70 179.50 178.17 176.73 175.17 173.50 171.72 169.83 167.85 165.76 163.59 161.33 158.99 156.57 m/s Properties of Dry Air D2.2 175 176 D2 Properties of Selected Important Pure Substances D2.2. Table 4. Density r of dry air in kg/m3 Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 1 2.860 2.366 2.019 1.762 1.5632 1.4049 1.2758 1.1685 1.0779 1.0004 0.93328 5 15.007 12.146 10.257 8.897 7.8645 7.0518 6.3940 5.8500 5.3923 5.0017 4.6643 10 32.203 25.162 20.931 18.013 15.8490 14.1700 12.8230 11.7170 10.7900 10.0020 20 79.159 54.508 43.667 36.923 32.1730 28.5940 25.7770 23.4920 21.5950 19.9920 18.617 30 605.220 90.103 68.511 56.770 48.9570 43.2480 38.8400 35.3080 32.4010 29.9600 27.876 40 624.490 135.840 95.798 77.577 66.1780 58.1070 51.9910 47.1490 43.1960 39.8960 37.091 50 639.390 199.180 125.820 99.339 83.8040 73.1430 65.2070 58.9970 53.9680 49.7920 46.257 60 651.750 288.200 158.700 122.000 101.790 88.320 78.4660 70.8380 64.7050 59.6390 55.367 70 662.390 377.410 194.180 145.440 120.060 103.600 91.7420 82.6540 75.3960 69.4300 64.415 80 671.790 437.030 231.440 169.460 138.540 118.940 105.010 94.428 86.0300 79.1560 73.397 96.5960 88.8100 82.307 9.3227 90 680.240 476.340 269.090 193.810 157.130 134.280 118.240 106.140 100 687.940 504.790 305.450 218.180 175.710 149.590 131.400 117.780 107.080 98.386 91.140 150 719.020 585.850 439.950 330.190 264.770 223.640 195.260 174.280 157.980 144.850 134.010 200 742.640 631.230 515.070 413.950 340.680 290.050 253.850 226.720 205.550 188.490 174.390 250 761.990 663.570 564.110 473.840 401.340 346.750 305.730 274.170 249.190 228.890 212.020 300 778.530 688.990 600.320 518.690 449.580 394.320 350.890 316.490 288.750 265.940 246.830 350 793.060 710.100 629.070 554.080 488.720 434.340 390.060 354.030 324.420 299.750 278.900 400 806.080 728.230 652.980 583.170 521.280 468.410 424.160 387.340 356.560 330.570 308.400 450 817.910 744.200 673.490 607.850 549.020 497.830 454.110 417.050 385.580 358.700 335.540 500 828.790 758.500 691.500 629.280 573.110 523.590 480.640 443.680 411.880 384.420 360.560 600 848.280 783.400 722.120 665.230 613.390 566.930 525.770 489.550 457.750 429.790 405.110 700 865.480 804.700 747.670 694.770 646.320 602.450 563.060 527.880 496.530 468.580 443.610 800 880.920 823.410 769.700 719.920 674.180 632.490 594.720 560.630 529.920 502.250 477.290 900 894.990 840.150 789.120 741.870 698.360 658.520 622.190 589.150 559.150 531.890 507.120 1000 907.950 855.340 806.540 761.380 719.740 681.480 646.430 614.380 585.080 558.310 533.810 Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 1 0.87461 0.8229 0.7359 0.6075 0.5172 0.4503 0.3988 0.3578 0.3245 0.2968 0.2735 5 4.3698 4.1106 3.6749 3.0329 2.5823 2.2484 1.9911 1.7867 1.6203 1.4824 1.3660 10 8.7310 8.2109 7.3382 6.0547 5.1550 4.4888 3.9755 3.5677 3.2359 2.9606 2.7285 8.9456 7.9241 7.1127 6.4525 5.9047 5.4428 9.6500 8.8324 8.1428 20 17.424 16.378 14.629 12.065 10.272 30 26.073 24.497 21.868 18.028 15.350 13.370 11.846 10.635 40 34.673 32.564 29.055 23.945 20.388 17.762 15.741 14.135 12.828 11.744 10.829 50 43.218 40.574 36.186 29.814 25.388 22.122 19.609 17.612 15.987 14.639 13.500 60 51.705 48.525 43.260 35.635 30.348 26.449 23.450 21.067 19.128 17.517 16.158 70 60.129 56.413 50.275 41.408 35.268 30.744 27.264 24.500 22.249 20.380 18.802 80 68.486 64.237 57.230 47.131 40.149 35.007 31.052 27.910 25.351 23.226 21.431 90 76.772 71.992 64.123 52.805 44.990 39.237 34.813 31.298 28.435 26.056 24.047 100 84.986 79.678 70.954 58.429 49.791 43.435 38.547 34.663 31.499 28.870 26.649 150 124.850 116.990 104.140 85.802 73.207 63.950 56.828 51.165 46.547 42.704 39.454 200 162.500 152.300 135.640 111.930 95.653 83.686 74.471 67.135 61.143 56.152 51.925 250 197.750 185.500 165.440 136.830 117.160 102.670 91.499 82.591 75.305 69.227 64.073 300 230.580 216.560 193.540 160.530 137.750 120.930 107.940 97.554 89.049 81.943 75.909 350 261.040 245.560 219.990 183.080 157.470 138.500 123.810 112.050 102.390 94.313 87.444 400 289.260 272.580 244.850 204.520 176.360 155.410 139.140 126.080 115.350 106.350 98.689 450 315.410 297.760 268.240 224.920 194.450 171.690 153.950 139.690 127.940 118.070 109.660 Properties of Dry Air D2.2 D2.2. Table 4. (continued) Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 500 339.670 321.250 290.230 244.330 211.790 187.370 168.270 152.880 140.170 129.480 120.350 600 383.230 363.730 330.480 280.410 244.370 217.040 195.530 178.090 163.630 151.430 140.980 700 421.230 401.090 366.390 313.240 274.400 244.660 221.070 201.850 185.850 172.300 160.660 800 454.720 434.260 398.620 343.240 302.170 270.420 245.060 224.290 206.920 192.160 179.450 900 484.550 463.950 427.770 370.770 327.940 294.520 267.650 245.520 226.950 211.110 197.420 1000 511.360 490.750 454.290 396.150 351.940 317.140 288.970 265.660 246.010 229.200 214.630 D2.2. Table 5. Compression factor Z of dry air Temperature in C Pressure in bar 1 150 125 100 75 50 25 0 25 50 75 100 0.9889 0.9937 0.9961 0.9976 0.9984 0.9990 0.9994 0.9997 0.9999 1.0000 1.0001 5 0.9423 0.9678 0.9806 0.9879 0.9923 0.9952 0.9971 0.9984 0.9994 1.0001 1.0006 10 0.8782 0.9343 0.9610 0.9758 0.9848 0.9905 0.9944 0.9970 0.9989 1.0002 1.0012 20 0.7146 0.8626 0.9213 0.9521 0.9702 0.9817 0.9893 0.9945 0.9982 1.0008 1.0027 30 0.1402 0.7827 0.8808 0.9289 0.9564 0.9736 0.9849 0.9926 0.9979 1.0017 1.0045 40 0.1812 0.6923 0.8399 0.9063 0.9434 0.9662 0.9810 0.9911 0.9980 1.0030 1.0066 50 0.2212 0.5902 0.7993 0.8847 0.9312 0.9595 0.9777 0.9900 0.9986 1.0046 1.0089 60 0.2604 0.4894 0.7605 0.8645 0.9200 0.9535 0.9750 0.9894 0.9994 1.0065 1.0115 70 0.2989 0.4360 0.7251 0.8460 0.9100 0.9483 0.9729 0.9893 1.0007 1.0086 1.0143 80 0.3368 0.4304 0.6953 0.8298 0.9013 0.9441 0.9714 0.9897 1.0022 1.0111 1.0173 90 0.3742 0.4442 0.6728 0.8162 0.8940 0.9407 0.9706 0.9905 1.0042 1.0138 1.0206 100 0.4111 0.4657 0.6585 0.8056 0.8883 0.9383 0.9704 0.9918 1.0065 1.0168 1.0241 150 0.5900 0.6019 0.6858 0.7985 0.8842 0.9414 0.9795 1.0054 1.0234 1.0359 1.0448 200 0.7617 0.7449 0.7811 0.8492 0.9163 0.9678 1.0046 1.0305 1.0487 1.0615 1.0705 250 0.9279 0.8857 0.8914 0.9274 0.9722 1.0119 1.0427 1.0652 1.0813 1.0927 1.1006 300 1.0898 1.0236 1.0052 1.0166 1.0415 1.0678 1.0902 1.1073 1.1198 1.1285 1.1344 350 1.2482 1.1588 1.1192 1.1103 1.1178 1.1310 1.1441 1.1549 1.1628 1.1681 1.1713 400 1.4034 1.2913 1.2322 1.2056 1.1977 1.1986 1.2024 1.2063 1.2091 1.2105 1.2106 450 1.5560 1.4215 1.3440 1.3013 1.2793 1.2687 1.2635 1.2605 1.2579 1.2550 1.2518 500 1.7062 1.5497 1.4544 1.3966 1.3617 1.3403 1.3264 1.3165 1.3084 1.3012 1.2943 600 2.0004 1.8006 1.6713 1.5854 1.5267 1.4854 1.4551 1.4317 1.4127 1.3966 1.3824 700 2.2874 2.0450 1.8832 1.7709 1.6904 1.6308 1.5852 1.5491 1.5195 1.4945 1.4728 800 2.5684 2.2841 2.0907 1.9532 1.8521 1.7753 1.7152 1.6669 1.6271 1.5935 1.5645 900 2.8440 2.5184 2.2941 2.1324 2.0114 1.9182 1.8444 1.7845 1.7348 1.6927 1.6565 1000 3.1149 2.7485 2.4940 2.3086 2.1685 2.0595 1.9725 1.9014 1.8421 1.7919 1.7485 Temperature in C Pressure in bar 1 125 150 200 300 400 500 600 700 800 900 1000 1.0002 1.0002 1.0003 1.0004 1.0004 1.0004 1.0003 1.0003 1.0003 1.0003 1.0003 5 1.0009 1.0012 1.0015 1.0018 1.0018 1.0018 1.0017 1.0016 1.0015 1.0014 1.0013 10 1.0019 1.0024 1.0031 1.0036 1.0037 1.0036 1.0034 1.0032 1.0030 1.0028 1.0026 20 1.0041 1.0051 1.0064 1.0074 1.0074 1.0072 1.0068 1.0064 1.0060 1.0056 1.0052 30 1.0065 1.0080 1.0098 1.0112 1.0112 1.0108 1.0102 1.0096 1.0090 1.0084 1.0079 177 178 D2 Properties of Selected Important Pure Substances D2.2. Table 5. (continued) Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 40 1.0092 1.0111 1.0134 1.0151 1.0151 1.0145 1.0137 1.0128 1.0120 1.0112 1.0105 50 1.0120 1.0143 1.0171 1.0191 1.0190 1.0182 1.0171 1.0160 1.0150 1.0141 1.0132 60 1.0151 1.0177 1.0210 1.0232 1.0230 1.0219 1.0206 1.0193 1.0181 1.0169 1.0158 70 1.0184 1.0213 1.0249 1.0273 1.0269 1.0257 1.0241 1.0226 1.0211 1.0197 1.0185 80 1.0218 1.0251 1.0290 1.0315 1.0310 1.0295 1.0277 1.0259 1.0242 1.0226 1.0212 90 1.0255 1.0290 1.0332 1.0357 1.0350 1.0333 1.0312 1.0292 1.0273 1.0255 1.0239 100 1.0293 1.0330 1.0374 1.0400 1.0392 1.0371 1.0348 1.0325 1.0303 1.0283 1.0265 150 1.0510 1.0554 1.0603 1.0624 1.0602 1.0566 1.0529 1.0492 1.0459 1.0428 1.0401 200 1.0767 1.0809 1.0853 1.0858 1.0818 1.0766 1.0713 1.0662 1.0616 1.0574 1.0537 250 1.1059 1.1093 1.1123 1.1103 1.1041 1.0969 1.0899 1.0833 1.0774 1.0721 1.0674 300 1.1381 1.1402 1.1410 1.1356 1.1268 1.1175 1.1087 1.1006 1.0934 1.0869 1.0812 350 1.1729 1.1732 1.1712 1.1617 1.1500 1.1384 1.1276 1.1180 1.1094 1.1018 1.0950 400 1.2097 1.2079 1.2025 1.1885 1.1735 1.1594 1.1467 1.1354 1.1255 1.1166 1.1088 450 1.2480 1.2439 1.2349 1.2158 1.1974 1.1807 1.1659 1.1530 1.1416 1.1315 1.1227 500 1.2877 1.2811 1.2681 1.2436 1.2215 1.2021 1.1852 1.1705 1.1577 1.1464 1.1365 600 1.3696 1.3578 1.3364 1.3003 1.2704 1.2453 1.2241 1.2058 1.1900 1.1763 1.1642 700 1.4537 1.4365 1.4064 1.3580 1.3199 1.2889 1.2631 1.2412 1.2224 1.2062 1.1919 800 1.5390 1.5163 1.4773 1.4164 1.3698 1.3327 1.3022 1.2766 1.2548 1.2360 1.2196 900 1.6248 1.5967 1.5487 1.4751 1.4200 1.3766 1.3413 1.3119 1.2871 1.2657 1.2471 1000 1.7107 1.6772 1.6204 1.5339 1.4702 1.4205 1.3804 1.3472 1.3193 1.2953 1.2746 D2.2. Table 6. Specific enthalpy h of dry air in kJ/kg Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 1 176.47 151.07 125.80 100.61 75.44 50.30 25.15 0.00 5 181.40 154.48 128.36 102.60 77.05 51.61 26.24 0.91 10 188.29 158.97 131.63 105.13 79.07 53.26 27.60 20 206.60 168.83 138.45 110.27 83.11 56.52 30 325.76 180.29 145.68 115.52 87.17 59.77 50 75 100 25.18 50.39 75.65 24.41 49.74 75.10 2.04 23.46 48.94 74.43 30.29 4.28 21.60 47.38 73.12 32.94 6.46 19.78 45.86 71.85 40 327.72 194.14 153.34 120.88 91.24 62.99 35.54 8.60 18.00 44.38 70.62 50 328.98 211.58 161.41 126.32 95.30 66.17 38.10 10.70 16.27 42.95 69.43 60 329.85 232.79 169.80 131.80 99.33 69.31 40.62 12.75 14.59 41.56 68.28 70 330.44 250.57 178.33 137.25 103.32 72.39 43.07 14.74 12.95 40.21 67.17 80 330.84 260.81 186.72 142.62 107.22 75.40 45.47 16.69 11.36 38.90 66.09 90 331.09 266.84 194.64 147.83 111.02 78.33 47.80 18.57 9.82 37.63 65.06 100 331.22 270.78 201.79 152.81 114.69 81.17 50.06 20.40 8.32 36.41 64.06 150 330.72 279.19 223.68 172.79 130.43 93.64 60.09 28.55 1.67 30.98 59.64 200 329.08 281.28 231.98 184.26 141.29 102.92 67.82 34.94 3.58 26.69 56.18 250 326.82 281.17 235.10 190.09 147.95 109.21 73.34 39.62 7.46 23.53 53.67 300 324.15 279.92 235.84 192.74 151.65 113.12 76.97 42.79 10.12 21.39 52.02 350 321.20 277.98 235.25 193.51 153.37 115.24 79.10 44.69 11.71 20.16 51.33 400 318.05 275.60 233.84 193.09 153.73 116.04 80.04 45.57 12.41 19.69 50.92 450 314.75 272.89 231.87 191.88 153.16 115.88 80.07 45.63 12.38 19.87 51.29 500 311.34 269.94 229.49 190.10 151.90 114.99 79.39 45.02 11.74 20.59 52.14 Properties of Dry Air D2.2 D2.2. Table 6. (continued) Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 600 304.24 263.54 223.93 185.40 147.97 111.67 76.46 42.29 9.05 23.35 55.05 700 296.89 256.68 217.64 179.70 142.81 106.95 72.07 38.11 4.97 27.43 59.19 800 289.38 249.52 210.88 173.35 136.86 101.34 66.72 32.93 0.10 32.46 64.23 900 281.74 242.14 203.80 166.58 130.38 95.11 60.69 27.06 5.88 38.19 69.95 1000 274.03 234.62 196.49 159.50 123.51 88.44 54.18 20.67 12.18 44.45 76.19 Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 1 100.97 126.36 177.42 280.90 386.60 494.67 605.09 717.68 832.22 948.49 1066.30 5 100.51 125.98 177.16 280.82 386.63 494.78 605.26 717.90 832.48 948.77 1066.60 10 99.95 125.51 176.84 280.72 386.67 494.93 605.48 718.17 832.80 949.13 1067.00 20 98.85 124.60 176.23 280.53 386.76 495.22 605.92 718.73 833.44 949.84 1067.70 30 97.79 123.72 175.65 280.37 386.88 495.53 606.37 719.29 834.08 950.55 1068.50 40 96.77 122.88 175.10 280.23 387.01 495.85 606.83 719.86 834.74 951.27 1069.30 50 95.79 122.07 174.58 280.11 387.15 496.18 607.31 720.43 835.40 952.00 1070.00 60 94.84 121.30 174.09 280.01 387.31 496.53 607.78 721.02 836.06 952.73 1070.80 70 93.93 120.55 173.62 279.92 387.48 496.88 608.27 721.61 836.73 953.46 1071.60 80 93.05 119.84 173.18 279.86 387.67 497.24 608.77 722.20 837.41 954.20 1072.40 90 92.20 119.16 172.76 279.81 387.87 497.62 609.27 722.81 838.09 954.94 1073.20 100 91.39 118.51 172.37 279.78 388.08 498.00 609.78 723.41 838.77 955.69 1074.00 150 87.83 115.68 170.74 279.85 389.29 500.04 612.43 726.53 842.27 959.48 1078.00 200 85.09 113.57 169.68 280.29 390.77 502.26 615.23 729.77 845.85 963.35 1082.10 250 83.15 112.15 169.14 281.07 392.48 504.66 618.15 733.11 849.52 967.28 1086.30 300 81.95 111.37 169.08 282.16 394.40 507.21 621.18 736.53 853.25 971.27 1090.50 350 81.42 111.16 169.48 283.53 396.51 509.90 624.32 740.03 857.05 975.31 1094.70 400 81.47 111.48 170.29 285.17 398.81 512.71 627.56 743.61 860.90 979.40 1099.00 450 82.04 112.25 171.45 287.05 401.28 515.65 630.88 747.24 864.80 983.52 1103.30 500 83.04 113.41 172.95 289.16 403.90 518.70 634.29 750.94 868.75 987.67 1107.60 600 86.14 116.74 176.76 293.95 409.56 525.10 641.32 758.51 876.77 996.08 1116.40 700 90.39 121.12 181.47 299.39 415.69 531.86 648.61 766.27 884.93 1004.60 1125.20 800 95.48 126.30 186.88 305.36 422.23 538.91 656.13 774.20 893.22 1013.20 1134.10 900 101.23 132.10 192.85 311.75 429.09 546.22 663.84 782.27 901.61 1021.90 1143.00 1000 107.49 138.39 199.25 318.50 436.22 553.73 671.71 790.46 910.10 1030.60 1152.00 75 100 D2.2. Table 7. Specific entropy s of dry air in kJ/(kg K) Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 1 0.8886 0.7008 0.5432 0.4073 0.2877 0.1809 0.0843 0.0038 0.0849 0.1600 0.2301 5 1.3777 1.1786 1.0156 0.8767 0.7552 0.6471 0.5497 0.4610 0.3794 0.3039 0.2336 10 1.6157 1.3985 1.2279 1.0849 0.9610 0.8514 0.7529 0.6634 0.5812 0.5053 0.4346 20 1.9258 1.6448 1.4551 1.3030 1.1739 1.0609 0.9602 0.8690 0.7857 0.7089 0.6375 30 2.9387 1.8184 1.6019 1.4391 1.3042 1.1878 1.0848 0.9921 0.9075 0.8298 0.7577 40 2.9678 1.9730 1.7173 1.5419 1.4010 1.2809 1.1755 1.0812 0.9955 0.9168 0.8440 50 2.9910 2.1320 1.8164 1.6268 1.4792 1.3554 1.2477 1.1516 1.0648 0.9852 0.9118 179 180 D2 Properties of Selected Important Pure Substances D2.2. Table 7. (continued) Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 60 3.0106 2.3034 1.9057 1.7002 1.5458 1.4181 1.3080 1.2103 1.1223 1.0419 0.9677 70 3.0277 2.4437 1.9879 1.7656 1.6041 1.4726 1.3601 1.2608 1.1716 1.0903 1.0156 80 3.0431 2.5293 2.0636 1.8248 1.6563 1.5211 1.4061 1.3053 1.2149 1.1328 1.0574 90 3.0572 2.5848 2.1325 1.8789 1.7037 1.5647 1.4475 1.3451 1.2536 1.1707 1.0946 100 3.0701 2.6251 2.1938 1.9286 1.7471 1.6046 1.4851 1.3812 1.2886 1.2049 1.1282 150 3.1237 2.7433 2.3972 2.1221 1.9204 1.7640 1.6351 1.5246 1.4272 1.3399 1.2604 200 3.1659 2.8128 2.5053 2.2477 2.0432 1.8801 1.7452 1.6300 1.5290 1.4387 1.3569 250 3.2015 2.8641 2.5768 2.3338 2.1334 1.9687 1.8309 1.7127 1.6091 1.5167 1.4331 300 3.2325 2.9055 2.6306 2.3979 2.2026 2.0388 1.8999 1.7801 1.6749 1.5810 1.4960 350 3.2603 2.9407 2.6741 2.4488 2.2580 2.0959 1.9571 1.8366 1.7303 1.6353 1.5494 400 3.2855 2.9715 2.7110 2.4911 2.3040 2.1438 2.0055 1.8847 1.7779 1.6822 1.5956 450 3.3087 2.9991 2.7431 2.5273 2.3432 2.1848 2.0473 1.9266 1.8195 1.7234 1.6362 500 3.3302 3.0241 2.7717 2.5591 2.3775 2.2207 2.0840 1.9635 1.8563 1.7599 1.6724 600 3.3694 3.0684 2.8213 2.6133 2.4354 2.2811 2.1459 2.0262 1.9191 1.8225 1.7346 700 3.4045 3.1071 2.8635 2.6587 2.4834 2.3310 2.1971 2.0781 1.9713 1.8747 1.7866 800 3.4365 3.1416 2.9006 2.6980 2.5246 2.3736 2.2407 2.1223 2.0159 1.9194 1.8313 900 3.4659 3.1730 2.9337 2.7329 2.5608 2.4109 2.2788 2.1609 2.0548 1.9585 1.8704 1000 3.4933 3.2018 2.9639 2.7643 2.5932 2.4442 2.3126 2.1952 2.0894 1.9932 1.9052 Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 1 0.2958 0.3576 0.4717 0.6700 0.8399 0.9896 1.1239 1.2459 1.3580 1.4615 1.5579 5 0.1677 0.1057 0.0087 0.2074 0.3775 0.5272 0.6616 0.7837 0.8958 0.9994 1.0957 10 0.3684 0.3061 0.1915 0.0076 0.1780 0.3279 0.4623 0.5845 0.6966 0.8003 0.8966 20 0.5707 0.5080 0.3927 0.1927 0.0219 0.1282 0.2629 0.3852 0.4974 0.6010 0.6975 30 0.6904 0.6272 0.5112 0.3105 0.1393 0.0112 0.1460 0.2684 0.3807 0.4844 0.5809 40 0.7762 0.7126 0.5960 0.3944 0.2228 0.0720 0.0629 0.1855 0.2978 0.4016 0.4982 50 0.8434 0.7794 0.6621 0.4598 0.2877 0.1367 0.0016 0.1211 0.2335 0.3374 0.4339 60 0.8989 0.8344 0.7165 0.5134 0.3409 0.1897 0.0544 0.0684 0.1809 0.2849 0.3815 70 0.9461 0.8813 0.7627 0.5589 0.3860 0.2345 0.0990 0.0238 0.1364 0.2404 0.3371 80 0.9875 0.9222 0.8030 0.5985 0.4252 0.2734 0.1378 0.0148 0.0978 0.2019 0.2986 90 1.0242 0.9585 0.8388 0.6336 0.4598 0.3078 0.1720 0.0490 0.0638 0.1679 0.2646 100 1.0573 0.9913 0.8710 0.6650 0.4909 0.3387 0.2027 0.0795 0.0333 0.1375 0.2342 150 1.1872 1.1194 0.9964 0.7872 0.6112 0.4578 0.3211 0.1974 0.0842 0.0202 0.1172 200 1.2819 1.2125 1.0872 0.8751 0.6974 0.5430 0.4056 0.2814 0.1679 0.0632 0.0339 250 1.3566 1.2860 1.1587 0.9440 0.7649 0.6095 0.4715 0.3468 0.2330 0.1281 0.0307 300 1.4183 1.3467 1.2177 1.0009 0.8204 0.6641 0.5255 0.4005 0.2863 0.1812 0.0836 350 1.4708 1.3983 1.2680 1.0493 0.8676 0.7106 0.5714 0.4460 0.3315 0.2261 0.1285 400 1.5163 1.4432 1.3118 1.0915 0.9087 0.7510 0.6113 0.4855 0.3707 0.2652 0.1674 450 1.5564 1.4828 1.3506 1.1288 0.9451 0.7867 0.6466 0.5204 0.4054 0.2997 0.2017 500 1.5922 1.5183 1.3852 1.1624 0.9778 0.8188 0.6782 0.5518 0.4365 0.3306 0.2325 600 1.6539 1.5794 1.4453 1.2205 1.0346 0.8746 0.7332 0.6062 0.4905 0.3842 0.2858 700 1.7057 1.6308 1.4960 1.2698 1.0828 0.9219 0.7799 0.6523 0.5362 0.4296 0.3310 800 1.7502 1.6752 1.5398 1.3126 1.1246 0.9630 0.8204 0.6924 0.5760 0.4691 0.3702 900 1.7892 1.7140 1.5783 1.3503 1.1616 0.9993 0.8563 0.7279 0.6111 0.5040 0.4049 1000 1.8240 1.7487 1.6127 1.3840 1.1947 1.0319 0.8884 0.7597 0.6426 0.5353 0.4360 Properties of Dry Air D2.2 D2.2. Table 8. Specific isobaric heat capacity cp of dry air in kJ/kg (kg K) Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 1 1.0206 1.0126 1.0090 1.0071 1.0061 1.0058 1.0059 1.0065 1.0077 1.0093 1.0115 5 1.1049 1.0565 1.0360 1.0254 1.0194 1.0159 1.0139 1.0129 1.0129 1.0137 1.0152 10 1.2512 1.1206 1.0729 1.0496 1.0366 1.0288 1.0239 1.0210 1.0196 1.0193 1.0199 20 1.9732 1.2939 1.1589 1.1025 1.0729 1.0553 1.0443 1.0372 1.0328 1.0302 1.0292 30 3.1906 1.5720 1.2651 1.1617 1.1115 1.0829 1.0651 1.0536 1.0460 1.0412 1.0384 40 2.8042 2.0715 1.3956 1.2273 1.1524 1.1113 1.0862 1.0700 1.0591 1.0520 1.0475 50 2.5864 3.0575 1.5531 1.2989 1.1951 1.1403 1.1075 1.0863 1.0722 1.0627 1.0564 60 2.4418 4.4725 1.7355 1.3751 1.2391 1.1697 1.1288 1.1026 1.0851 1.0733 1.0652 70 2.3367 4.3335 1.9317 1.4537 1.2836 1.1991 1.1499 1.1187 1.0979 1.0836 1.0739 80 2.2560 3.5940 2.1197 1.5319 1.3278 1.2281 1.1708 1.1346 1.1104 1.0939 1.0824 90 2.1915 3.0994 2.2702 1.6064 1.3706 1.2565 1.1912 1.1501 1.1227 1.1038 1.0907 100 2.1384 2.7881 2.3592 1.6741 1.4113 1.2837 1.2109 1.1652 1.1347 1.1136 1.0988 150 1.9679 2.1643 2.2000 1.8506 1.5625 1.3960 1.2960 1.2318 1.1883 1.1578 1.1360 200 1.8729 1.9514 1.9704 1.8228 1.6184 1.4609 1.3540 1.2812 1.2302 1.1936 1.1668 250 1.8114 1.8398 1.8350 1.7521 1.6161 1.4873 1.3875 1.3143 1.2606 1.2209 1.1912 300 1.7679 1.7697 1.7507 1.6898 1.5932 1.4911 1.4035 1.3345 1.2815 1.2410 1.2100 350 1.7355 1.7213 1.6938 1.6415 1.5666 1.4843 1.4087 1.3457 1.2952 1.2554 1.2242 400 1.7105 1.6857 1.6528 1.6045 1.5420 1.4733 1.4079 1.3510 1.3037 1.2654 1.2347 450 1.6907 1.6585 1.6219 1.5757 1.5206 1.4614 1.4040 1.3525 1.3086 1.2722 1.2425 500 1.6747 1.6371 1.5979 1.5529 1.5026 1.4499 1.3987 1.3519 1.3112 1.2767 1.2481 600 1.6504 1.6058 1.5631 1.5194 1.4746 1.4300 1.3870 1.3474 1.3120 1.2813 1.2551 700 1.6334 1.5843 1.5395 1.4964 1.4546 1.4143 1.3764 1.3415 1.3101 1.2824 1.2585 800 1.6209 1.5690 1.5227 1.4800 1.4399 1.4024 1.3676 1.3359 1.3073 1.2820 1.2599 900 1.6117 1.5577 1.5105 1.4679 1.4289 1.3931 1.3605 1.3309 1.3044 1.2809 1.2604 1000 1.6048 1.5494 1.5015 1.4589 1.4207 1.3861 1.3548 1.3268 1.3018 1.2797 1.2603 Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 1 1.0142 1.0174 1.0252 1.0454 1.0688 1.0927 1.1154 1.1361 1.1544 1.1706 1.1846 5 1.0174 1.0202 1.0274 1.0467 1.0697 1.0934 1.1159 1.1365 1.1547 1.1708 1.1849 10 1.0214 1.0237 1.0301 1.0485 1.0709 1.0942 1.1166 1.1370 1.1551 1.1711 1.1851 20 1.0294 1.0305 1.0354 1.0519 1.0732 1.0959 1.1178 1.1379 1.1559 1.1717 1.1856 30 1.0372 1.0373 1.0405 1.0552 1.0755 1.0976 1.1191 1.1389 1.1567 1.1724 1.1861 40 1.0449 1.0440 1.0456 1.0584 1.0778 1.0992 1.1203 1.1398 1.1574 1.1730 1.1866 50 1.0525 1.0505 1.0507 1.0616 1.0800 1.1008 1.1215 1.1408 1.1581 1.1735 1.1871 60 1.0600 1.0569 1.0556 1.0648 1.0821 1.1024 1.1227 1.1417 1.1589 1.1741 1.1876 70 1.0673 1.0633 1.0604 1.0678 1.0843 1.1039 1.1238 1.1426 1.1596 1.1747 1.1880 80 1.0745 1.0694 1.0651 1.0709 1.0863 1.1054 1.1250 1.1435 1.1603 1.1753 1.1885 90 1.0816 1.0755 1.0697 1.0738 1.0884 1.1069 1.1261 1.1444 1.1610 1.1758 1.1889 100 1.0885 1.0814 1.0743 1.0767 1.0904 1.1084 1.1272 1.1452 1.1617 1.1764 1.1894 150 1.1202 1.1088 1.0954 1.0904 1.1000 1.1154 1.1326 1.1494 1.1650 1.1791 1.1916 200 1.1470 1.1323 1.1138 1.1027 1.1087 1.1219 1.1375 1.1533 1.1681 1.1816 1.1937 250 1.1688 1.1519 1.1297 1.1136 1.1166 1.1279 1.1422 1.1570 1.1711 1.1840 1.1957 300 1.1861 1.1678 1.1431 1.1232 1.1238 1.1334 1.1465 1.1604 1.1739 1.1864 1.1976 350 1.1997 1.1806 1.1543 1.1317 1.1303 1.1384 1.1505 1.1637 1.1766 1.1886 1.1995 400 1.2103 1.1909 1.1637 1.1391 1.1361 1.1431 1.1542 1.1667 1.1791 1.1907 1.2012 181 182 D2 Properties of Selected Important Pure Substances D2.2. Table 8. (continued) Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 450 1.2184 1.1990 1.1714 1.1456 1.1413 1.1473 1.1577 1.1696 1.1815 1.1927 1.2029 500 1.2246 1.2056 1.1779 1.1512 1.1460 1.1512 1.1610 1.1723 1.1837 1.1946 1.2046 600 1.2331 1.2149 1.1879 1.1605 1.1541 1.1580 1.1667 1.1772 1.1879 1.1982 1.2076 700 1.2381 1.2209 1.1950 1.1678 1.1607 1.1638 1.1718 1.1815 1.1917 1.2014 1.2105 800 1.2410 1.2248 1.2001 1.1735 1.1661 1.1687 1.1761 1.1854 1.1951 1.2044 1.2131 900 1.2426 1.2274 1.2039 1.1782 1.1707 1.1730 1.1800 1.1888 1.1981 1.2071 1.2155 1000 1.2435 1.2291 1.2068 1.1820 1.1746 1.1767 1.1833 1.1919 1.2009 1.2096 1.2177 D2.2. Table 9. Thermal conductivity l of dry air in mW/(mK) Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 1 11.679 13.984 16.205 18.347 20.416 22.418 24.360 26.247 28.082 29.872 31.620 5 12.088 14.293 16.456 18.558 20.599 22.579 24.504 26.376 28.201 29.981 31.720 10 12.809 14.765 16.817 18.854 20.849 22.797 24.696 26.549 28.357 30.124 31.852 20 15.903 16.074 17.714 19.550 21.422 23.284 25.118 26.925 28.696 30.432 32.134 30 68.194 18.097 18.865 20.386 22.086 23.836 25.589 27.340 29.067 30.767 32.439 40 71.300 21.364 20.305 21.360 22.835 24.447 26.102 27.789 29.466 31.126 32.765 50 74.010 26.955 22.064 22.469 23.663 25.111 26.653 28.269 29.892 31.508 33.111 60 76.460 35.540 24.166 23.708 24.564 25.823 27.238 28.777 30.340 31.909 33.473 70 78.718 42.807 26.611 25.071 25.530 26.577 27.853 29.309 30.808 32.327 33.851 80 80.829 47.734 29.356 26.547 26.557 27.370 28.495 29.862 31.295 32.761 34.243 90 82.820 51.522 32.298 28.127 27.639 28.198 29.160 30.435 31.798 33.209 34.646 100 84.710 54.641 35.290 29.795 28.770 29.056 29.846 31.024 32.314 33.669 35.061 150 93.066 65.987 47.908 38.623 34.939 33.716 33.534 34.170 35.065 36.115 37.263 200 100.160 74.556 56.916 46.559 41.223 38.672 37.508 37.550 38.011 38.731 39.617 250 106.410 81.886 64.314 53.295 46.985 43.506 41.545 41.025 41.059 41.445 42.064 300 112.030 88.410 70.883 59.302 52.228 48.044 45.469 44.465 44.115 44.190 44.552 350 117.150 94.330 76.900 64.864 57.126 52.319 49.228 47.800 47.112 46.908 47.037 400 121.850 99.765 82.487 70.108 61.798 56.414 52.848 51.020 50.021 49.566 49.484 450 126.170 104.800 87.712 75.092 66.302 60.392 56.371 54.149 52.848 52.154 51.876 500 130.300 109.480 92.621 79.846 70.664 64.285 59.831 57.219 55.613 54.682 54.213 600 137.810 117.990 101.630 88.733 78.994 71.852 66.630 63.266 61.041 59.618 58.761 700 144.540 125.530 109.720 96.878 86.815 79.127 73.285 69.251 66.424 64.496 63.226 800 150.640 132.430 117.060 104.370 94.144 86.084 79.767 75.169 71.796 69.375 67.683 900 156.220 138.710 123.710 111.270 101.010 92.706 86.039 80.986 77.140 74.267 72.164 1000 161.380 144.490 129.930 117.660 107.430 98.991 92.074 86.664 82.423 79.149 76.665 Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 1 33.328 35.000 38.248 44.417 50.240 55.795 61.139 66.312 71.348 76.271 81.099 5 33.421 35.088 38.325 44.479 50.292 55.839 61.177 66.347 71.379 76.298 81.124 10 33.543 35.201 38.425 44.559 50.358 55.896 61.227 66.390 71.418 76.334 81.157 20 33.803 35.442 38.635 44.726 50.496 56.014 61.329 66.480 71.499 76.406 81.223 30 34.084 35.701 38.860 44.903 50.641 56.136 61.435 66.574 71.582 76.481 81.291 Properties of Dry Air D2.2 D2.2. Table 9. (continued) Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 40 34.382 35.977 39.097 45.088 50.793 56.264 61.545 66.670 71.667 76.558 81.361 50 34.698 36.267 39.347 45.282 50.951 56.396 61.659 66.770 71.756 76.638 81.433 60 35.028 36.570 39.607 45.484 51.114 56.533 61.776 66.872 71.847 76.719 81.506 70 35.372 36.886 39.877 45.692 51.283 56.674 61.897 66.978 71.940 76.803 81.582 80 35.729 37.212 40.156 45.907 51.457 56.819 62.021 67.086 72.035 76.888 81.659 90 36.096 37.549 40.444 46.129 51.635 56.968 62.148 67.196 72.133 76.975 81.737 100 36.473 37.894 40.739 46.356 51.818 57.121 62.278 67.309 72.233 77.064 81.818 150 38.475 39.728 42.307 47.562 52.791 57.931 62.969 67.909 72.761 77.535 82.241 200 40.615 41.690 43.987 48.860 53.840 58.806 63.715 68.556 73.331 78.042 82.698 250 42.843 43.735 45.742 50.222 54.946 59.730 64.505 69.243 73.936 78.581 83.183 300 45.117 45.828 47.546 51.629 56.093 60.693 65.330 69.962 74.570 79.147 83.692 350 47.402 47.941 49.378 53.069 57.271 61.685 66.183 70.707 75.228 79.735 84.221 400 49.667 50.047 51.220 54.530 58.474 62.701 67.059 71.473 75.907 80.342 84.769 450 51.893 52.127 53.055 56.002 59.693 63.736 67.953 72.257 76.603 80.966 85.333 500 54.072 54.171 54.872 57.477 60.924 64.785 68.863 73.057 77.314 81.604 85.910 600 58.306 58.144 58.424 60.407 63.397 66.909 70.714 74.691 78.772 82.915 87.098 700 62.437 62.004 61.868 63.281 65.858 69.047 72.592 76.358 80.265 84.263 88.324 800 66.542 65.816 65.238 66.087 68.284 71.176 74.479 78.044 81.782 85.638 89.577 900 70.664 69.632 68.580 68.836 70.666 73.282 76.360 79.735 83.312 87.031 90.851 1000 74.817 73.478 71.928 71.551 73.007 75.359 78.226 81.424 84.848 88.434 92.139 D2.2. Table 10. Dynamic viscosity Z of dry air in 106 Pa·s Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 1 8.664 10.261 11.780 13.229 14.614 15.942 17.218 18.448 19.635 20.783 21.896 5 8.750 10.344 11.859 13.303 14.684 16.008 17.280 18.506 19.690 20.836 21.946 10 8.918 10.480 11.977 13.409 14.780 16.097 17.363 18.583 19.762 20.904 22.010 20 9.631 10.884 12.285 13.666 15.004 16.296 17.544 18.749 19.916 21.047 22.144 30 45.850 11.539 12.701 13.984 15.267 16.523 17.745 18.931 20.082 21.200 22.286 40 49.163 12.617 13.247 14.369 15.571 16.778 17.966 19.127 20.259 21.361 22.435 50 51.933 14.525 13.947 14.823 15.916 17.059 18.205 19.337 20.447 21.532 22.591 60 54.379 18.094 14.829 15.350 16.300 17.366 18.463 19.560 20.644 21.709 22.753 70 56.603 23.028 15.918 15.952 16.725 17.698 18.737 19.795 20.851 21.894 22.921 80 58.665 27.373 17.223 16.629 17.187 18.053 19.028 20.042 21.066 22.086 23.094 90 60.602 30.839 18.729 17.379 17.687 18.430 19.333 20.300 21.290 22.284 23.272 100 62.438 33.705 20.388 18.197 18.221 18.829 19.653 20.568 21.521 22.488 23.455 150 70.614 43.949 28.901 23.009 21.323 21.090 21.431 22.036 22.774 23.583 24.429 200 77.771 51.399 36.003 28.162 24.859 23.671 23.437 23.671 24.154 24.776 25.480 250 84.346 57.676 41.945 33.032 28.507 26.419 25.590 25.423 25.624 26.041 26.590 300 90.546 63.288 47.165 37.524 32.095 29.230 27.828 27.254 27.162 27.362 27.746 350 96.486 68.468 51.906 41.691 35.561 32.038 30.109 29.138 28.751 28.727 28.939 400 102.240 73.345 56.308 45.596 38.893 34.810 32.405 31.057 30.377 30.129 30.164 450 107.860 77.997 60.458 49.291 42.099 37.532 34.697 32.994 32.032 31.559 31.417 500 113.370 82.479 64.412 52.816 45.191 40.197 36.974 34.940 33.706 33.013 32.694 183 184 D2 Properties of Selected Important Pure Substances D2.2. Table 10. (continued) Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 600 124.190 91.067 71.885 59.472 51.086 45.358 41.457 38.827 37.087 35.973 35.306 700 134.830 99.307 78.939 65.731 56.669 50.315 45.833 42.681 40.483 38.977 37.976 800 145.380 107.310 85.697 71.699 62.009 55.095 50.102 46.484 43.872 42.001 40.684 900 155.890 115.160 92.242 77.446 67.156 59.727 54.270 50.232 47.240 45.032 43.417 1000 166.410 122.910 98.627 83.021 72.146 64.233 58.348 53.922 50.581 48.058 46.163 Temperature in C Pressure in bar 1 125 150 200 300 400 500 600 700 800 900 1000 22.977 24.027 26.046 29.811 33.284 36.530 39.597 42.517 45.317 48.018 50.635 5 23.024 24.072 26.087 29.845 33.314 36.557 39.621 42.538 45.337 48.036 50.651 10 23.085 24.129 26.139 29.890 33.352 36.591 39.650 42.565 45.361 48.058 50.672 20 23.211 24.249 26.247 29.980 33.429 36.658 39.710 42.619 45.410 48.103 50.713 30 23.344 24.374 26.358 30.071 33.508 36.726 39.771 42.674 45.459 48.148 50.754 40 23.482 24.503 26.473 30.165 33.587 36.796 39.832 42.728 45.509 48.193 50.796 50 23.626 24.637 26.591 30.261 33.668 36.865 39.893 42.783 45.558 48.238 50.837 60 23.775 24.775 26.712 30.358 33.750 36.936 39.955 42.838 45.608 48.284 50.879 70 23.929 24.917 26.836 30.457 33.832 37.007 40.018 42.894 45.658 48.329 50.921 80 24.087 25.063 26.962 30.557 33.915 37.078 40.080 42.950 45.709 48.375 50.963 90 24.249 25.212 27.090 30.658 33.999 37.150 40.143 43.006 45.759 48.421 51.005 100 24.415 25.364 27.221 30.761 34.084 37.223 40.207 43.062 45.810 48.467 51.047 150 25.293 26.164 27.902 31.290 34.518 37.591 40.527 43.346 46.065 48.698 51.259 200 26.234 27.016 28.620 31.838 34.964 37.967 40.853 43.634 46.322 48.931 51.472 250 27.222 27.907 29.366 32.402 35.419 38.349 41.183 43.924 46.581 49.165 51.685 300 28.248 28.830 30.133 32.978 35.881 38.736 41.515 44.216 46.842 49.401 51.900 350 29.306 29.779 30.920 33.564 36.348 39.126 41.850 44.509 47.103 49.636 52.114 400 30.392 30.752 31.724 34.159 36.821 39.519 42.186 44.804 47.365 49.872 52.329 450 31.502 31.747 32.544 34.764 37.300 39.915 42.525 45.099 47.627 50.108 52.543 500 32.635 32.762 33.380 35.377 37.783 40.314 42.865 45.396 47.890 50.344 52.758 600 34.960 34.847 35.098 36.633 38.767 41.122 43.551 45.992 48.418 50.818 53.188 700 37.348 36.997 36.874 37.926 39.775 41.946 44.247 46.595 48.950 51.294 53.618 800 39.784 39.199 38.701 39.259 40.810 42.787 44.954 47.205 49.486 51.772 54.050 900 42.255 41.443 40.574 40.630 41.873 43.648 45.675 47.824 50.029 52.255 54.486 1000 44.752 43.720 42.487 42.038 42.964 44.529 46.411 48.454 50.579 52.744 54.925 D2.2. Table 11. Kinematic viscosity n of dry air in 107 m2/s Temperature in C Pressure in bar 1 150 125 100 75 50 25 0 25 50 75 100 30.293 43.371 58.338 75.078 93.485 113.470 134.960 157.870 182.150 207.750 234.620 5 5.8303 8.5168 11.5630 14.9530 18.6710 22.7000 27.0260 31.6350 36.5160 41.6570 47.0510 10 2.7694 4.1651 5.7224 7.4443 9.3256 11.3600 13.5400 15.8600 18.3150 20.9000 23.6090 20 1.2166 1.9969 2.8133 3.7011 4.6634 5.6991 6.8059 7.9812 9.2226 10.5280 11.8950 30 0.7576 1.2806 1.8539 2.4633 3.1185 3.8206 4.5687 5.3616 6.1979 7.0761 7.9949 40 0.7873 0.9288 1.3828 1.8522 2.3529 2.8874 3.4556 4.0568 4.6900 5.3543 6.0487 Properties of Dry Air D2.2 D2.2. Table 11. (continued) Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 50 0.8122 0.7293 1.1085 1.4922 1.8991 2.3323 2.7919 3.2776 3.7886 4.3243 4.8839 60 0.8344 0.6278 0.9344 1.2582 1.6014 1.9662 2.3530 2.7612 3.1905 3.6401 4.1096 70 0.8545 0.6102 0.8198 1.0968 1.3930 1.7083 2.0424 2.3950 2.7655 3.1535 3.5583 80 0.8733 0.6263 0.7442 0.9813 1.2406 1.5178 1.8120 2.1225 2.4487 2.7902 3.1465 90 0.8909 0.6474 0.6960 0.8967 1.1257 1.3725 1.6351 1.9125 2.2040 2.5092 2.8275 100 0.9076 0.6677 0.6675 0.8340 1.0370 1.2587 1.4956 1.7462 2.0098 2.2857 2.5735 150 0.9821 0.7502 0.6569 0.6968 0.8053 0.9430 1.0976 1.2644 1.4416 1.6280 1.8230 200 1.0472 0.8143 0.6990 0.6803 0.7297 0.8161 0.9233 1.0441 1.1751 1.3144 1.4611 250 1.1069 0.8692 0.7436 0.6971 0.7103 0.7619 0.8370 0.9273 1.0283 1.1377 1.2541 300 1.1630 0.9186 0.7857 0.7234 0.7139 0.7413 0.7931 0.8611 0.9407 1.0289 1.1241 350 1.2166 0.9642 0.8251 0.7525 0.7276 0.7376 0.7719 0.8231 0.8862 0.9584 1.0376 400 1.2684 1.0072 0.8623 0.7819 0.7461 0.7432 0.7640 0.8018 0.8520 0.9114 0.9781 450 1.3187 1.0481 0.8977 0.8109 0.7668 0.7539 0.7641 0.7911 0.8307 0.8798 0.9363 500 1.3680 1.0874 0.9315 0.8393 0.7885 0.7677 0.7693 0.7875 0.8183 0.8588 0.9068 600 1.4640 1.1625 0.9955 0.8940 0.8328 0.8001 0.7885 0.7931 0.8102 0.8370 0.8715 700 1.5579 1.2341 1.0558 0.9461 0.8768 0.8352 0.8140 0.8085 0.8153 0.8318 0.8561 800 1.6503 1.3033 1.1134 0.9959 0.9198 0.8711 0.8425 0.8292 0.8279 0.8363 0.8524 900 1.7419 1.3708 1.1689 1.0439 0.9616 0.9070 0.8723 0.8526 0.8449 0.8466 0.8562 1000 1.8328 1.4369 1.2228 1.0904 1.0024 0.9426 0.9026 0.8777 0.8645 0.8608 0.8648 Temperature in C Pressure in bar 1 125 150 200 300 400 500 600 700 800 900 1000 262.700 291.980 353.940 490.740 643.520 811.210 993.010 1188.300 1396.700 1617.800 1851.400 5 52.6880 58.5610 70.9870 98.4060 129.0100 162.5900 198.9900 238.0900 279.8000 324.0500 370.7900 10 26.4400 29.3870 35.6210 49.3660 64.6980 81.5150 99.7370 119.3100 140.1800 162.3300 185.7100 20 13.3210 14.8060 17.9420 24.8490 32.5450 40.9790 50.1130 59.9200 70.3760 81.4650 93.1750 30 8.9531 9.9495 12.0530 16.6800 21.8300 27.4690 33.5740 40.1250 47.1080 54.5130 62.3300 40 6.7725 7.5246 9.1115 12.5980 16.4740 20.7160 25.3050 30.2290 35.4750 41.0370 46.9090 50 5.4667 6.0721 7.3485 10.1500 13.2610 16.6650 20.3450 24.2920 28.4960 32.9530 37.6560 60 4.5982 5.1056 6.1748 8.5191 11.1210 13.9650 17.0390 20.3340 23.8440 27.5640 31.4880 70 3.9796 4.4169 5.3378 7.3553 9.5928 12.0370 14.6780 17.5080 20.5220 23.7150 27.0830 80 3.5171 3.9016 4.7111 6.4834 8.4475 10.5920 12.9080 15.3890 18.0300 20.8280 23.7800 90 3.1586 3.5020 4.2247 5.8060 7.5572 9.4681 11.5310 13.7410 16.0930 18.5830 21.2100 100 2.8728 3.1833 3.8364 5.2647 6.8455 8.5697 10.4310 12.4230 14.5430 16.7880 19.1550 150 2.0259 2.2364 2.6794 3.6467 4.7151 5.8782 7.1316 8.4718 9.8965 11.4040 12.9920 200 1.6144 1.7739 2.1099 2.8445 3.6553 4.5369 5.4858 6.4994 7.5760 8.7141 9.9126 250 1.3766 1.5045 1.7750 2.3681 3.0232 3.7352 4.5009 5.3182 6.1857 7.1021 8.0666 300 1.2251 1.3312 1.5569 2.0543 2.6047 3.2031 3.8463 4.5324 5.2602 6.0287 6.8371 350 1.1227 1.2127 1.4055 1.8333 2.3082 2.8249 3.3802 3.9724 4.6003 5.2629 5.9597 400 1.0507 1.1282 1.2956 1.6702 2.0879 2.5428 3.0320 3.5535 4.1063 4.6894 5.3024 450 0.9988 1.0662 1.2133 1.5456 1.9182 2.3248 2.7622 3.2286 3.7228 4.2440 4.7917 500 0.9608 1.0198 1.1501 1.4479 1.7840 2.1516 2.5473 2.9694 3.4166 3.8882 4.3836 600 0.9122 0.9581 1.0620 1.3064 1.5864 1.8947 2.2274 2.5826 2.9590 3.3558 3.7726 700 0.8866 0.9224 1.0064 1.2108 1.4496 1.7145 2.0015 2.3084 2.6338 2.9770 3.3374 800 0.8749 0.9027 0.9709 1.1438 1.3506 1.5822 1.8344 2.1046 2.3915 2.6942 3.0120 900 0.8721 0.8933 0.9485 1.0958 1.2768 1.4820 1.7065 1.9478 2.2044 2.4753 2.7599 1000 0.8752 0.8909 0.9352 1.0612 1.2208 1.4041 1.6061 1.8239 2.0560 2.3012 2.5591 185 186 D2 Properties of Selected Important Pure Substances D2.2. Table 12. Thermal diffusivity a of dry air in 107 m2/s Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 1 40.011 58.368 79.536 103.390 129.810 158.660 189.810 223.150 258.540 295.850 334.960 5 7.291 11.138 15.487 20.343 25.693 31.519 37.800 44.512 51.630 59.130 66.986 10 3.179 5.236 7.489 9.972 12.690 15.639 18.809 22.193 25.777 29.550 33.499 20 1.018 2.279 3.500 4.803 6.206 7.716 9.331 11.050 12.866 14.775 16.771 30 0.3532 1.2776 2.1767 3.0911 4.0587 5.0894 6.1854 7.3495 8.5764 9.8633 11.2070 40 0.4072 0.7592 1.5188 2.2434 2.9942 3.7857 4.6220 5.5086 6.4405 7.4163 8.4335 50 0.4475 0.4426 1.1290 1.7414 2.3626 3.0106 3.6908 4.4108 5.1657 5.9546 6.7759 60 0.4805 0.2757 0.8774 1.4132 1.9475 2.4996 3.0753 3.6843 4.3210 4.9851 5.6756 70 0.5086 0.2617 0.7095 1.1858 1.6566 2.1395 2.6402 3.1697 3.7218 4.2967 4.8936 80 0.5333 0.3039 0.5984 1.0226 1.4437 1.8738 2.3177 2.7873 3.2759 3.7837 4.3104 90 0.5556 0.3490 0.5287 0.9034 1.2834 1.6713 2.0704 2.4931 2.9321 3.3876 3.8594 100 0.5758 0.3882 0.4897 0.8157 1.1602 1.5131 1.8757 2.2606 2.6596 3.0731 3.5010 150 0.6577 0.5204 0.4950 0.6321 0.8446 1.0800 1.3251 1.5917 1.8678 2.1533 2.4478 200 0.7201 0.6053 0.5608 0.6170 0.7477 0.9127 1.0913 1.2927 1.5031 1.7215 1.9470 250 0.7710 0.6708 0.6213 0.6420 0.7244 0.8436 0.9794 1.1385 1.3070 1.4830 1.6654 300 0.8140 0.7251 0.6745 0.6766 0.7292 0.8171 0.9233 1.0528 1.1922 1.3389 1.4917 350 0.8511 0.7718 0.7217 0.7132 0.7461 0.8116 0.8959 1.0033 1.1212 1.2465 1.3777 400 0.8837 0.8127 0.7643 0.7493 0.7688 0.8175 0.8849 0.9750 1.0761 1.1849 1.2995 450 0.9124 0.8490 0.8030 0.7840 0.7942 0.8301 0.8842 0.9600 1.0474 1.1429 1.2443 500 0.9388 0.8817 0.8383 0.8171 0.8206 0.8468 0.8900 0.9540 1.0298 1.1141 1.2047 600 0.9843 0.9379 0.9004 0.8779 0.8733 0.8863 0.9137 0.9591 1.0164 1.0826 1.1557 700 1.0225 0.9846 0.9533 0.9318 0.9235 0.9286 0.9456 0.9779 1.0211 1.0733 1.1325 800 1.0550 1.0251 0.9987 0.9795 0.9698 0.9705 0.9807 1.0037 1.0364 1.0774 1.1255 900 1.0830 1.0599 1.0379 1.0218 1.0122 1.0105 1.0164 1.0328 1.0576 1.0900 1.1290 1000 1.1075 1.0902 1.0729 1.0593 1.0506 1.0480 1.0513 1.0632 1.0821 1.1078 1.1395 Temperature in C Pressure in bar 125 150 200 300 400 1 375.740 5 75.175 10 20 500 418.070 506.98 699.48 908.87 83.672 101.510 140.110 182.060 227.140 275.340 326.750 381.480 37.613 41.881 50.835 70.192 91.220 113.800 137.930 163.670 191.070 220.160 250.980 18.847 20.999 25.509 35.245 45.806 57.136 69.238 82.137 95.862 110.430 125.870 30 12.6030 14.0500 17.0770 23.6040 30.6750 38.2540 46.3440 54.9640 64.1310 40 9.4899 10.5830 12.8690 17.7900 23.1150 28.8170 34.9010 41.3800 4.2690 55.5790 63.3200 50 7.6278 8.5086 10.3490 14.3060 18.5830 23.1590 28.0380 33.2330 38.7540 44.6110 50.8130 60 6.3912 7.1303 8.6737 11.9870 15.5640 19.3890 23.4660 27.8030 32.4120 37.3010 42.4760 70 5.5116 6.1495 7.4802 10.3340 13.4110 16.6990 20.2010 23.9270 27.8840 32.0810 36.5230 80 4.8551 5.4169 6.5878 9.0959 11.7980 14.6830 17.7540 21.0210 24.4900 28.1680 32.0600 1133.90 600 1374.60 700 1631.40 800 1904.90 900 2195.30 439.620 73.8620 1000 2503.10 501.210 84.1670 90 4.3470 4.8496 5.8961 8.1352 10.5450 13.1160 15.8530 18.7620 21.8500 25.1250 28.5890 100 3.9428 4.3979 5.3448 7.3684 9.5443 11.8650 14.3330 16.9560 19.7400 22.6910 25.8130 150 2.7511 3.0626 3.7090 5.0838 6.5559 8.1215 9.7836 11.5470 13.4180 15.3990 17.4930 200 2.1792 2.4175 2.9114 3.9588 5.0770 6.2635 7.5213 8.8545 10.2670 11.7620 13.3420 250 1.8536 2.0469 2.4474 3.2960 4.2002 5.1581 6.1723 7.2464 8.3838 9.5869 10.8580 300 1.6496 1.8121 2.1491 2.8633 3.6235 4.4281 5.2793 6.1801 7.1335 8.1416 9.2060 350 1.5136 1.6537 1.9445 2.5613 3.2178 3.9121 4.6463 5.4230 6.2446 7.1131 8.0298 400 1.4187 1.5418 1.7977 2.3406 2.9185 3.5296 4.1755 4.8587 5.5812 6.3448 7.1506 Properties of Dry Air D2.2 D2.2. Table 12. (continued) Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 450 1.3503 1.4601 1.6885 2.1735 2.6897 3.2356 3.8126 4.4227 5.0679 5.7497 6.4691 500 1.2999 1.3987 1.6050 2.0435 2.5101 3.0035 3.5250 4.0764 4.6596 5.2758 5.9259 600 1.2338 1.3158 1.4882 1.8562 2.2480 2.6621 3.0998 3.5627 4.0524 4.5698 5.1157 700 1.1972 1.2661 1.4130 1.7299 2.0679 2.4250 2.8024 3.2017 3.6241 4.0706 4.5417 800 1.1792 1.2374 1.3637 1.6407 1.9379 2.2520 2.5841 2.9354 3.3072 3.7002 4.1150 900 1.1736 1.2228 1.3317 1.5758 1.8406 2.1212 2.4179 2.7318 3.0640 3.4153 3.7861 1000 1.1766 1.2181 1.3120 1.5281 1.7661 2.0195 2.2876 2.5715 2.8720 3.1899 3.5254 D2.2. Table 13. Prandtl number Pr of dry air Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 1 0.7571 0.7431 0.7335 0.7262 0.7202 0.7152 0.7110 0.7075 0.7045 0.7022 0.7004 5 0.7997 0.7646 0.7466 0.7351 0.7267 0.7202 0.7150 0.7107 0.7073 0.7045 0.7024 10 0.8711 0.7954 0.7641 0.7465 0.7349 0.7264 0.7199 0.7147 0.7105 0.7073 0.7048 20 1.1950 0.8761 0.8038 0.7707 0.7514 0.7386 0.7294 0.7223 0.7168 0.7125 0.7093 30 2.1452 1.0023 0.8517 0.7969 0.7684 0.7507 0.7386 0.7295 0.7227 0.7174 0.7134 40 1.9336 1.2234 0.9105 0.8256 0.7858 0.7627 0.7476 0.7365 0.7282 0.7220 0.7172 50 1.8149 1.6476 0.9818 0.8569 0.8038 0.7747 0.7565 0.7431 0.7334 0.7262 0.7208 60 1.7366 2.2770 1.0650 0.8903 0.8223 0.7866 0.7651 0.7495 0.7384 0.7302 0.7241 70 1.6802 2.3312 1.1555 0.9250 0.8409 0.7985 0.7736 0.7556 0.7431 0.7339 0.7271 80 1.6374 2.0609 1.2436 0.9596 0.8593 0.8100 0.7818 0.7615 0.7475 0.7374 0.7300 90 1.6036 1.8552 1.3164 0.9926 0.8771 0.8212 0.7898 0.7671 0.7517 0.7407 0.7326 100 1.5762 1.7198 1.3629 1.0224 0.8939 0.8319 0.7974 0.7725 0.7557 0.7438 0.7351 150 1.4931 1.4415 1.3272 1.1025 0.9535 0.8732 0.8283 0.7944 0.7718 0.7561 0.7447 200 1.4542 1.3453 1.2464 1.1026 0.9759 0.8942 0.8461 0.8077 0.7817 0.7636 0.7505 250 1.4358 1.2958 1.1968 1.0859 0.9805 0.9032 0.8546 0.8144 0.7867 0.7672 0.7530 300 1.4289 1.2668 1.1649 1.0693 0.9790 0.9072 0.8590 0.8179 0.7890 0.7684 0.7536 350 1.4295 1.2494 1.1432 1.0551 0.9752 0.9089 0.8616 0.8203 0.7904 0.7688 0.7532 400 1.4352 1.2393 1.1282 1.0435 0.9705 0.9091 0.8633 0.8224 0.7917 0.7692 0.7527 450 1.4453 1.2344 1.1179 1.0343 0.9656 0.9082 0.8642 0.8241 0.7932 0.7698 0.7525 500 1.4572 1.2333 1.1112 1.0272 0.9609 0.9066 0.8643 0.8255 0.7947 0.7708 0.7527 600 1.4873 1.2394 1.1056 1.0184 0.9537 0.9027 0.8630 0.8269 0.7971 0.7731 0.7541 700 1.5237 1.2533 1.1076 1.0153 0.9495 0.8994 0.8608 0.8268 0.7985 0.7750 0.7559 800 1.5644 1.2714 1.1148 1.0168 0.9484 0.8975 0.8590 0.8261 0.7989 0.7762 0.7574 900 1.6083 1.2933 1.1263 1.0217 0.9501 0.8976 0.8582 0.8255 0.7988 0.7767 0.7583 1000 1.6549 1.3180 1.1397 1.0294 0.9541 0.8994 0.8586 0.8255 0.7989 0.7770 0.7589 Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 1 0.6992 0.6984 0.6981 0.7016 0.7081 0.7154 0.7224 0.7284 0.7333 0.7370 0.7396 5 0.7009 0.6999 0.6993 0.7024 0.7086 0.7158 0.7227 0.7286 0.7335 0.7371 0.7398 10 0.7029 0.7017 0.7007 0.7033 0.7093 0.7163 0.7231 0.7289 0.7337 0.7373 0.7399 20 0.7068 0.7051 0.7034 0.7051 0.7105 0.7172 0.7238 0.7295 0.7341 0.7377 0.7403 187 188 D2 Properties of Selected Important Pure Substances D2.2. Table 13. (continued) Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 30 0.7104 0.7082 0.7058 0.7067 0.7116 0.7181 0.7245 0.7300 0.7346 0.7380 0.7406 40 0.7137 0.7110 0.7080 0.7081 0.7127 0.7189 0.7251 0.7305 0.7350 0.7384 0.7408 50 0.7167 0.7136 0.7101 0.7095 0.7136 0.7196 0.7256 0.7310 0.7353 0.7387 0.7411 60 0.7195 0.7161 0.7119 0.7107 0.7145 0.7202 0.7261 0.7314 0.7357 0.7390 0.7413 70 0.7220 0.7183 0.7136 0.7118 0.7153 0.7208 0.7266 0.7317 0.7360 0.7392 0.7415 80 0.7244 0.7203 0.7151 0.7128 0.7160 0.7214 0.7270 0.7321 0.7362 0.7394 0.7417 90 0.7266 0.7221 0.7165 0.7137 0.7167 0.7219 0.7274 0.7324 0.7365 0.7397 0.7419 100 0.7286 0.7238 0.7178 0.7145 0.7172 0.7223 0.7277 0.7327 0.7367 0.7399 0.7421 150 0.7364 0.7302 0.7224 0.7173 0.7192 0.7238 0.7289 0.7337 0.7376 0.7406 0.7427 200 0.7409 0.7338 0.7247 0.7185 0.7200 0.7243 0.7294 0.7340 0.7379 0.7409 0.7430 250 0.7427 0.7350 0.7253 0.7185 0.7198 0.7241 0.7292 0.7339 0.7378 0.7408 0.7429 300 0.7427 0.7346 0.7245 0.7175 0.7188 0.7234 0.7286 0.7334 0.7374 0.7405 0.7427 350 0.7417 0.7333 0.7228 0.7158 0.7173 0.7221 0.7275 0.7325 0.7367 0.7399 0.7422 400 0.7406 0.7317 0.7207 0.7136 0.7154 0.7204 0.7261 0.7314 0.7357 0.7391 0.7415 450 0.7396 0.7302 0.7186 0.7111 0.7132 0.7185 0.7245 0.7300 0.7346 0.7381 0.7407 500 0.7391 0.7291 0.7166 0.7086 0.7107 0.7164 0.7227 0.7284 0.7332 0.7370 0.7397 600 0.7394 0.7282 0.7137 0.7038 0.7057 0.7117 0.7186 0.7249 0.7302 0.7343 0.7375 700 0.7406 0.7285 0.7122 0.6999 0.7010 0.7070 0.7142 0.7210 0.7268 0.7313 0.7348 800 0.7419 0.7295 0.7119 0.6972 0.6969 0.7026 0.7099 0.7170 0.7231 0.7281 0.7320 900 0.7431 0.7305 0.7123 0.6954 0.6937 0.6986 0.7058 0.7130 0.7195 0.7248 0.7290 1000 0.7438 0.7314 0.7128 0.6944 0.6912 0.6953 0.7021 0.7093 0.7159 0.7214 0.7259 D2.2. Table 14. Isobaric expansion coefficient b of dry air in 103/K Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 1 8.3947 6.8834 5.8490 5.0909 4.5094 4.0485 3.6738 3.3630 3.1010 2.8770 2.6833 5 9.6919 7.4647 6.1576 5.2720 4.6231 4.1233 3.7248 3.3987 3.1264 2.8954 2.6968 10 11.9870 8.3180 6.5768 5.5083 4.7678 4.2171 3.7880 3.4426 3.1576 2.9179 2.7132 20 23.4830 10.6350 7.5455 6.0152 5.0658 4.4052 3.9127 3.5281 3.2177 2.9608 2.7442 30 20.3790 14.3470 8.7203 6.5682 5.3735 4.5933 4.0346 3.6103 3.2747 3.0012 2.7732 40 15.9500 20.8880 10.1310 7.1628 5.6876 4.7795 4.1530 3.6891 3.3288 3.0391 2.8001 50 13.4970 33.1700 11.7720 7.7866 6.0026 4.9616 4.2669 3.7640 3.3797 3.0745 2.8250 60 11.8890 48.2830 13.5650 8.4182 6.3114 5.1369 4.3751 3.8345 3.4272 3.1073 2.8479 70 10.7310 41.2590 15.3220 9.0276 6.6055 5.3023 4.4766 3.9002 3.4713 3.1374 2.8688 80 9.8472 29.2540 16.7560 9.5802 6.8759 5.4548 4.5701 3.9605 3.5115 3.1648 2.8876 90 9.1449 22.0780 17.5530 10.0420 7.1142 5.5915 4.6544 4.0150 3.5479 3.1895 2.9045 100 8.5696 17.8280 17.5460 10.3870 7.3134 5.7100 4.7286 4.0634 3.5801 3.2113 2.9193 150 6.7302 9.8964 12.3270 10.1820 7.6376 5.9945 4.9334 4.2052 3.6771 3.2768 2.9626 200 5.7054 7.3535 8.7385 8.4420 7.0936 5.8302 4.8844 4.1920 3.6736 3.2742 2.9581 250 5.0330 6.0436 6.8646 6.9330 6.2757 5.4248 4.6713 4.0684 3.5942 3.2182 2.9150 300 4.5500 5.2236 5.7483 5.8604 5.5196 4.9577 4.3848 3.8842 3.4683 3.1268 2.8451 350 4.1821 4.6530 5.0060 5.0985 4.9004 4.5179 4.0845 3.6764 3.3194 3.0158 2.7590 400 3.8903 4.2285 4.4733 4.5382 4.4066 4.1332 3.8002 3.4676 3.1635 2.8962 2.6647 Properties of Dry Air D2.2 D2.2. Table 14. (continued) Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 450 3.6517 3.8981 4.0698 4.1105 4.0115 3.8050 3.5429 3.2694 3.0101 2.7755 2.5678 500 3.4520 3.6320 3.7521 3.7733 3.6911 3.5269 3.3147 3.0868 2.8643 2.6581 2.4719 600 3.1346 3.2271 3.2805 3.2740 3.2060 3.0882 2.9375 2.7713 2.6030 2.4414 2.2908 700 2.8914 2.9305 2.9443 2.9200 2.8568 2.7617 2.6447 2.5156 2.3830 2.2529 2.1290 800 2.6976 2.7021 2.6904 2.6543 2.5930 2.5106 2.4135 2.3078 2.1990 2.0912 1.9873 900 2.5385 2.5195 2.4908 2.4466 2.3860 2.3115 2.2271 2.1370 2.0446 1.9529 1.8638 1000 2.4048 2.3694 2.3289 2.2791 2.2188 2.1495 2.0739 1.9945 1.9139 1.8340 1.7561 Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 1 2.5142 2.3651 2.1145 1.7450 1.4855 1.2932 1.1451 1.0274 0.9317 0.8522 0.7853 5 2.5241 2.3724 2.1185 1.7458 1.4852 1.2926 1.1443 1.0266 0.9309 0.8515 0.7846 10 2.5361 2.3813 2.1232 1.7468 1.4849 1.2917 1.1433 1.0256 0.9299 0.8506 0.7838 20 2.5587 2.3978 2.1318 1.7484 1.4839 1.2899 1.1412 1.0235 0.9280 0.8488 0.7822 30 2.5796 2.4129 2.1395 1.7495 1.4828 1.2880 1.1391 1.0214 0.9260 0.8470 0.7805 40 2.5988 2.4266 2.1463 1.7502 1.4814 1.2859 1.1369 1.0193 0.9240 0.8452 0.7789 50 2.6165 2.4391 2.1523 1.7505 1.4798 1.2838 1.1346 1.0171 0.9220 0.8433 0.7772 60 2.6325 2.4503 2.1575 1.7505 1.4781 1.2815 1.1323 1.0149 0.9199 0.8415 0.7755 70 2.6470 2.4603 2.1619 1.7501 1.4762 1.2792 1.1299 1.0127 0.9179 0.8396 0.7738 80 2.6600 2.4691 2.1655 1.7494 1.4741 1.2767 1.1275 1.0104 0.9158 0.8377 0.7721 90 2.6715 2.4768 2.1685 1.7484 1.4719 1.2742 1.1251 1.0081 0.9137 0.8359 0.7704 100 2.6814 2.4833 2.1708 1.7471 1.4696 1.2717 1.1226 1.0058 0.9117 0.8340 0.7687 150 2.7089 2.4994 2.1724 1.7368 1.4561 1.2581 1.1098 0.9941 0.9011 0.8245 0.7602 200 2.7018 2.4899 2.1593 1.7208 1.4402 1.2433 1.0965 0.9822 0.8905 0.8150 0.7518 250 2.6664 2.4592 2.1339 1.7001 1.4223 1.2277 1.0828 0.9702 0.8799 0.8056 0.7434 300 2.6104 2.4127 2.0988 1.6756 1.4029 1.2114 1.0689 0.9581 0.8693 0.7963 0.7351 350 2.5414 2.3556 2.0569 1.6482 1.3822 1.1947 1.0548 0.9461 0.8589 0.7871 0.7270 400 2.4650 2.2922 2.0106 1.6187 1.3606 1.1776 1.0407 0.9341 0.8485 0.7780 0.7189 450 2.3856 2.2259 1.9618 1.5880 1.3384 1.1604 1.0266 0.9222 0.8383 0.7691 0.7110 500 2.3060 2.1587 1.9120 1.5565 1.3160 1.1430 1.0125 0.9104 0.8282 0.7603 0.7033 600 2.1530 2.0280 1.8132 1.4934 1.2709 1.1085 0.9847 0.8873 0.8084 0.7432 0.6882 700 2.0134 1.9067 1.7193 1.4319 1.2268 1.0747 0.9576 0.8648 0.7893 0.7267 0.6738 800 1.8888 1.7968 1.6324 1.3736 1.1845 1.0421 0.9315 0.8432 0.7710 0.7108 0.6598 900 1.7787 1.6983 1.5529 1.3188 1.1442 1.0109 0.9064 0.8224 0.7533 0.6955 0.6465 1000 1.6814 1.6104 1.4806 1.2679 1.1063 0.9813 0.8825 0.8025 0.7364 0.6809 0.6337 D2.2. Table 15. Isentropic speed of sound ws in dry air in m/s Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 1 221.3 243.4 263.5 282.1 299.5 315.9 331.5 346.3 360.5 374.0 387.0 5 215.8 240.4 261.9 281.3 299.2 316.0 331.8 346.7 361.0 374.7 387.8 10 208.3 236.7 259.9 280.3 298.9 316.1 332.2 347.4 361.8 375.6 388.8 20 188.9 229.0 256.3 278.8 298.6 316.6 333.2 348.8 363.5 377.5 390.8 189 190 D2 Properties of Selected Important Pure Substances D2.2. Table 15. (continued) Temperature in C Pressure in bar 150 125 100 75 50 25 0 25 50 75 100 30 389.0 221.4 253.2 277.7 298.7 317.4 334.5 350.5 365.4 379.6 393.0 40 427.5 214.7 250.9 277.3 299.3 318.6 336.1 352.3 367.5 381.8 395.3 50 458.1 211.3 249.9 277.6 300.3 320.2 338.0 354.5 369.8 384.2 397.8 60 484.1 219.0 250.7 278.8 302.0 322.1 340.2 356.8 372.2 386.7 400.4 70 506.9 248.8 253.9 281.0 304.2 324.5 342.7 359.4 374.8 389.3 403.0 80 527.5 287.9 260.0 284.4 307.1 327.3 345.4 362.1 377.6 392.1 405.8 90 546.2 324.1 269.3 289.0 310.6 330.5 348.5 365.1 380.6 395.1 408.7 100 563.5 355.6 281.8 294.9 314.9 334.1 351.9 368.3 383.7 398.1 411.7 150 635.2 468.7 366.3 340.3 345.5 358.4 372.9 387.5 401.6 415.2 428.2 200 691.6 546.1 445.8 399.0 387.3 390.8 399.9 411.1 423.0 435.0 446.8 250 738.8 607.0 511.5 456.5 433.1 427.5 430.6 437.8 446.9 456.9 467.2 300 779.8 658.0 567.0 509.0 478.3 465.7 463.2 466.4 472.5 480.2 488.7 350 816.2 702.2 615.2 556.3 521.3 503.3 496.2 495.6 498.8 504.3 511.0 400 849.2 741.6 658.0 599.1 561.4 539.7 528.8 525.0 525.5 528.8 533.7 450 879.4 777.1 696.6 638.2 598.9 574.4 560.5 553.9 552.0 553.2 556.5 500 907.3 809.7 731.9 674.1 633.8 607.3 591.1 582.1 578.1 577.5 579.3 600 957.9 867.8 794.7 738.6 697.4 668.4 648.7 636.1 628.7 625.0 623.9 700 1002.9 918.9 849.8 795.4 754.1 723.7 701.9 686.7 676.7 670.5 667.1 800 1043.8 964.7 899.0 846.3 805.3 774.1 750.9 734.0 722.0 713.8 708.5 900 1081.3 1006.4 943.7 892.7 852.2 820.6 796.4 778.2 764.7 754.9 748.1 1000 1116.2 1044.9 984.8 935.3 895.4 863.7 838.9 819.7 805.0 794.0 785.9 Temperature in C Pressure in bar 125 150 200 300 400 500 600 700 800 900 1000 1 399.6 411.7 434.7 476.6 514.3 549.0 581.3 611.7 640.6 668.3 694.8 5 400.4 412.5 435.6 477.5 515.2 549.9 582.1 612.5 641.4 669.0 695.6 10 401.4 413.6 436.7 478.7 516.4 551.0 583.2 613.6 642.4 670.0 696.5 20 403.6 415.8 439.0 481.1 518.7 553.3 585.4 615.7 644.5 672.0 698.4 30 405.9 418.2 441.4 483.5 521.1 555.6 587.6 617.8 646.5 674.0 700.3 40 408.3 420.6 443.9 486.0 523.5 557.9 589.9 620.0 648.6 676.0 702.2 50 410.8 423.2 446.5 488.5 526.0 560.2 592.1 622.1 650.7 677.9 704.1 60 413.4 425.8 449.1 491.0 528.4 562.6 594.4 624.3 652.8 679.9 706.1 70 416.1 428.5 451.8 493.6 530.9 565.0 596.7 626.5 654.8 682.0 708.0 80 418.8 431.2 454.5 496.3 533.4 567.4 598.9 628.7 656.9 684.0 709.9 90 421.7 434.1 457.3 498.9 536.0 569.8 601.2 630.9 659.0 686.0 711.9 100 424.7 437.0 460.1 501.6 538.5 572.2 603.6 633.1 661.2 688.0 713.8 150 440.6 452.5 475.0 515.4 551.5 584.5 615.2 644.2 671.8 698.2 723.6 200 458.3 469.5 490.9 529.8 564.8 597.0 627.0 655.4 682.5 708.5 733.5 250 477.5 487.7 507.6 544.6 578.4 609.7 639.0 666.7 693.3 718.8 743.4 300 497.7 506.8 525.0 559.8 592.2 622.4 651.0 678.1 704.1 729.1 753.3 350 518.5 526.4 542.8 575.3 606.2 635.3 663.0 689.5 714.9 739.5 763.2 400 539.8 546.5 561.0 590.9 620.2 648.2 675.1 700.9 725.7 749.8 773.1 450 561.2 566.7 579.3 606.7 634.3 661.2 687.2 712.3 736.6 760.1 783.0 500 582.6 586.9 597.7 622.5 648.5 674.2 699.3 723.6 747.3 770.4 792.9 Properties of Dry Air D2.2 D2.2. Table 15. (continued) Temperature in C Pressure in bar 3 1. 125 150 200 300 400 500 600 700 800 900 1000 600 624.8 627.1 634.3 654.2 676.8 700.1 723.3 746.3 768.8 790.9 812.5 700 665.9 666.2 670.3 685.5 704.9 725.8 747.2 768.7 790.1 811.2 832.0 800 705.5 704.2 705.4 716.3 732.6 751.2 770.9 791.0 811.2 831.3 851.3 900 743.6 740.9 739.5 746.4 759.8 776.3 794.2 812.9 832.0 851.2 870.3 1000 780.2 776.2 772.6 775.9 786.6 800.9 817.2 834.6 852.5 870.8 889.1 Bibliography Lemmon EW, Jacobsen RT, Penoncello SG, Friend DG (2000) Thermodynamic properties of air and mixtures of nitrogen, argon, and oxygen from 60 to 2000 K at pressures to 2000 MPa. J Phys Chem Ref Data 29(3):331–385 2. Lemmon EW, Jacobsen RT (2004) Viscosity and thermal conductivity equations for nitrogen, oxygen, argon, and air. Int J Thermophys 25 (1):21–69 191 192 D2 Properties of Selected Important Pure Substances D2.3 Properties of Nitrogen Roland Span1 . Rolf Krauss2 1 2 Ruhr-Universität Bochum, Bochum, Germany Universität Stuttgart, Stuttgart, Germany 1 Properties of Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 4 Triple Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 2 Characteristic Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . 192 5 Reference States of Enthalpy and Entropy . . . . . . . . . 192 3 Critical Point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 6 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 1 Properties of Nitrogen Tables with thermodynamic properties of nitrogen were calculated with the reference equation of state established by Span et al. [1], see also Span et al. [2]. The thermal conductivity and viscosity of nitrogen were calculated with the corresponding equations by Stephan and Krauss [3]. The densities required as input for the equations by Stephan and Krauss were calculated using the equation by Span et al. p Pressure in bar n Specific volume in m3/kg r Density in kg/m3 l Thermal conductivity in mW/(m K) # Temperature in C n Kinematic viscosity n in 107m2/s h Specific enthalpy in kJ/kg Dynamic viscosity in 106 Pa·s s Specific entropy in kJ/(kg K) a Thermal diffusivity in 107 m2/s Z Compression factor Z = p/(rRT ) b Isobaric expansion coefficient in 103/K b = n1·(∂n/∂T )p Pr Prandtl number Pr = Z cp/l cp Specific isobaric heat capacity in kJ/(kg K) ws Isentropic speed of sound in m/s cv Specific isochoric heat capacity in kJ/(kg K) 2 Characteristic Quantities e = 28.01348 g/mol, specific gas constant Molecular mass M R = 296.8039 J/(kg K) 3 Critical Point [1] pc = 33.958 bar, Tc = 126.192 K (Wc = 146.958 C), rc = 313.3 kg/m3 4 Triple Point [1] Tt = 63.151 K (#t = 209.999 C) 5 Reference States of Enthalpy and Entropy [1] h = 309.494 kJ/kg, s = 6.8360 kJ/(kg K) at T = 298.15 K (# = 25 C), p = 1.01325 bar corresponding to h = 0 kJ/kg, s = 0 kJ/(kg K) for a perfect crystal at T = 0 K Properties of Nitrogen D2.3 D2.3. Table 1. Properties of nitrogen at p = 1 bar q C r kg/m3 h kJ/kg s cp cn kJ/(kg K) kJ/(kg K) kJ/(kg K) b 103/K ws m/s l h n a mW/(m K) 106 Pa·s 107 m2/s 107 m2/s Pr – 210 867.38 150.7 2.425 2.000 1.177 4.727 995.8 176.1 215.9 2.489 1.015 200 824.94 130.6 2.721 2.024 1.110 5.339 894.3 155.7 159.1 1.929 0.9327 2.068 83.64 5.494 1.102 0.7627 13.32 182.3 94.54 2.451 190 4.1949 180 3.7067 5.617 1.080 0.7546 11.53 194.1 6.201 16.73 22.74 0.7355 170 3.3259 105.3 5.727 1.068 0.7503 10.22 205.0 10.13 6.912 20.78 28.52 0.7288 160 3.0187 115.9 5.825 1.061 0.7478 9.200 215.3 11.13 7.603 25.19 34.75 0.7248 150 2.7651 126.5 5.915 1.056 0.7462 8.380 225.0 12.10 8.276 29.93 41.44 0.7222 140 2.5517 137.0 5.997 1.052 0.7452 7.703 234.2 13.04 8.931 35.00 48.57 0.7205 130 2.3695 147.5 6.073 1.050 0.7445 7.132 243.1 13.96 9.568 40.38 56.13 0.7193 120 2.2119 158.0 6.144 1.048 0.7440 6.643 251.7 14.86 10.19 46.06 64.11 0.7185 110 2.0742 168.5 6.210 1.047 0.7437 6.218 259.9 15.74 10.79 52.04 72.49 0.7179 100 1.9529 179.0 6.273 1.045 0.7434 5.847 267.9 16.59 11.38 58.30 81.27 0.7174 90 1.8451 189.4 6.331 1.045 0.7432 5.518 275.6 17.43 11.96 64.83 90.42 0.7170 80 1.7486 199.9 6.387 1.044 0.7431 5.224 283.1 18.24 12.53 71.63 99.95 0.7167 70 1.6619 210.3 6.439 1.043 0.7430 4.961 290.4 19.04 13.08 78.70 109.8 0.7165 60 1.5833 220.7 6.490 1.043 0.7429 4.724 297.5 19.83 13.62 86.01 120.1 0.7163 50 1.5119 231.1 6.537 1.042 0.7429 4.508 304.4 20.59 14.15 93.58 130.7 0.7162 40 1.4467 241.6 6.583 1.042 0.7428 4.312 311.2 21.35 14.67 101.4 141.6 0.7161 30 1.3869 252.0 6.627 1.042 0.7428 4.132 317.9 22.09 15.18 109.4 152.8 0.7160 20 1.3319 262.4 6.669 1.042 0.7428 3.967 324.4 22.81 15.68 117.7 164.4 0.7159 10 1.2811 272.8 6.709 1.042 0.7428 3.814 330.7 23.53 16.17 126.2 176.3 0.7158 0 1.2340 283.2 6.748 1.041 0.7429 3.673 337.0 24.23 16.65 134.9 188.5 0.7158 10 1.1903 293.7 6.785 1.041 0.7430 3.542 343.1 24.92 17.13 143.9 201.0 0.7158 20 1.1496 304.1 6.822 1.041 0.7431 3.420 349.1 25.60 17.60 153.1 213.8 0.7157 30 1.1116 314.5 6.857 1.041 0.7432 3.307 355.0 26.27 18.06 162.4 226.9 0.7157 40 1.0760 324.9 6.890 1.041 0.7434 3.200 360.8 26.93 18.51 172.0 240.3 0.7157 50 1.0426 335.3 6.923 1.042 0.7436 3.101 366.5 27.59 18.96 181.8 254.0 0.7158 60 1.0113 345.7 6.955 1.042 0.7439 3.007 372.1 28.23 19.40 191.8 268.0 0.7158 70 0.98177 356.1 6.986 1.042 0.7443 2.919 377.7 28.87 19.83 202.0 282.2 0.7158 80 0.95392 366.6 7.016 1.042 0.7447 2.836 383.1 29.50 20.26 212.4 296.7 0.7159 90 0.92762 377.0 7.045 1.043 0.7451 2.757 388.5 30.13 20.69 223.0 311.5 0.7160 100 0.90273 387.4 7.073 1.043 0.7457 2.683 393.7 30.75 21.10 233.8 326.5 0.7160 110 0.87914 397.9 7.101 1.044 0.7463 2.613 398.9 31.36 21.52 244.8 341.8 0.7161 120 0.85676 408.3 7.128 1.044 0.7469 2.546 404.0 31.97 21.93 255.9 357.3 0.7163 130 0.83549 418.7 7.154 1.045 0.7477 2.483 409.1 32.58 22.33 267.3 373.1 0.7164 140 0.81525 429.2 7.179 1.046 0.7485 2.422 414.1 33.18 22.73 278.8 389.1 0.7165 150 0.79597 439.7 7.204 1.047 0.7495 2.365 419.0 33.78 23.13 290.5 405.4 0.7167 160 0.77758 450.1 7.229 1.048 0.7505 2.310 423.8 34.37 23.52 302.4 421.9 0.7169 170 0.76003 460.6 7.253 1.049 0.7515 2.258 428.6 34.96 23.90 314.5 438.6 0.7171 180 0.74325 471.1 7.276 1.050 0.7527 2.208 433.3 35.55 24.29 326.8 455.6 0.7173 190 0.72719 481.6 7.299 1.051 0.7539 2.160 438.0 36.14 24.67 339.2 472.7 0.7175 200 0.71181 492.1 7.322 1.053 0.7553 2.114 442.6 36.72 25.04 351.8 490.2 0.7177 250 0.64376 545.0 7.428 1.060 0.7630 1.912 464.7 39.61 26.87 417.4 580.4 0.7191 300 0.58760 598.2 7.525 1.070 0.7725 1.745 485.5 42.47 28.62 487.1 675.8 0.7208 350 0.54045 651.9 7.615 1.080 0.7831 1.605 505.3 45.30 30.31 560.8 776.0 0.7227 400 0.50031 706.2 7.699 1.092 0.7947 1.485 524.1 48.12 31.94 638.4 881.0 0.7247 450 0.46572 761.1 7.777 1.104 0.8067 1.383 542.1 50.91 33.52 719.8 990.4 0.7267 8.061 9.108 5.470 13.04 17.44 0.7477 193 194 D2 Properties of Selected Important Pure Substances D2.3. Table 1. (continued) b 103/K ws m/s l h n a mW/(m K) 106 Pa·s 107 m2/s 107 m2/s Pr – 0.8189 1.293 559.4 53.68 35.06 804.8 1,104 0.7288 0.8309 1.215 576.1 56.42 36.56 893.5 1,223 0.7308 r kg/m3 h kJ/kg 500 0.43561 816.6 7.851 1.116 550 0.40915 872.7 7.922 1.128 600 0.38573 929.4 7.989 1.140 0.8427 1.145 592.2 59.13 38.02 1,345 0.7327 700 0.34610 1,044 8.113 1.162 0.8649 1.027 623.1 64.45 40.85 1,180 1,603 0.7363 800 0.31385 1,162 8.228 1.182 0.8850 0.9316 652.4 69.63 43.57 1,388 1,877 0.7394 900 0.28711 1,281 8.334 1.200 0.9028 0.8522 680.4 74.67 46.19 1,609 2,168 0.7422 1,000 0.26456 1,402 8.433 1.215 0.9184 0.7853 707.3 79.57 48.74 1,842 2,475 0.7445 q C s cp cn kJ/(kg K) kJ/(kg K) kJ/(kg K) 985.6 D2.3. Table 2. Properties of the saturated liquid q C p bar r0 kg/m3 h0 kJ/kg s0 cp0 cn0 b0 kJ/(kg K) kJ/(kg K) kJ/(kg K) 103/K ws0 m/s h0 l0 n0 a0 mW/(m K) 106 Pa·s 107 m2/s 107 m2/s Pr0 – 210 0.12517 867.23 150.7 2.426 2.000 1.176 4.733 995.3 176.1 215.6 2.486 1.015 2.450 208 0.17860 858.97 146.7 2.488 2.004 1.162 4.840 974.8 171.9 202.6 2.359 0.9989 2.361 206 0.24894 850.62 142.7 2.549 2.008 1.149 4.953 954.5 167.8 190.5 2.240 0.9827 2.279 204 0.33973 842.15 138.7 2.608 2.012 1.135 5.075 934.3 163.7 179.3 2.129 0.9662 2.203 202 0.45484 833.56 134.6 2.665 2.018 1.122 5.204 914.1 159.7 168.8 2.025 0.9495 2.133 200 0.59842 824.85 130.6 2.721 2.024 1.109 5.343 894.0 155.7 159.0 1.928 0.9324 2.068 198 0.77491 816.00 126.5 2.775 2.032 1.097 5.492 873.8 151.7 149.9 1.837 0.9150 2.008 196 0.98899 807.01 122.4 2.829 2.041 1.085 5.653 853.5 147.7 141.4 1.752 0.8972 1.952 194 1.2456 797.87 118.3 2.881 2.051 1.074 5.828 833.1 143.8 133.4 1.671 0.8789 1.902 192 1.5497 788.56 114.2 2.932 2.063 1.063 6.018 812.5 139.9 125.8 1.596 0.8602 1.855 190 1.9067 779.08 110.0 2.982 2.076 1.052 6.225 791.8 136.0 118.8 1.525 0.8409 1.813 188 2.3219 769.40 105.8 3.031 2.092 1.042 6.453 770.9 132.2 112.1 1.457 0.8211 1.775 186 2.8009 759.51 101.6 3.080 2.110 1.033 6.705 749.7 128.3 105.9 1.394 0.8006 1.741 184 3.3492 749.40 97.34 3.127 2.131 1.023 6.984 728.2 124.5 99.96 1.334 0.7795 1.711 182 3.9725 739.03 93.03 3.174 2.155 1.015 7.296 706.4 120.7 94.36 1.277 0.7576 1.685 180 4.6767 728.38 88.66 3.221 2.183 1.007 7.647 684.3 116.8 89.07 1.223 0.7349 1.664 178 5.4677 717.43 84.24 3.266 2.215 0.9990 8.044 661.8 113.0 84.05 1.172 0.7112 1.647 176 6.3514 706.13 79.74 3.312 2.253 0.9920 8.498 638.8 109.2 79.28 1.123 0.6866 1.635 174 7.3338 694.45 75.18 3.357 2.297 0.9857 9.022 615.4 105.4 74.74 1.076 0.6608 1.629 172 8.4212 682.33 70.52 3.402 2.349 0.9800 9.631 591.3 101.6 70.41 1.032 0.6338 1.628 170 9.6198 669.70 65.77 3.447 2.411 0.9751 10.35 566.7 97.72 66.28 0.9896 0.6053 1.635 168 10.936 656.50 60.90 3.492 2.485 0.9712 11.21 541.4 93.84 62.31 0.9492 0.5752 1.650 166 12.377 642.63 55.89 3.537 2.575 0.9684 12.26 515.2 89.91 58.50 0.9104 0.5433 1.676 164 13.949 627.97 50.73 3.582 2.687 0.9669 13.56 488.2 85.92 54.83 0.8731 0.5092 1.715 162 15.659 612.34 45.38 3.628 2.829 0.9671 15.21 460.2 81.86 51.27 0.8373 0.4726 1.772 160 17.516 595.55 39.80 3.675 3.013 0.9694 17.39 431.0 77.69 47.81 0.8027 0.4330 1.854 158 19.527 577.27 33.94 3.723 3.262 0.9747 20.37 400.3 73.39 44.41 0.7693 0.3897 1.974 156 21.702 557.07 27.70 3.774 3.617 0.9842 24.70 367.9 68.89 41.04 0.7368 0.3419 2.155 154 24.051 534.19 20.95 3.827 4.168 1.000 31.59 333.1 64.13 37.66 0.7049 0.2880 2.447 152 26.588 507.27 13.44 3.886 5.147 1.029 44.25 294.6 58.93 34.16 0.6734 0.2257 2.983 150 29.329 473.20 4.608 3.954 7.421 1.089 75.00 249.6 148 32.300 420.66 7.586 4.046 147 33.889 347.58 22.34 4.160 19.01 632.7 1.262 1.725 243.2 190.0 139.7 Properties of Nitrogen D2.3 D2.3. Table 3. Properties of the saturated vapor q C p bar r00 kg/m3 h00 kJ/kg s00 kJ/(kg K) cp00 kJ/(kg K) cn00 kJ/(kg K) b00 103/K ws00 m/s l00 mW/(m K) h00 106 Pa·s n00 107 m2/s a00 107 m2/s Pr – 210 0.12517 0.67416 64.78 5.838 1.058 0.7499 16.30 161.1 5.680 3.898 57.82 79.62 0.7263 208 0.17860 0.93502 66.68 5.764 1.064 0.7519 15.93 163.4 5.919 4.057 43.39 59.50 0.7292 206 0.24894 1.2688 68.53 5.695 1.070 0.7542 15.61 165.5 6.160 4.217 33.23 45.36 0.7327 204 0.33973 1.6884 70.34 5.630 1.078 0.7568 15.35 167.6 6.403 4.377 25.92 35.18 0.7368 202 0.45484 2.2074 72.10 5.571 1.087 0.7598 15.13 169.5 6.651 4.537 20.55 27.72 0.7415 200 0.59842 2.8403 73.80 5.515 1.097 0.7631 14.95 171.4 6.902 4.698 16.54 22.15 0.7468 198 0.77491 3.6025 75.44 5.463 1.109 0.7668 14.83 173.1 7.158 4.860 13.49 17.92 0.7529 196 0.98899 4.5102 77.00 5.414 1.122 0.7708 14.75 174.7 7.419 5.023 11.14 14.65 0.7599 194 1.2456 5.5807 78.49 5.368 1.138 0.7753 14.72 176.1 7.686 5.187 9.294 12.10 0.7678 192 1.5497 6.8322 79.90 5.324 1.155 0.7802 14.74 177.5 7.961 5.352 7.834 10.09 190 1.9067 8.2843 81.22 5.282 1.175 0.7856 14.81 178.7 8.243 5.520 6.663 188 2.3219 82.44 5.243 1.197 0.7914 14.94 179.8 8.534 5.690 5.714 7.156 0.7984 186 2.8009 11.875 83.56 5.204 1.223 0.7978 15.14 180.7 8.834 5.862 4.936 6.083 0.8116 184 3.3492 14.062 84.57 5.168 1.252 0.8047 15.39 181.5 9.146 6.038 4.294 5.195 0.8265 182 3.9725 16.544 85.47 5.133 1.285 0.8123 15.73 182.1 9.470 6.218 3.758 4.454 0.8437 180 4.6767 19.353 86.24 5.098 1.323 0.8205 16.14 182.7 9.808 6.401 3.308 3.831 0.8634 178 5.4677 22.523 86.87 5.065 1.366 0.8295 16.66 183.0 10.16 6.591 2.926 3.302 0.8862 176 6.3514 26.093 87.36 5.032 1.416 0.8393 17.28 183.2 10.53 6.786 2.601 2.850 0.9127 174 7.3338 30.107 87.68 5.000 1.475 0.8500 18.04 183.3 10.92 6.990 2.322 2.460 0.9438 172 8.4212 34.621 87.83 4.967 1.543 0.8617 18.97 183.2 11.34 7.202 2.080 2.121 0.9806 170 9.6198 39.696 87.79 4.935 1.625 0.8745 20.09 182.9 11.77 7.425 1.871 1.826 1.024 9.9578 8.468 0.7767 0.7869 168 10.936 45.412 87.53 4.903 1.722 0.8885 21.48 182.5 12.24 7.662 1.687 1.566 1.077 166 12.377 51.863 87.03 4.870 1.840 0.9038 23.19 181.9 12.75 7.915 1.526 1.336 1.142 164 13.949 59.174 86.26 4.837 1.987 0.9205 25.36 181.1 13.30 8.189 1.384 1.131 1.224 162 15.659 67.505 85.16 4.803 2.177 0.9398 28.17 180.2 13.90 8.489 1.257 0.9456 1.330 160 17.516 77.074 83.69 4.766 2.429 0.9630 31.93 179.1 14.56 8.822 1.145 0.7777 1.472 158 19.527 88.191 81.75 4.728 2.780 0.9920 37.14 177.6 15.31 9.201 1.043 0.6245 1.671 156 21.702 101.32 79.22 4.687 3.295 1.028 44.77 175.9 16.17 9.641 0.9516 0.4844 1.964 154 24.051 117.20 75.90 4.640 4.116 1.075 56.92 173.7 17.20 10.17 0.8680 0.3566 2.434 152 26.588 137.23 71.43 4.586 5.613 1.136 79.04 170.9 18.50 10.85 0.7908 0.2401 3.293 150 29.329 164.48 65.01 4.519 9.169 1.229 131.3 148 32.300 210.05 53.83 4.416 1.427 394.7 147 33.889 278.92 36.95 4.276 27.29 832.3 1.831 167.1 159.3 141.9 D2.3. Table 4. Density r of nitrogen in kg/m3 Temperature in C Pressure in bar 200 1 824.9 175 3.505 19.36 150 2.765 125 2.288 100 1.953 9.908 75 1.704 1.512 7.601 25 1.359 6.816 0 1.234 6.181 25 50 1.130 1.043 0.9676 5.213 4.836 5.656 75 5 825.8 14.47 11.73 10 827.0 702.2 30.90 24.24 20.19 17.39 15.30 13.69 12.39 11.32 10.43 20 829.2 707.7 74.04 52.15 41.97 35.55 31.01 27.57 24.87 22.67 20.84 19.30 30 831.3 712.8 479.8 85.18 65.53 54.50 47.09 41.64 37.42 34.03 31.24 28.90 40 833.4 717.6 527.6 125.6 91.03 74.22 63.50 55.85 50.02 45.39 41.61 38.45 50 835.5 722.2 552.0 176.6 94.66 80.21 70.17 62.65 56.73 51.93 47.94 118.6 8.597 50 9.665 195 196 D2 Properties of Selected Important Pure Substances D2.3. Table 4. (continued) Temperature in C Pressure in bar 200 60 837.5 726.5 569.6 239.7 148.1 115.7 70 839.5 730.6 583.6 306.5 179.2 137.3 114.3 80 841.5 734.6 595.3 362.1 211.3 159.2 131.4 113.4 100.4 175 150 125 100 75 50 97.16 25 0 25 50 75 84.57 75.27 68.04 62.20 57.37 99.00 87.87 79.29 72.40 66.72 90.47 82.52 76.00 92.56 85.19 90 843.4 738.3 605.6 403.3 243.3 181.1 148.6 127.8 112.9 101.6 100 845.3 742.0 614.6 434.2 274.1 203.0 165.7 142.0 125.2 112.5 102.5 150 854.2 758.3 649.6 522.1 393.3 302.3 246.5 210.3 184.7 165.5 150.4 138.2 200 862.4 772.3 675.1 569.7 464.7 377.7 315.0 270.8 238.6 214.1 194.8 179.1 250 870.1 784.7 695.4 603.0 512.3 432.9 370.1 322.4 286.2 257.9 235.2 216.7 300 877.3 795.8 712.6 628.8 547.7 475.0 414.4 365.9 327.5 296.8 271.8 251.1 350 884.1 806.0 727.5 650.0 575.8 508.5 450.6 402.7 363.5 331.3 304.7 282.4 400 890.6 815.3 740.8 668.1 599.1 536.1 481.0 434.1 394.9 362.0 334.4 310.9 450 896.7 824.1 752.8 684.0 619.1 559.7 507.0 461.4 422.5 389.4 361.1 336.9 500 902.5 832.2 763.7 698.2 636.7 580.2 529.7 485.4 447.1 414.0 385.4 360.7 600 913.5 847.1 783.2 722.8 666.4 614.6 567.7 525.9 489.0 456.5 427.9 402.6 700 923.6 860.6 800.3 743.7 691.2 642.9 598.9 559.3 523.8 492.1 463.8 438.6 800 933.1 872.8 815.6 762.0 712.5 666.9 625.3 587.6 553.4 522.6 494.9 469.9 900 942.0 884.1 829.4 778.4 731.3 688.0 648.3 612.1 579.2 549.3 522.1 497.5 1,000 950.3 894.6 842.0 793.2 748.1 706.6 668.6 633.8 602.0 572.9 546.4 522.1 94.29 Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1 0.9027 0.8460 0.7960 0.7118 0.5876 0.5003 0.4356 0.3857 0.3461 0.3139 0.2871 0.2646 5 4.510 4.225 3.975 3.554 2.933 2.497 2.175 1.926 1.728 1.567 1.434 1.321 10 9.010 8.439 7.936 7.094 5.854 1,000 4.984 4.340 3.844 3.450 3.129 2.863 2.639 9.927 8.646 7.660 6.876 6.238 5.709 5.262 20 17.98 16.83 15.82 14.13 11.66 30 26.89 25.16 23.64 21.11 17.41 14.83 12.92 11.45 10.28 40 35.75 33.43 31.40 28.03 23.11 19.69 17.15 15.20 13.66 12.39 11.35 10.46 50 44.55 41.64 39.10 34.89 28.76 24.50 21.36 18.93 17.01 15.44 14.14 13.04 60 53.28 49.78 46.73 41.68 34.36 29.28 25.53 22.64 20.34 18.47 16.92 15.61 70 61.94 57.85 54.29 48.42 39.91 34.01 29.66 26.31 23.65 21.48 19.68 18.16 80 70.52 65.84 61.78 55.08 45.41 38.70 33.76 29.96 26.93 24.47 22.42 20.69 90 79.02 73.75 69.20 61.68 50.85 43.35 37.83 33.58 30.19 27.44 25.15 23.21 100 87.43 81.58 76.53 68.22 56.24 47.96 41.86 37.17 33.43 30.39 27.86 25.72 99.85 82.42 70.40 61.54 54.72 49.29 44.86 41.17 38.04 91.84 80.43 71.63 64.61 58.87 54.09 50.03 98.56 87.92 79.41 72.45 66.63 61.69 93.72 85.60 78.81 73.04 98.36 90.66 84.10 9.326 8.537 7.871 150 128.0 119.4 112.0 200 166.0 154.9 145.4 129.7 107.3 250 201.2 188.0 176.6 157.9 131.0 112.3 300 233.6 218.7 205.7 184.3 153.4 131.9 116.0 103.6 350 263.4 247.0 232.8 209.1 174.7 150.6 132.7 118.7 107.6 400 290.7 273.3 257.9 232.4 194.9 168.5 148.7 133.3 120.9 110.7 102.2 450 315.9 297.5 281.4 254.2 214.1 185.6 164.2 147.4 133.9 122.8 113.4 105.4 500 339.0 320.0 303.2 274.7 232.3 201.9 179.0 161.0 146.5 134.4 124.3 115.6 600 380.3 360.4 342.7 312.3 266.1 232.6 207.1 186.9 170.4 156.8 145.2 135.3 700 416.0 395.7 377.4 345.7 296.8 260.8 233.1 211.0 193.0 177.9 165.1 154.1 800 447.3 426.8 408.2 375.7 324.8 286.9 257.4 233.7 214.2 197.9 184.0 172.0 900 475.0 454.5 435.8 402.8 350.5 311.0 280.0 255.0 234.3 216.9 202.0 189.1 1,000 499.9 479.5 460.7 427.5 374.2 333.5 301.3 275.1 253.4 235.0 219.2 205.5 94.86 D2.3 Properties of Nitrogen D2.3. Table 5. Compression factor Z of nitrogen Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 1 0.006 0.979 0.989 0.994 0.996 0.998 0.999 0.999 1.000 1.000 1.000 1.000 5 0.028 0.886 0.945 0.970 0.982 0.989 0.993 0.996 0.998 0.999 1.000 1.001 10 0.056 0.049 0.885 0.938 0.964 0.978 0.987 0.992 0.996 0.998 1.000 1.001 20 0.111 0.097 0.739 0.872 0.927 0.957 0.974 0.985 0.992 0.997 1.000 1.003 30 0.166 0.144 0.171 0.801 0.891 0.936 0.962 0.978 0.989 0.996 1.001 1.005 40 0.221 0.191 0.207 0.724 0.855 0.916 0.951 0.972 0.986 0.996 1.002 1.007 50 0.276 0.238 0.248 0.644 0.820 0.898 0.941 0.967 0.984 0.996 1.004 1.009 60 0.330 0.283 0.288 0.569 0.788 0.882 0.932 0.963 0.983 0.997 1.006 1.012 70 0.384 0.329 0.328 0.519 0.760 0.867 0.925 0.960 0.983 0.998 1.008 1.015 80 0.438 0.374 0.368 0.502 0.737 0.855 0.919 0.958 0.983 0.999 1.011 1.019 90 0.492 0.418 0.407 0.507 0.720 0.845 0.914 0.956 0.983 1.001 1.014 1.022 100 0.545 0.463 0.445 0.524 0.710 0.838 0.911 0.956 0.985 1.004 1.017 1.026 150 0.809 0.679 0.632 0.653 0.742 0.844 0.919 0.969 1.002 1.024 1.040 1.050 200 1.068 0.889 0.811 0.798 0.837 0.900 0.959 1.003 1.034 1.056 1.071 1.081 250 1.323 1.094 0.984 0.943 0.950 0.982 1.020 1.053 1.078 1.096 1.108 1.116 300 1.575 1.294 1.152 1.085 1.066 1.074 1.093 1.113 1.130 1.142 1.151 1.156 350 1.823 1.491 1.316 1.225 1.183 1.170 1.173 1.180 1.188 1.194 1.198 1.200 400 2.069 1.684 1.477 1.362 1.299 1.269 1.256 1.251 1.250 1.249 1.247 1.245 450 2.311 1.875 1.635 1.496 1.414 1.367 1.340 1.324 1.314 1.306 1.299 1.293 500 2.552 2.062 1.791 1.629 1.528 1.465 1.425 1.399 1.380 1.365 1.353 1.342 600 3.025 2.431 2.096 1.888 1.752 1.660 1.596 1.549 1.513 1.485 1.462 1.442 700 3.491 2.792 2.393 2.140 1.971 1.851 1.765 1.699 1.648 1.607 1.573 1.545 800 3.949 3.146 2.684 2.387 2.185 2.040 1.932 1.849 1.783 1.730 1.685 1.648 900 4.401 3.494 2.969 2.630 2.395 2.224 2.096 1.996 1.917 1.852 1.797 1.751 1,000 4.847 3.837 3.249 2.867 2.601 2.406 2.258 2.142 2.049 1.972 1.908 1.854 Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 5 1.001 1.001 1.002 1.002 1.002 1.002 1.002 1.002 1.002 1.002 1.002 1.001 10 1.002 1.003 1.003 1.004 1.004 1.004 1.004 1.004 1.004 1.003 1.003 1.003 20 1.005 1.006 1.007 1.008 1.009 1.008 1.008 1.008 1.007 1.007 1.006 1.006 30 1.007 1.009 1.010 1.012 1.013 1.013 1.012 1.011 1.011 1.010 1.009 1.009 40 1.010 1.012 1.014 1.016 1.017 1.017 1.016 1.015 1.014 1.013 1.012 1.012 50 1.013 1.016 1.018 1.021 1.022 1.021 1.020 1.019 1.018 1.017 1.015 1.014 60 1.017 1.020 1.022 1.025 1.026 1.026 1.024 1.023 1.021 1.020 1.019 1.017 70 1.020 1.024 1.027 1.030 1.031 1.030 1.028 1.027 1.025 1.023 1.022 1.020 80 1.024 1.028 1.031 1.034 1.036 1.035 1.033 1.030 1.028 1.026 1.025 1.023 90 1.028 1.033 1.036 1.039 1.040 1.039 1.037 1.034 1.032 1.030 1.028 1.026 100 1.033 1.037 1.040 1.044 1.045 1.044 1.041 1.038 1.036 1.033 1.031 1.029 150 1.058 1.063 1.066 1.070 1.070 1.066 1.062 1.058 1.054 1.050 1.046 1.043 200 1.088 1.092 1.095 1.098 1.096 1.090 1.084 1.077 1.072 1.067 1.062 1.058 250 1.122 1.125 1.127 1.128 1.122 1.114 1.105 1.097 1.090 1.083 1.078 1.072 300 1.160 1.161 1.161 1.159 1.150 1.138 1.127 1.117 1.108 1.100 1.093 1.087 350 1.200 1.199 1.197 1.192 1.178 1.163 1.150 1.137 1.127 1.117 1.109 1.101 400 1.242 1.239 1.235 1.226 1.207 1.188 1.172 1.158 1.145 1.134 1.124 1.116 197 198 D2 Properties of Selected Important Pure Substances D2.3. Table 5. (continued) Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 450 1.286 1.280 1.273 1.260 1.236 1.214 1.195 1.178 1.163 1.151 1.140 1.130 500 1.332 1.322 1.313 1.296 1.265 1.239 1.217 1.198 1.182 1.168 1.156 1.145 600 1.424 1.409 1.394 1.368 1.326 1.291 1.263 1.239 1.219 1.202 1.187 1.174 700 1.519 1.497 1.477 1.442 1.386 1.343 1.309 1.280 1.256 1.235 1.218 1.202 800 1.615 1.586 1.551 1.516 1.448 1.396 1.355 1.321 1.293 1.269 1.249 1.231 900 1.711 1.676 1.644 1.591 1.509 1.448 1.400 1.362 1.330 1.303 1.280 1.260 1,000 1.806 1.765 1.728 1.666 1.571 1.501 1.446 1.403 1.367 1.336 1.310 1.288 D2.3. Table 6. Specific enthalpy h of nitrogen in kJ/kg Temperature in C Pressure in bar 200 175 1 130.6 99.92 150 126.5 125 100 75 50 25 0 25 50 75 152.8 179.0 205.1 231.1 257.2 283.2 309.3 335.3 361.4 5 130.3 91.95 121.7 149.4 176.4 203.1 229.5 255.9 282.2 308.4 334.6 360.7 10 129.9 77.40 115.0 145.0 173.2 200.6 227.5 254.3 280.8 307.3 333.6 360.0 20 129.1 77.15 97.97 135.4 166.4 195.5 223.5 251.0 278.2 305.1 331.8 358.5 30 128.4 76.84 5.654 124.5 159.4 190.3 219.6 247.9 275.6 303.0 330.1 357.0 40 127.6 76.48 12.73 112.0 152.1 185.1 215.6 244.7 273.1 300.9 328.4 355.6 50 126.9 76.08 15.80 97.49 144.6 179.9 211.7 241.6 270.6 298.9 326.7 354.3 60 126.1 75.64 17.67 81.40 136.8 174.8 207.8 238.6 268.2 296.9 325.1 352.9 70 125.3 75.18 18.92 66.46 129.2 169.7 204.0 235.7 265.8 295.0 323.6 351.7 80 124.6 74.68 19.78 55.50 121.7 164.7 200.4 232.9 263.6 293.2 322.1 350.5 90 123.8 74.17 20.36 48.20 114.7 159.9 196.8 230.1 261.4 291.4 320.6 349.3 100 123.0 73.63 20.75 43.25 108.3 155.3 193.4 227.5 259.3 289.7 319.3 348.2 150 119.0 70.67 20.92 32.52 87.93 137.2 179.1 216.0 250.1 282.3 313.3 343.3 200 115.0 67.38 19.49 29.74 79.60 126.8 169.3 207.8 243.2 276.7 308.7 339.7 250 110.8 63.88 17.23 29.67 76.44 121.5 163.5 202.3 238.5 272.8 305.5 337.2 300 106.7 60.22 14.47 30.92 75.77 119.2 160.4 199.1 235.6 270.3 303.6 335.7 350 102.5 56.44 11.37 32.97 76.49 118.7 159.2 197.6 234.1 269.0 302.6 335.1 400 98.30 52.56 8.032 35.52 78.10 119.4 159.2 197.3 233.8 268.8 302.5 335.2 450 94.06 48.61 4.515 38.44 80.31 121.0 160.2 198.0 234.3 269.3 303.1 336.0 500 89.80 44.61 0.8618 41.62 82.93 123.0 161.8 199.3 235.4 270.4 304.3 337.3 600 81.23 36.45 6.745 48.53 89.05 128.3 166.5 203.4 239.3 274.1 308.0 341.0 700 72.61 28.16 14.63 55.94 95.92 134.7 172.3 208.9 244.5 279.1 313.0 346.1 800 63.96 19.78 22.71 63.68 103.3 141.7 179.0 215.3 250.6 285.1 318.9 352.0 900 55.29 11.33 30.93 71.64 111.0 149.1 186.1 222.2 257.4 291.8 325.5 358.6 1,000 46.61 39.24 79.76 118.9 156.8 193.7 229.6 264.7 299.0 332.6 365.7 2.841 Temperature in C Pressure in bar 100 125 150 200 300 400 500 1 387.4 413.5 439.7 492.1 598.2 706.2 816.6 600 700 800 900 1,000 929.4 1,044 1,162 1,281 1,402 5 386.9 413.1 439.3 491.9 598.1 706.3 816.8 929.6 1,045 1,162 1,281 1,402 10 386.3 412.6 438.9 491.7 598.1 706.4 817.0 929.9 1,045 1,162 1,281 1,402 20 385.0 411.6 438.1 491.1 598.0 706.6 817.4 930.4 1,046 1,163 1,282 1,403 30 383.8 410.6 437.3 490.6 597.9 706.8 817.8 931.0 1,046 1,164 1,283 1,404 D2.3 Properties of Nitrogen D2.3. Table 6. (continued) Temperature in C Pressure in bar 100 125 150 200 300 400 500 40 382.7 409.6 436.5 490.2 597.9 707.0 818.2 50 381.6 408.7 435.8 489.7 597.9 707.3 818.6 60 380.5 407.9 435.1 489.3 597.9 707.5 70 379.5 407.0 434.4 488.9 597.9 80 378.5 406.2 433.8 488.6 597.9 90 377.5 405.5 433.2 488.3 100 376.6 404.8 432.6 150 372.8 401.7 430.3 200 369.9 399.6 250 368.0 300 367.0 350 400 600 700 800 900 1,000 931.6 1,047 1,165 1,284 1,405 932.1 1,048 1,165 1,285 1,406 819.1 932.7 1,048 1,166 1,286 1,407 707.8 819.5 933.3 1,049 1,167 1,287 1,408 708.1 820.0 933.9 1,050 1,168 1,287 1,409 597.9 708.4 820.5 934.5 1,051 1,169 1,288 1,410 488.0 598.0 708.7 821.0 935.1 1,051 1,169 1,289 1,410 486.8 598.5 710.4 823.5 938.3 1,055 1,173 1,293 1,415 428.8 486.3 599.5 712.4 826.2 941.6 1,059 1,178 1,298 1,420 398.2 427.9 486.3 600.8 714.6 829.1 945.0 1,063 1,182 1,302 1,424 397.6 427.7 486.8 602.4 717.0 832.2 948.6 1,066 1,186 1,307 1,429 366.8 397.7 428.1 487.8 604.3 719.7 835.4 952.2 1,071 1,190 1,311 1,434 367.1 398.4 429.0 489.1 606.5 722.5 838.7 956.0 1,075 1,195 1,316 1,439 450 368.1 399.5 430.4 490.9 608.9 725.5 842.2 959.8 1,079 1,199 1,321 1,443 500 369.5 401.0 432.1 492.9 611.6 728.7 845.8 963.8 1,083 1,204 1,325 1,448 600 373.4 405.2 436.5 497.8 617.4 735.4 853.2 971.9 1,092 1,213 1,335 1,458 700 378.5 410.4 441.8 503.5 623.9 742.6 861.0 980.2 1,100 1,222 1,344 1,468 800 384.5 416.5 448.0 509.9 630.9 750.1 869.1 988.7 1,109 1,231 1,354 1,478 900 391.1 423.1 454.7 516.8 638.3 758.0 877.4 997.5 1,118 1,240 1,364 1,488 1,000 398.2 430.2 461.9 524.1 646.0 766.1 886.0 1,128 1,250 1,373 1,498 1,006 D2.3. Table 7. Specific entropy s of nitrogen in kJ/(kg K) Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 1 2.721 5.674 5.915 6.109 6.273 6.413 6.537 6.648 6.748 6.839 6.923 7.001 5 2.718 5.141 5.411 5.616 5.785 5.928 6.054 6.166 6.267 6.359 6.443 6.521 10 2.715 3.331 5.167 5.389 5.565 5.713 5.841 5.955 6.057 6.150 6.235 6.313 20 2.709 3.319 4.860 5.138 5.332 5.488 5.622 5.739 5.843 5.937 6.023 6.103 30 2.702 3.308 3.944 4.963 5.182 5.348 5.487 5.608 5.714 5.810 5.897 5.978 40 2.696 3.297 3.870 4.814 5.065 5.243 5.388 5.512 5.621 5.718 5.807 5.888 50 2.690 3.287 3.830 4.670 4.966 5.157 5.308 5.435 5.546 5.645 5.735 5.817 60 2.685 3.277 3.801 4.529 4.877 5.082 5.240 5.371 5.484 5.585 5.676 5.759 70 2.679 3.268 3.777 4.403 4.798 5.017 5.180 5.315 5.431 5.533 5.625 5.709 80 2.673 3.259 3.756 4.309 4.725 4.957 5.127 5.265 5.383 5.487 5.580 5.665 90 2.668 3.251 3.738 4.242 4.659 4.904 5.079 5.221 5.341 5.446 5.540 5.626 100 2.662 3.242 3.721 4.192 4.600 4.854 5.036 5.180 5.302 5.409 5.504 5.591 150 2.636 3.205 3.656 4.050 4.396 4.663 4.862 5.019 5.150 5.262 5.362 5.452 200 2.612 3.171 3.606 3.970 4.281 4.536 4.738 4.901 5.038 5.155 5.258 5.350 250 2.589 3.142 3.565 3.912 4.204 4.447 4.647 4.812 4.951 5.071 5.176 5.271 300 2.568 3.114 3.530 3.865 4.145 4.380 4.576 4.740 4.880 5.002 5.109 5.205 350 2.547 3.089 3.499 3.826 4.098 4.326 4.518 4.682 4.822 4.944 5.052 5.149 400 2.528 3.066 3.470 3.793 4.058 4.281 4.471 4.632 4.772 4.895 5.004 5.101 450 2.509 3.044 3.445 3.762 4.024 4.243 4.430 4.590 4.729 4.852 4.961 5.059 199 200 D2 Properties of Selected Important Pure Substances D2.3. Table 7. (continued) Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 500 2.492 3.024 3.421 3.735 3.993 4.209 4.394 4.553 4.692 4.814 4.923 5.022 600 2.458 2.985 3.378 3.687 3.939 4.152 4.333 4.490 4.627 4.749 4.859 4.957 700 2.427 2.950 3.339 3.645 3.894 4.103 4.282 4.438 4.574 4.696 4.805 4.903 800 2.398 2.918 3.304 3.607 3.854 4.062 4.239 4.393 4.529 4.650 4.759 4.857 900 2.371 2.888 3.272 3.573 3.819 4.025 4.201 4.354 4.489 4.610 4.718 4.817 1,000 2.345 2.860 3.243 3.542 3.787 3.991 4.166 4.319 4.454 4.574 4.682 4.781 Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 1 7.073 7.141 7.204 7.322 7.525 7.699 7.851 7.989 8.113 8.228 8.334 8.433 5 6.594 6.662 6.726 6.843 7.047 7.221 7.373 7.511 7.636 7.750 7.856 7.955 10 6.386 6.454 6.518 6.636 6.840 7.014 7.167 7.305 7.430 7.544 7.650 7.749 20 6.176 6.245 6.310 6.428 6.633 6.808 6.961 7.099 7.224 7.338 7.445 7.543 30 6.052 6.121 6.186 6.306 6.511 6.686 6.840 6.978 7.103 7.218 7.324 7.423 40 5.963 6.033 6.098 6.218 6.425 6.600 6.754 6.892 7.017 7.132 7.238 7.337 50 5.893 5.963 6.029 6.150 6.357 6.533 6.687 6.825 6.951 7.066 7.172 7.271 60 5.835 5.906 5.972 6.093 6.302 6.478 6.632 6.771 6.896 7.011 7.118 7.217 70 5.786 5.857 5.924 6.046 6.255 6.431 6.586 6.724 6.850 6.965 7.072 7.171 80 5.742 5.814 5.882 6.004 6.214 6.391 6.546 6.684 6.810 6.925 7.032 7.131 90 5.704 5.777 5.844 5.967 6.177 6.355 6.510 6.649 6.775 6.890 6.997 7.096 100 5.669 5.742 5.810 5.934 6.145 6.323 6.478 6.617 6.743 6.859 6.965 7.065 150 5.533 5.609 5.678 5.804 6.019 6.199 6.355 6.495 6.621 6.737 6.844 6.944 200 5.434 5.511 5.582 5.711 5.928 6.109 6.267 6.407 6.534 6.651 6.758 6.857 250 5.356 5.434 5.507 5.637 5.857 6.040 6.198 6.339 6.467 6.583 6.691 6.791 300 5.292 5.371 5.445 5.576 5.798 5.983 6.142 6.284 6.411 6.528 6.636 6.736 350 5.237 5.317 5.392 5.525 5.748 5.934 6.094 6.236 6.364 6.482 6.589 6.690 400 5.190 5.271 5.345 5.480 5.705 5.891 6.052 6.195 6.324 6.441 6.549 6.649 450 5.148 5.230 5.305 5.440 5.666 5.854 6.016 6.159 6.288 6.405 6.514 6.614 500 5.111 5.193 5.268 5.404 5.632 5.820 5.982 6.126 6.255 6.373 6.482 6.582 600 5.047 5.129 5.206 5.343 5.572 5.762 5.925 6.069 6.199 6.317 6.426 6.527 700 4.993 5.076 5.153 5.290 5.521 5.712 5.876 6.021 6.152 6.270 6.379 6.481 800 4.947 5.030 5.107 5.245 5.477 5.669 5.834 5.980 6.110 6.229 6.339 6.440 900 4.907 4.990 5.067 5.206 5.439 5.631 5.797 5.943 6.074 6.193 6.303 6.404 1,000 4.871 4.954 5.031 5.170 5.404 5.597 5.763 5.910 6.041 6.161 6.271 6.372 D2.3. Table 8. Specific isobaric heat capacity cp of nitrogen in kJ/(kg K) Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 1 2.024 1.073 1.056 1.049 1.045 1.044 1.042 1.042 1.041 1.041 1.042 1.042 5 2.020 1.278 1.134 1.091 1.072 1.062 1.056 1.052 1.050 1.048 1.047 1.047 10 2.016 2.258 1.269 1.153 1.108 1.086 1.073 1.065 1.060 1.056 1.054 1.052 20 2.008 2.214 1.847 1.315 1.191 1.138 1.109 1.092 1.080 1.073 1.067 1.064 30 2.000 2.176 6.534 1.557 1.291 1.195 1.147 1.119 1.101 1.089 1.081 1.075 40 1.993 2.144 3.649 1.940 1.408 1.257 1.187 1.147 1.122 1.105 1.094 1.086 D2.3 Properties of Nitrogen D2.3. Table 8. (continued) Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 50 1.986 2.115 3.047 2.544 1.545 1.323 1.227 1.175 1.143 1.122 1.107 1.096 60 1.979 2.090 2.752 3.294 1.696 1.391 1.268 1.203 1.164 1.138 1.120 1.107 70 1.973 2.068 2.568 3.644 1.853 1.461 1.309 1.231 1.184 1.153 1.132 1.117 80 1.966 2.047 2.440 3.436 1.999 1.529 1.349 1.258 1.204 1.168 1.144 1.127 90 1.961 2.029 2.345 3.110 2.115 1.594 1.388 1.284 1.223 1.183 1.156 1.137 100 1.955 2.012 2.270 2.843 2.190 1.652 1.424 1.309 1.241 1.198 1.168 1.146 150 1.931 1.947 2.050 2.222 2.139 1.806 1.559 1.412 1.320 1.260 1.218 1.189 200 1.911 1.901 1.938 1.998 1.965 1.797 1.611 1.471 1.374 1.306 1.258 1.223 250 1.895 1.868 1.869 1.881 1.849 1.746 1.614 1.496 1.405 1.337 1.287 1.248 300 1.880 1.841 1.822 1.809 1.773 1.696 1.598 1.502 1.421 1.356 1.306 1.268 350 1.868 1.820 1.787 1.759 1.719 1.656 1.577 1.498 1.427 1.368 1.320 1.282 400 1.857 1.803 1.761 1.724 1.681 1.624 1.558 1.490 1.427 1.373 1.328 1.291 450 1.848 1.789 1.740 1.697 1.651 1.599 1.540 1.481 1.425 1.376 1.334 1.298 500 1.840 1.777 1.724 1.676 1.629 1.579 1.525 1.472 1.421 1.376 1.337 1.303 600 1.825 1.758 1.699 1.645 1.596 1.548 1.501 1.455 1.412 1.373 1.339 1.308 700 1.814 1.744 1.681 1.625 1.574 1.528 1.484 1.443 1.404 1.369 1.338 1.310 800 1.803 1.733 1.668 1.610 1.559 1.513 1.471 1.433 1.397 1.365 1.337 1.311 900 1.795 1.723 1.658 1.600 1.548 1.502 1.462 1.425 1.392 1.362 1.335 1.311 1,000 1.787 1.716 1.651 1.592 1.540 1.495 1.455 1.419 1.387 1.359 1.333 1.311 Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 1 1.043 1.045 1.047 1.053 1.070 1.092 1.116 1.140 1.162 1.182 1.200 1.215 5 1.047 1.048 1.050 1.055 1.071 1.093 1.117 1.140 1.162 1.182 1.200 1.215 10 1.052 1.052 1.053 1.058 1.073 1.094 1.117 1.141 1.163 1.183 1.200 1.216 20 1.061 1.060 1.060 1.063 1.076 1.096 1.119 1.142 1.164 1.183 1.201 1.216 30 1.071 1.068 1.067 1.068 1.080 1.099 1.121 1.143 1.165 1.184 1.202 1.217 40 1.080 1.076 1.074 1.073 1.083 1.101 1.123 1.145 1.166 1.185 1.202 1.217 50 1.089 1.084 1.081 1.079 1.086 1.103 1.124 1.146 1.167 1.186 1.203 1.218 60 1.098 1.091 1.087 1.084 1.089 1.105 1.126 1.147 1.168 1.186 1.203 1.218 70 1.106 1.099 1.093 1.088 1.093 1.108 1.127 1.148 1.169 1.187 1.204 1.219 80 1.115 1.106 1.100 1.093 1.096 1.110 1.129 1.150 1.170 1.188 1.205 1.219 90 1.123 1.113 1.106 1.098 1.099 1.112 1.130 1.151 1.170 1.189 1.205 1.220 100 1.131 1.120 1.112 1.102 1.102 1.114 1.132 1.152 1.171 1.189 1.206 1.220 150 1.167 1.150 1.138 1.123 1.115 1.124 1.139 1.157 1.176 1.193 1.209 1.223 200 1.196 1.176 1.161 1.141 1.127 1.132 1.146 1.162 1.180 1.196 1.211 1.225 250 1.219 1.197 1.180 1.156 1.138 1.140 1.152 1.167 1.183 1.199 1.214 1.227 300 1.237 1.214 1.195 1.169 1.148 1.147 1.157 1.171 1.187 1.202 1.216 1.229 350 1.251 1.227 1.207 1.180 1.156 1.154 1.162 1.175 1.190 1.205 1.218 1.231 400 1.261 1.237 1.217 1.189 1.163 1.159 1.167 1.179 1.193 1.207 1.220 1.232 450 1.269 1.245 1.226 1.197 1.169 1.164 1.171 1.182 1.196 1.210 1.222 1.234 500 1.275 1.251 1.232 1.204 1.175 1.169 1.175 1.186 1.199 1.212 1.224 1.236 600 1.282 1.260 1.242 1.214 1.184 1.177 1.181 1.191 1.203 1.216 1.228 1.239 700 1.286 1.266 1.248 1.221 1.192 1.184 1.187 1.196 1.208 1.220 1.231 1.242 800 1.289 1.269 1.252 1.226 1.198 1.189 1.192 1.201 1.211 1.223 1.234 1.244 900 1.290 1.271 1.256 1.231 1.203 1.194 1.197 1.205 1.215 1.226 1.236 1.246 1,000 1.291 1.273 1.258 1.234 1.207 1.198 1.200 1.208 1.218 1.229 1.239 1.249 201 202 D2 Properties of Selected Important Pure Substances D2.3. Table 9. Specific isochoric heat capacity cn of nitrogen in kJ/(kg K) Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 1 1.110 0.7522 0.7462 0.7443 0.7434 0.7430 0.7429 0.7428 0.7429 0.7431 0.7436 0.7445 5 1.111 0.8058 0.7642 0.7529 0.7484 0.7462 0.7451 0.7444 0.7441 0.7441 0.7445 0.7452 10 1.112 0.9891 0.7914 0.7644 0.7547 0.7502 0.7478 0.7465 0.7457 0.7454 0.7455 0.7460 20 1.114 0.9905 0.8760 0.7905 0.7678 0.7582 0.7533 0.7504 0.7488 0.7478 0.7475 0.7477 30 1.117 0.9922 1.064 0.8210 0.7815 0.7662 0.7586 0.7543 0.7517 0.7502 0.7495 0.7494 40 1.120 0.9941 0.9711 0.8560 0.7954 0.7741 0.7638 0.7581 0.7546 0.7525 0.7514 0.7510 50 1.122 0.9961 0.9503 0.8935 0.8092 0.7817 0.7688 0.7617 0.7574 0.7548 0.7533 0.7526 60 1.125 0.9982 0.9412 0.9234 0.8223 0.7891 0.7737 0.7652 0.7602 0.7570 0.7551 0.7542 70 1.127 1.000 0.9367 0.9310 0.8338 0.7960 0.7783 0.7686 0.7628 0.7591 0.7569 0.7557 80 1.129 1.002 0.9346 0.9228 0.8432 0.8023 0.7826 0.7718 0.7653 0.7612 0.7586 0.7572 90 1.132 1.005 0.9337 0.9128 0.8501 0.8079 0.7867 0.7749 0.7678 0.7632 0.7603 0.7587 100 1.134 1.007 0.9338 0.9054 0.8547 0.8129 0.7905 0.7778 0.7701 0.7652 0.7620 0.7601 150 1.146 1.018 0.9393 0.8943 0.8607 0.8287 0.8054 0.7903 0.7805 0.7740 0.7696 0.7668 200 1.156 1.028 0.9477 0.8977 0.8637 0.8365 0.8152 0.7998 0.7891 0.7816 0.7764 0.7728 250 1.167 1.038 0.9567 0.9043 0.8689 0.8428 0.8226 0.8075 0.7963 0.7882 0.7824 0.7784 300 1.176 1.048 0.9656 0.9119 0.8754 0.8490 0.8292 0.8141 0.8027 0.7943 0.7880 0.7835 350 1.186 1.057 0.9743 0.9197 0.8823 0.8554 0.8354 0.8202 0.8086 0.7998 0.7932 0.7883 400 1.194 1.065 0.9826 0.9275 0.8893 0.8619 0.8415 0.8261 0.8142 0.8050 0.7981 0.7929 450 1.203 1.074 0.9906 0.9350 0.8962 0.8683 0.8475 0.8317 0.8195 0.8100 0.8028 0.7973 500 1.211 1.081 0.9983 0.9423 0.9030 0.8746 0.8533 0.8372 0.8246 0.8149 0.8073 0.8015 600 1.226 1.096 1.013 0.9562 0.9161 0.8867 0.8646 0.8477 0.8345 0.8241 0.8159 0.8096 700 1.240 1.110 1.026 0.9692 0.9283 0.8982 0.8754 0.8577 0.8438 0.8328 0.8241 0.8173 800 1.253 1.123 1.039 0.9813 0.9399 0.9091 0.8856 0.8673 0.8528 0.8412 0.8320 0.8247 900 1.264 1.135 1.051 0.9928 0.9509 0.9194 0.8953 0.8764 0.8613 0.8492 0.8395 0.8317 1,000 1.275 1.146 1.062 1.004 0.9612 0.9293 0.9046 0.8851 0.8695 0.8569 0.8467 0.8385 Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 1 0.7457 0.7473 0.7495 0.7553 0.7725 0.7947 0.8189 0.8427 0.8649 0.8850 0.9028 0.9184 5 0.7463 0.7478 0.7499 0.7556 0.7727 0.7949 0.8190 0.8428 0.8650 0.8851 0.9029 0.9185 10 0.7470 0.7485 0.7505 0.7561 0.7731 0.7952 0.8192 0.8430 0.8652 0.8852 0.9030 0.9187 20 0.7485 0.7498 0.7516 0.7570 0.7737 0.7957 0.8197 0.8434 0.8655 0.8855 0.9033 0.9189 30 0.7499 0.7510 0.7528 0.7580 0.7744 0.7962 0.8201 0.8437 0.8658 0.8858 0.9035 0.9191 40 0.7513 0.7523 0.7539 0.7589 0.7751 0.7967 0.8205 0.8441 0.8661 0.8861 0.9038 0.9193 50 0.7527 0.7535 0.7550 0.7597 0.7757 0.7972 0.8209 0.8445 0.8665 0.8864 0.9040 0.9196 60 0.7541 0.7547 0.7560 0.7606 0.7764 0.7977 0.8214 0.8448 0.8668 0.8866 0.9043 0.9198 70 0.7554 0.7559 0.7571 0.7615 0.7770 0.7983 0.8218 0.8452 0.8671 0.8869 0.9045 0.9200 80 0.7567 0.7570 0.7581 0.7624 0.7776 0.7988 0.8222 0.8455 0.8674 0.8872 0.9048 0.9202 90 0.7580 0.7582 0.7592 0.7632 0.7783 0.7993 0.8226 0.8459 0.8677 0.8875 0.9050 0.9205 100 0.7593 0.7593 0.7602 0.7641 0.7789 0.7998 0.8230 0.8463 0.8680 0.8877 0.9053 0.9207 150 0.7652 0.7647 0.7650 0.7682 0.7820 0.8023 0.8251 0.8480 0.8696 0.8891 0.9065 0.9218 200 0.7707 0.7696 0.7696 0.7720 0.7850 0.8047 0.8271 0.8498 0.8711 0.8905 0.9077 0.9229 250 0.7757 0.7743 0.7739 0.7757 0.7879 0.8070 0.8291 0.8515 0.8726 0.8918 0.9089 0.9240 300 0.7805 0.7787 0.7779 0.7793 0.7907 0.8093 0.8311 0.8532 0.8741 0.8931 0.9101 0.9251 350 0.7849 0.7828 0.7818 0.7827 0.7934 0.8116 0.8330 0.8548 0.8755 0.8944 0.9113 0.9262 400 0.7892 0.7868 0.7856 0.7860 0.7961 0.8138 0.8349 0.8565 0.8770 0.8957 0.9125 0.9272 D2.3 Properties of Nitrogen D2.3. Table 9. (continued) Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 450 0.7933 0.7907 0.7892 0.7892 0.7987 0.8160 0.8367 0.8581 0.8784 0.8970 0.9136 0.9283 500 0.7973 0.7944 0.7927 0.7923 0.8012 0.8181 0.8386 0.8597 0.8798 0.8983 0.9148 0.9293 600 0.8049 0.8015 0.7994 0.7983 0.8061 0.8222 0.8421 0.8628 0.8826 0.9008 0.9170 0.9314 700 0.8121 0.8083 0.8058 0.8041 0.8108 0.8262 0.8456 0.8658 0.8853 0.9032 0.9192 0.9334 800 0.8190 0.8149 0.8120 0.8096 0.8154 0.8301 0.8489 0.8688 0.8879 0.9056 0.9214 0.9354 900 0.8257 0.8212 0.8179 0.8150 0.8199 0.8339 0.8522 0.8717 0.8905 0.9079 0.9235 0.9373 1,000 0.8321 0.8272 0.8237 0.8202 0.8242 0.8376 0.8554 0.8745 0.8931 0.9102 0.9256 0.9393 D2.3. Table 10. Isobaric expansion coefficient b of nitrogen in 103/K Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 1 5.339 10.83 8.380 6.878 5.847 5.089 4.508 4.048 3.673 3.362 3.101 2.877 5 5.300 14.62 9.599 7.433 6.143 5.264 4.617 4.119 3.722 3.396 3.124 2.894 10 5.253 8.589 11.70 8.236 6.542 5.489 4.756 4.209 3.782 3.437 3.153 2.914 20 5.162 8.133 20.73 10.33 7.441 5.965 5.037 4.386 3.899 3.518 3.209 2.954 30 5.076 7.744 62.97 13.42 8.489 6.470 5.321 4.561 4.012 3.594 3.262 2.991 40 4.993 7.407 25.73 18.17 9.689 6.996 5.604 4.730 4.120 3.666 3.311 3.025 50 4.915 7.111 18.52 25.26 11.02 7.530 5.880 4.892 4.222 3.733 3.356 3.056 60 4.840 6.849 15.08 32.90 12.39 8.054 6.144 5.044 4.317 3.794 3.398 3.085 70 4.768 6.614 12.98 33.96 13.67 8.544 6.388 5.183 4.403 3.850 3.435 3.110 80 4.699 6.402 11.55 28.50 14.66 8.976 6.607 5.309 4.480 3.901 3.469 3.133 10.48 90 4.634 6.209 22.90 15.18 9.326 6.795 5.418 4.548 3.944 3.498 3.152 100 4.570 6.033 9.656 18.83 15.19 9.574 6.948 5.510 4.606 3.982 3.523 3.169 150 4.288 5.334 7.241 10.36 11.55 9.302 7.135 5.698 4.744 4.076 3.585 3.208 200 4.050 4.832 6.013 7.574 8.492 7.882 6.623 5.507 4.663 4.034 3.557 3.185 250 3.846 4.449 5.244 6.166 6.758 6.592 5.907 5.126 4.446 3.900 3.465 3.117 300 3.669 4.144 4.706 5.298 5.684 5.639 5.240 4.701 4.174 3.717 3.336 3.020 350 3.512 3.894 4.303 4.702 4.957 4.944 4.686 4.303 3.895 3.518 3.189 2.908 400 3.373 3.683 3.987 4.263 4.432 4.422 4.238 3.952 3.632 3.321 3.039 2.791 450 3.248 3.503 3.730 3.923 4.033 4.017 3.876 3.653 3.395 3.136 2.893 2.674 500 3.135 3.346 3.517 3.651 3.719 3.695 3.578 3.397 3.184 2.965 2.755 2.561 600 2.937 3.086 3.181 3.238 3.253 3.214 3.122 2.990 2.834 2.670 2.508 2.355 700 2.769 2.876 2.924 2.937 2.920 2.871 2.790 2.683 2.561 2.431 2.301 2.176 800 2.624 2.703 2.720 2.706 2.669 2.613 2.537 2.445 2.343 2.236 2.128 2.023 900 2.497 2.556 2.553 2.520 2.472 2.410 2.337 2.255 2.166 2.074 1.982 1.892 1,000 2.384 2.430 2.412 2.368 2.312 2.247 2.176 2.100 2.020 1.939 1.858 1.779 Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 1 2.683 2.514 2.365 2.114 1.745 1.485 1.293 1.145 1.027 0.9316 0.8522 0.7853 5 2.695 2.523 2.371 2.118 1.745 1.485 1.292 1.144 1.026 0.9307 0.8514 0.7845 10 2.710 2.534 2.379 2.122 1.746 1.484 1.291 1.143 1.025 0.9296 0.8504 0.7836 20 2.739 2.554 2.394 2.129 1.746 1.482 1.289 1.140 1.023 0.9274 0.8483 0.7817 203 204 D2 Properties of Selected Important Pure Substances D2.3. Table 10. (continued) Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 30 2.765 2.572 2.407 2.135 1.746 1.481 1.286 1.138 1.020 0.9251 0.8463 0.7799 40 2.789 2.589 2.419 2.140 1.746 1.479 1.284 1.135 1.018 0.9229 0.8442 0.7780 50 2.810 2.604 2.429 2.145 1.746 1.476 1.281 1.133 1.015 0.9206 0.8422 0.7762 60 2.830 2.618 2.438 2.148 1.745 1.474 1.279 1.130 1.013 0.9184 0.8401 0.7743 70 2.847 2.630 2.446 2.151 1.744 1.472 1.276 1.127 1.010 0.9161 0.8381 0.7725 80 2.863 2.640 2.452 2.153 1.742 1.469 1.273 1.125 1.008 0.9138 0.8360 0.7707 90 2.876 2.648 2.458 2.155 1.740 1.466 1.270 1.122 1.005 0.9115 0.8340 0.7688 100 2.886 2.655 2.462 2.156 1.738 1.463 1.267 1.119 1.003 0.9092 0.8319 0.7670 150 2.909 2.667 2.465 2.149 1.723 1.447 1.251 1.105 0.9901 0.8978 0.8217 0.7578 200 2.888 2.646 2.444 2.127 1.703 1.428 1.235 1.090 0.9771 0.8863 0.8115 0.7488 250 2.834 2.601 2.405 2.095 1.678 1.408 1.217 1.075 0.9641 0.8749 0.8015 0.7398 300 2.758 2.538 2.352 2.055 1.650 1.386 1.199 1.060 0.9510 0.8635 0.7915 0.7310 350 2.670 2.466 2.292 2.009 1.619 1.363 1.181 1.044 0.9380 0.8523 0.7817 0.7224 400 2.575 2.389 2.226 1.961 1.587 1.339 1.162 1.029 0.9251 0.8412 0.7720 0.7139 450 2.480 2.309 2.159 1.910 1.555 1.316 1.144 1.014 0.9123 0.8303 0.7625 0.7055 500 2.387 2.231 2.093 1.860 1.522 1.292 1.125 0.9989 0.8997 0.8195 0.7532 0.6973 600 2.212 2.082 1.964 1.761 1.457 1.245 1.089 0.9695 0.8751 0.7985 0.7350 0.6814 700 2.058 1.948 1.846 1.669 1.395 1.200 1.054 0.9411 0.8515 0.7784 0.7176 0.6661 800 1.923 1.828 1.740 1.584 1.337 1.157 1.020 0.9139 0.8288 0.7591 0.7009 0.6514 900 1.805 1.723 1.646 1.507 1.283 1.116 0.9884 0.8880 0.8072 0.7406 0.6849 0.6374 1,000 1.703 1.630 1.562 1.437 1.233 1.078 0.9584 0.8635 0.7866 0.7231 0.6696 0.6240 D2.3. Table 11. Isentropic speed of sound ws in nitrogen in m/s Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 1 894 199 225 247 267 286.8 304.4 321.1 337.0 352.1 366.5 380.4 5 897 189 219 244 266 286.1 304.3 321.3 337.4 352.7 367.3 381.2 10 901 632 213 241 264 285.4 304.2 321.7 338.0 353.5 368.2 382.3 20 908 649 196 234 261 284.4 304.4 322.6 339.5 355.3 370.3 384.6 30 915 664 262 228 259 284.0 305.0 323.9 341.2 357.4 372.6 387.0 40 922 678 351 224 258 284.3 306.2 325.6 343.3 359.7 375.1 389.6 50 929 692 399 223 258 285.4 307.9 327.7 345.6 362.2 377.7 392.4 60 936 704 434 229 260 287.4 310.2 330.2 348.3 365.0 380.6 395.3 70 943 716 464 249 264 290.5 313.1 333.1 351.3 368.0 383.6 398.3 80 949 728 489 278 271 294.6 316.6 336.5 354.5 371.2 386.8 401.5 90 956 739 511 310 280 299.9 320.8 340.2 358.1 374.7 390.2 404.8 100 962 750 531 340 292 306.3 325.7 344.4 362.0 378.4 393.7 408.2 150 992 798 612 455 370 352.4 358.5 371.1 385.3 399.7 413.7 427.2 200 1,020 839 674 536 447 409.5 400.9 404.9 414.0 425.1 436.9 448.8 250 1,045 876 725 600 513 466.1 446.6 442.5 446.0 453.2 462.3 472.1 300 1,069 909 769 653 569 518.3 491.8 481.0 479.4 482.8 489.0 496.6 350 1,092 940 808 700 619 565.8 534.7 519.0 513.0 512.9 516.3 521.8 400 1,113 968 844 741 663 609.0 575.1 555.7 546.1 542.9 543.7 547.2 450 1,133 995 876 778 702 648.7 612.8 590.7 578.3 572.4 571.0 572.4 D2.3 Properties of Nitrogen D2.3. Table 11. (continued) Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 500 1,153 1,020 906 812 739 685.4 648.2 624.0 609.3 601.2 597.7 597.4 600 1,190 1,066 960 873 804 751.4 712.8 685.8 667.7 656.2 649.4 646.1 700 1,223 1,108 1,009 927 861 809.7 770.6 742.0 721.6 707.5 698.2 692.5 800 1,255 1,146 1,053 975 912 862.0 823.0 793.4 771.4 755.5 744.3 736.7 900 1,285 1,181 1,093 1,020 958 909.6 870.9 840.8 817.7 800.5 787.7 778.6 1,000 1,313 1,214 1,131 1,060 1,001 953.5 915.1 884.7 861.0 842.7 828.7 818.3 Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 1 393.7 406.6 419.0 442.6 485.5 524.1 559.4 592.2 623.1 652.4 680.4 707.3 5 394.6 407.5 420.0 443.6 486.6 525.2 560.4 593.2 624.0 653.3 681.3 708.2 10 395.8 408.8 421.2 444.9 487.9 526.5 561.7 594.4 625.2 654.5 682.4 709.2 20 398.2 411.3 423.8 447.6 490.6 529.1 564.2 596.9 627.6 656.7 684.6 711.3 30 400.8 413.9 426.5 450.3 493.4 531.8 566.8 599.4 629.9 659.0 686.8 713.4 40 403.4 416.6 429.3 453.1 496.1 534.5 569.4 601.8 632.3 661.3 689.0 715.5 50 406.3 419.5 432.1 456.0 498.9 537.2 572.0 604.3 634.7 663.6 691.1 717.6 60 409.2 422.4 435.1 458.9 501.8 539.9 574.6 606.8 637.1 665.8 693.3 719.7 70 412.2 425.5 438.1 461.9 504.6 542.6 577.2 609.3 639.5 668.1 695.5 721.9 80 415.4 428.6 441.2 464.9 507.5 545.4 579.8 611.8 641.8 670.4 697.7 724.0 90 418.6 431.8 444.4 468.0 510.5 548.1 582.4 614.3 644.2 672.7 699.9 726.1 100 422.0 435.1 447.6 471.1 513.4 550.9 585.1 616.8 646.6 675.0 702.1 728.2 150 440.3 452.8 464.8 487.5 528.5 565.0 598.4 629.4 658.6 686.4 713.1 738.7 200 460.6 472.1 483.3 504.8 544.1 579.4 611.8 642.0 670.6 697.9 724.0 749.2 250 482.3 492.6 502.9 522.8 560.0 594.0 625.3 654.7 682.6 709.3 734.9 759.7 300 505.1 514.1 523.2 541.3 576.3 608.7 639.0 667.5 694.6 720.7 745.8 770.1 350 528.5 536.0 543.9 560.3 592.7 623.5 652.6 680.2 706.7 732.1 756.7 780.5 400 552.2 558.2 565.0 579.4 609.3 638.4 666.3 693.0 718.6 743.4 767.5 790.8 450 575.8 580.5 586.1 598.6 625.9 653.3 679.9 705.7 730.6 754.7 778.3 801.1 500 599.3 602.7 607.1 617.8 642.5 668.2 693.6 718.3 742.5 766.0 789.0 811.4 600 645.3 646.3 648.6 655.9 675.6 697.9 720.7 743.5 766.1 788.4 810.3 831.7 700 689.5 688.5 689.0 693.1 708.2 727.2 747.6 768.5 789.5 810.5 831.3 851.9 800 731.8 729.1 728.0 729.4 740.1 756.0 774.0 793.1 812.6 832.4 852.1 871.8 900 772.2 768.0 765.6 764.5 771.3 784.3 800.1 817.3 835.4 854.0 872.7 891.4 1,000 810.7 805.3 801.7 798.4 801.7 811.9 825.6 841.2 857.9 875.2 892.9 910.8 D2.3. Table 12. Thermal conductivity l of nitrogen in mW/(m K) Temperature in C Pressure in bar 200 1 155.7 175 9.623 10.33 150 125 100 75 50 25 0 25 50 75 12.10 14.41 16.59 18.65 20.59 22.45 24.23 25.94 27.59 29.19 5 156.2 12.62 14.83 16.95 18.95 20.86 22.69 24.45 26.14 27.77 29.36 10 156.7 108.0 13.36 15.40 17.41 19.35 21.21 23.00 24.72 26.39 28.00 29.58 20 157.8 109.9 15.39 16.68 18.40 20.17 21.92 23.63 25.29 26.90 28.47 30.01 30 158.8 111.7 54.09 18.28 19.51 21.05 22.66 24.27 25.86 27.42 28.94 30.44 40 159.9 113.4 63.15 20.38 20.77 22.00 23.44 24.94 26.44 27.94 29.42 30.88 205 206 D2 Properties of Selected Important Pure Substances D2.3. Table 12. (continued) Temperature in C Pressure in bar 200 50 160.9 60 161.9 70 175 150 125 100 75 50 25 0 25 50 75 115.1 68.36 23.36 22.20 23.01 24.25 25.62 27.04 28.47 29.90 31.32 116.7 72.35 27.75 23.84 24.11 25.10 26.33 27.65 29.01 30.39 31.76 162.9 118.2 75.70 33.50 25.72 25.29 25.99 27.06 28.27 29.56 30.88 32.21 80 163.8 119.7 78.62 39.42 27.86 26.56 26.92 27.81 28.91 30.12 31.38 32.66 90 164.8 121.1 81.25 44.61 30.21 27.91 27.89 28.58 29.56 30.68 31.88 33.11 100 165.8 122.5 83.65 49.02 32.74 29.35 28.91 29.38 30.23 31.26 32.39 33.57 150 170.3 129.0 93.55 64.37 45.47 37.35 34.49 33.67 33.74 34.25 35.01 35.92 200 174.6 134.7 101.4 74.73 56.03 45.55 40.54 38.34 37.52 37.44 37.77 38.36 250 178.7 140.0 108.1 82.91 64.63 53.08 46.58 43.16 41.47 40.76 40.63 40.88 300 182.7 144.9 114.1 89.87 71.93 59.84 52.35 47.95 45.46 44.15 43.58 43.47 350 186.4 149.5 119.6 96.00 78.35 65.95 57.77 52.60 49.44 47.58 46.56 46.10 400 190.0 153.9 124.6 101.6 84.12 71.52 62.85 57.08 53.34 50.98 49.55 48.76 450 193.5 158.0 129.3 106.7 89.40 76.67 67.62 61.38 57.15 54.35 52.53 51.42 500 196.9 161.9 133.7 111.4 94.29 81.47 72.13 65.49 60.85 57.65 55.49 54.09 600 203.4 169.4 141.9 120.1 103.2 90.24 80.47 73.23 67.92 64.07 61.30 59.35 700 209.5 176.3 149.4 128.1 111.2 98.16 88.08 80.40 74.58 70.20 66.93 64.52 800 215.4 182.9 156.5 135.3 118.6 105.4 95.13 87.09 80.87 76.06 72.37 69.55 900 221.0 189.1 163.1 142.2 125.5 112.2 101.7 93.40 86.83 81.67 77.61 74.45 1,000 226.4 195.0 169.3 148.6 131.9 118.6 107.9 99.37 92.52 87.05 82.68 79.21 Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 1 30.75 32.28 33.78 36.72 42.47 48.12 53.68 59.13 64.45 69.63 74.67 79.57 5 30.91 32.43 33.92 36.85 42.58 48.21 53.75 59.20 64.51 69.69 74.72 79.61 10 31.11 32.62 34.10 37.01 42.71 48.32 53.85 59.28 64.59 69.76 74.78 79.67 20 31.51 32.99 34.45 37.32 42.96 48.54 54.04 59.45 64.74 69.89 74.91 79.79 30 31.92 33.37 34.80 37.64 43.22 48.76 54.23 59.62 64.89 70.03 75.04 79.90 40 32.32 33.74 35.15 37.95 43.48 48.97 54.42 59.79 65.04 70.17 75.16 80.02 50 32.73 34.12 35.51 38.26 43.74 49.19 54.61 59.96 65.19 70.31 75.29 80.14 60 33.13 34.50 35.86 38.58 43.99 49.41 54.80 60.12 65.34 70.44 75.41 80.25 70 33.54 34.88 36.22 38.89 44.25 49.63 54.99 60.29 65.49 70.58 75.54 80.37 80 33.96 35.26 36.57 39.20 44.50 49.84 55.18 60.46 65.64 70.71 75.66 80.48 90 34.37 35.64 36.93 39.51 44.76 50.06 55.36 60.62 65.79 70.85 75.78 80.59 100 34.79 36.03 37.28 39.83 45.01 50.27 55.55 60.79 65.94 70.98 75.91 80.71 150 36.92 37.98 39.09 41.40 46.28 51.34 56.47 61.60 66.67 71.65 76.52 81.27 200 39.11 39.98 40.92 42.99 47.54 52.40 57.39 62.41 67.40 72.31 77.12 81.83 250 41.37 42.02 42.80 44.60 48.81 53.45 58.30 63.21 68.12 72.96 77.72 82.38 300 43.68 44.11 44.71 46.24 50.09 54.51 59.21 64.01 68.83 73.61 78.31 82.93 350 46.03 46.24 46.65 47.89 51.38 55.58 60.12 64.81 69.54 74.25 78.90 83.47 400 48.42 48.40 48.62 49.57 52.68 56.65 61.03 65.61 70.25 74.89 79.49 84.01 450 50.82 50.58 50.61 51.27 53.99 57.72 61.94 66.41 70.97 75.54 80.07 84.55 500 53.22 52.77 52.62 52.98 55.32 58.80 62.86 67.21 71.68 76.18 80.66 85.09 600 58.02 57.15 56.65 56.44 58.00 60.99 64.72 68.82 73.10 77.46 81.83 86.16 700 62.76 61.52 60.69 59.93 60.71 63.21 66.59 70.44 74.54 78.75 83.00 87.24 800 67.42 65.84 64.71 63.43 63.46 65.45 68.49 72.09 75.99 80.05 84.18 88.32 900 71.99 70.10 68.69 66.92 66.23 67.72 70.41 73.75 77.46 81.37 85.37 89.41 1,000 76.46 74.29 72.62 70.40 69.00 70.02 72.35 75.43 78.94 82.69 86.57 90.50 D2.3 Properties of Nitrogen D2.3. Table 13. Dynamic viscosity of nitrogen in 106 Pa · s Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 1 6.559 8.276 9.880 11.38 12.80 14.15 15.43 16.65 17.83 18.96 20.05 5 6.762 8.422 9.996 11.48 12.89 14.22 15.49 16.71 17.88 19.01 20.09 10 77.72 8.656 10.17 11.62 13.00 14.32 15.58 16.79 17.95 19.07 20.15 20 80.00 9.434 10.62 11.95 13.27 14.54 15.77 16.96 18.10 19.21 20.28 30 82.21 31.06 11.28 12.38 13.59 14.81 16.00 17.15 18.27 19.36 20.42 40 84.35 36.98 12.27 12.92 13.98 15.11 16.25 17.37 18.46 19.53 20.57 50 86.46 40.63 13.81 13.60 14.43 15.45 16.52 17.60 18.66 19.71 20.73 60 88.52 43.57 16.18 14.42 14.94 15.83 16.83 17.85 18.88 19.90 20.90 70 90.54 46.13 19.35 15.41 15.53 16.25 17.16 18.13 19.11 20.10 21.08 80 92.53 48.44 22.65 16.55 16.18 16.71 17.51 18.42 19.36 20.32 21.27 90 94.50 50.59 25.60 17.84 16.89 17.20 17.89 18.72 19.62 20.54 21.47 100 96.44 52.60 28.17 19.23 17.66 17.73 18.29 19.05 19.89 20.77 21.67 50 105.9 61.54 37.84 26.34 22.06 20.75 20.57 20.87 21.41 22.07 22.81 200 115.0 69.42 45.20 32.58 26.63 24.09 23.12 22.92 23.11 23.53 24.08 250 124.0 76.78 51.64 38.05 30.98 27.46 25.78 25.09 24.93 25.09 25.44 300 133.0 83.84 57.59 43.07 35.08 30.75 28.46 27.30 26.80 26.70 26.85 350 141.9 90.74 63.25 47.80 38.98 33.96 31.11 29.52 28.70 28.35 28.30 400 150.9 97.54 68.75 52.34 42.75 37.08 33.72 31.73 30.60 30.01 29.77 450 160.0 104.3 74.14 56.76 46.42 40.14 36.30 33.93 32.50 31.67 31.25 500 169.2 111.1 79.47 61.11 50.03 43.17 38.85 36.13 34.40 33.35 32.74 600 124.7 90.08 69.70 57.13 49.13 43.92 40.49 38.21 36.70 35.73 700 138.6 100.7 78.27 64.20 55.06 48.98 44.85 42.02 40.08 38.74 800 152.9 111.6 86.91 71.30 61.02 54.06 49.25 45.87 43.48 41.79 900 167.7 122.7 95.71 78.50 67.05 59.20 53.70 49.77 46.94 44.88 85.83 73.18 64.43 58.22 53.73 50.45 48.02 1,000 134.1 104.7 Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 1 21.10 22.13 23.13 25.04 28.62 31.94 35.06 38.02 40.85 43.57 46.19 48.74 5 21.15 22.17 23.16 25.07 28.65 31.96 35.08 38.04 40.86 43.58 46.21 48.76 10 21.20 22.22 23.21 25.12 28.68 31.99 35.10 38.06 40.88 43.60 46.22 48.77 20 21.32 22.33 23.31 25.21 28.76 32.05 35.16 38.10 40.92 43.64 46.26 48.80 30 21.45 22.45 23.42 25.30 28.83 32.12 35.21 38.15 40.97 43.67 46.29 48.83 40 21.58 22.57 23.54 25.40 28.91 32.18 35.27 38.20 41.01 43.71 46.33 48.87 50 21.73 22.70 23.66 25.51 28.99 32.25 35.33 38.25 41.05 43.75 46.36 48.90 60 21.88 22.84 23.79 25.62 29.08 32.32 35.39 38.30 41.10 43.79 46.40 48.93 70 22.04 22.99 23.92 25.73 29.17 32.40 35.45 38.36 41.15 43.84 46.44 48.97 80 22.21 23.14 24.06 25.85 29.26 32.47 35.51 38.41 41.20 43.88 46.48 49.00 90 22.39 23.30 24.21 25.98 29.36 32.55 35.58 38.47 41.24 43.92 46.52 49.04 100 22.57 23.47 24.36 26.10 29.46 32.63 35.64 38.52 41.29 43.97 46.56 49.07 150 23.58 24.37 25.18 26.80 29.98 33.05 36.00 38.83 41.56 44.20 46.77 49.27 200 24.70 25.38 26.09 27.57 30.56 33.51 36.38 39.15 41.84 44.45 46.99 49.47 250 25.91 26.46 27.07 28.39 31.18 34.01 36.79 39.50 42.15 44.72 47.23 49.68 300 27.17 27.59 28.10 29.25 31.83 34.53 37.22 39.87 42.46 45.00 47.48 49.91 350 28.46 28.76 29.15 30.14 32.51 35.07 37.67 40.25 42.80 45.29 47.74 50.14 400 29.77 29.94 30.23 31.06 33.20 35.62 38.13 40.65 43.14 45.60 48.01 50.39 450 31.10 31.14 31.33 31.99 33.91 36.20 38.61 41.05 43.49 45.91 48.29 50.64 207 208 D2 Properties of Selected Important Pure Substances D2.3. Table 13. (continued) Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 500 32.44 32.36 32.44 32.93 34.63 36.78 39.09 41.47 43.85 46.23 48.58 50.90 600 35.13 34.80 34.68 34.84 36.10 37.97 40.09 42.32 44.60 46.88 49.16 51.43 700 37.85 37.28 36.94 36.78 37.60 39.18 41.11 43.20 45.36 47.56 49.77 51.98 800 40.60 39.78 39.24 38.74 39.12 40.42 42.15 44.09 46.15 48.26 50.40 52.54 900 43.39 42.32 41.57 40.73 40.66 41.67 43.20 45.00 46.95 48.97 51.04 53.12 1,000 46.23 44.90 43.93 42.76 42.23 42.95 44.27 45.93 47.76 49.69 51.69 53.71 D2.3. Table 14. Kinematic viscosity n of nitrogen in 107 m2/s Temperature in C Pressure in bar 200 1 175 18.71 150 29.93 125 43.18 100 75 50 58.30 75.13 93.58 11.59 14.99 18.71 25 113.5 0 25 50 75 134.9 157.7 181.8 207.2 5 3.492 5.820 8.524 22.73 27.04 31.61 36.46 41.55 10 1.107 2.801 4.194 5.754 7.478 9.357 20 1.130 1.274 2.036 2.848 3.732 4.691 11.38 5.721 13.55 6.820 15.86 7.986 18.29 9.216 20.85 30 1.153 0.6474 1.325 1.889 2.494 3.145 3.842 4.584 5.370 6.197 7.066 40 1.175 0.7010 0.9772 1.420 1.883 2.379 2.909 3.472 4.067 4.693 5.350 50 1.197 0.7360 0.7821 1.147 1.524 1.926 2.355 2.809 3.290 3.795 4.324 60 1.218 0.7649 0.6750 0.9737 1.291 1.630 1.990 2.372 2.775 3.199 3.643 70 1.239 0.7904 0.6313 0.8596 1.131 1.422 1.733 2.063 2.411 2.776 3.159 80 1.260 0.8137 0.6254 0.7835 1.016 1.271 1.544 1.834 2.140 2.462 2.798 10.51 90 1.280 0.8354 0.6347 0.7333 0.9326 1.158 1.400 1.659 1.932 2.219 2.520 100 1.300 0.8559 0.6487 0.7015 0.8704 1.070 1.288 1.521 1.767 2.027 2.298 150 1.396 0.9473 0.7247 0.6698 0.7297 0.8416 0.9781 1.130 1.294 1.467 1.650 200 1.490 1.028 0.7934 0.7011 0.7052 0.7647 0.8538 0.9605 1.079 1.208 1.344 250 1.581 1.104 0.8564 0.7428 0.7157 0.7419 0.7997 0.8767 0.9667 1.066 1.174 300 1.671 1.177 0.9159 0.7864 0.7385 0.7422 0.7777 0.8335 0.9030 0.9823 1.069 350 1.761 1.247 0.9732 0.8301 0.7667 0.7536 0.7725 0.8122 0.8661 0.9302 1.002 400 1.851 1.317 1.029 0.8736 0.7973 0.7709 0.7767 0.8037 0.8453 0.8974 0.9576 450 1.942 1.386 1.084 0.9169 0.8294 0.7918 0.7867 0.8032 0.8347 0.8771 0.9276 500 2.033 1.454 1.138 0.9599 0.8622 0.8149 0.8005 0.8081 0.8311 0.8652 0.9076 600 1.592 1.246 1.046 0.9296 0.8654 0.8352 0.8280 0.8370 0.8578 0.8873 700 1.732 1.355 1.132 0.9986 0.9194 0.8757 0.8563 0.8540 0.8640 0.8833 800 1.875 1.464 1.220 1.069 0.9758 0.9201 0.8899 0.8777 0.8786 0.8894 900 2.021 1.576 1.309 1.141 1.034 0.9672 0.9271 0.9061 0.8989 0.9022 1.691 1.400 1.215 1.095 1.017 0.9671 0.9378 0.9233 0.9198 700 800 900 1,000 Temperature in C Pressure in bar 1 100 233.8 125 261.6 150 290.5 200 300 400 500 600 351.8 487.1 638.4 804.8 985.6 128.0 161.3 197.5 5 46.89 52.47 58.27 70.56 97.68 10 23.53 26.33 29.25 35.41 49.00 64.10 80.88 99.00 20 11.86 13.27 14.74 17.84 24.67 32.29 40.66 49.75 1,180 1,388 1,609 1,000 1,842 236.5 278.1 322.3 369.0 118.5 139.3 161.4 184.8 59.52 69.95 81.03 92.74 D2.3 Properties of Nitrogen D2.3. Table 14. (continued) Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 30 7.975 8.922 9.906 11.99 16.56 21.66 27.26 40 6.036 6.751 7.494 9.062 12.51 16.35 20.56 50 4.877 5.452 6.050 7.311 10.08 13.16 60 4.107 4.589 5.090 6.146 8.463 11.04 70 3.559 3.974 4.406 5.315 7.309 9.525 80 3.150 3.515 3.895 4.693 6.445 8.390 700 800 900 1,000 33.33 39.86 46.83 54.23 62.04 25.12 30.03 35.27 40.83 46.70 16.54 20.20 24.14 28.33 32.79 37.49 13.86 16.92 20.21 23.71 27.43 31.35 11.95 14.58 17.40 20.41 23.60 26.97 10.52 12.82 15.30 17.93 20.73 23.68 90 2.833 3.160 3.498 4.211 5.774 7.508 9.404 11.46 13.66 16.01 18.50 21.12 100 2.582 2.877 3.183 3.827 5.237 6.803 8.514 10.37 12.35 14.47 16.71 19.08 150 1.842 2.041 2.248 2.684 3.638 4.695 5.849 7.095 8.431 9.854 11.36 12.95 200 1.488 1.638 1.795 2.125 2.848 3.649 4.523 5.466 6.476 7.551 8.689 9.888 250 1.288 1.408 1.533 1.798 2.381 3.027 3.733 4.493 5.307 6.173 7.089 8.053 300 1.163 1.262 1.366 1.587 2.075 2.618 3.210 3.848 4.531 5.257 6.025 6.833 350 1.081 1.164 1.253 1.441 1.861 2.328 2.839 3.390 3.979 4.605 5.266 5.963 400 1.024 1.096 1.172 1.336 1.704 2.115 2.564 3.048 3.567 4.117 4.699 5.312 450 0.9845 1.047 1.113 1.258 1.584 1.951 2.352 2.785 3.248 3.740 4.260 4.807 500 0.9567 1.011 1.070 1.198 1.491 1.821 2.184 2.575 2.994 3.439 3.909 4.404 600 0.9237 0.9656 1.012 1.116 1.357 1.632 1.936 2.265 2.617 2.991 3.386 3.801 700 0.9099 0.9421 0.9790 1.064 1.267 1.502 1.763 2.047 2.351 2.674 3.015 3.374 800 0.9078 0.9321 0.9614 1.031 1.204 1.409 1.638 1.887 2.154 2.439 2.739 3.055 900 0.9135 0.9311 0.9539 1.011 1.160 1.340 1.543 1.765 2.003 2.258 2.527 2.810 1,000 0.9248 0.9365 0.9536 1.000 1.128 1.288 1.469 1.669 1.885 2.115 2.358 2.614 0 25 50 75 188.5 220.4 254.0 289.4 D2.3. Table 15. Thermal diffusivity a of nitrogen in 107 m2/s Temperature in C Pressure in bar 200 1 0.9327 5 0.9360 4.174 7.690 10 0.9399 0.6808 3.409 5.511 7.779 20 0.9477 0.7012 1.126 2.434 3.680 4.985 6.372 7.847 9.411 30 0.9553 0.7199 0.1725 1.378 2.307 3.232 4.195 5.208 6.275 7.397 8.573 9.803 40 0.9626 0.7372 0.3280 0.8365 1.620 2.358 3.110 3.893 4.711 5.568 6.464 7.399 50 0.9698 0.7533 0.4063 0.5202 1.212 1.838 2.464 3.107 3.777 4.475 5.202 5.959 60 0.9767 0.7683 0.4616 0.3514 0.9490 1.497 2.037 2.588 3.157 3.749 4.364 5.002 70 0.9835 0.7825 0.5051 0.2999 0.7745 1.261 1.738 2.221 2.718 3.233 3.767 4.321 80 0.9901 0.7958 0.5412 0.3168 0.6597 1.091 1.518 1.949 2.392 2.849 3.323 3.813 175 25.57 150 41.44 125 100 60.07 81.27 11.59 15.95 75 104.8 50 130.7 25 158.6 20.76 26.00 31.64 37.69 44.10 50.88 58.00 10.24 12.91 15.78 18.83 22.07 25.49 29.08 11.06 12.80 14.62 90 0.9966 0.8085 0.5723 0.3557 0.5873 0.9668 1.352 1.742 2.142 2.553 2.979 3.419 100 1.003 0.8205 0.5996 0.3971 0.5454 0.8755 1.225 1.580 1.944 2.319 2.706 3.106 150 1.033 0.8735 0.7025 0.5550 0.5406 0.6843 0.8972 1.134 1.384 1.643 1.910 2.186 200 1.060 0.9175 0.7752 0.6566 0.6137 0.6710 0.7989 0.9625 1.145 1.339 1.541 1.752 250 1.084 0.9555 0.8320 0.7311 0.6823 0.7023 0.7798 0.8946 1.031 1.182 1.343 1.511 300 1.107 0.9889 0.8791 0.7903 0.7410 0.7427 0.7906 0.8724 0.9770 1.097 1.227 1.366 350 1.129 1.019 0.9195 0.8395 0.7914 0.7831 0.8127 0.8721 0.9533 1.050 1.158 1.274 400 1.149 1.046 0.9550 0.8818 0.8354 0.8213 0.8388 0.8826 0.9465 1.025 1.116 1.215 209 210 D2 Properties of Selected Important Pure Substances D2.3. Table 15. (continued) Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 450 1.168 1.072 0.9868 0.9191 0.8743 0.8567 0.8660 0.8984 500 1.186 1.095 1.016 0.9524 0.9094 0.8895 0.8929 0.9169 0.9493 1.015 1.091 1.176 0.9578 1.012 1.077 600 1.220 1.137 1.067 1.010 0.9703 0.9483 0.9442 1.151 0.9566 0.9834 1.022 1.070 1.127 700 1.251 1.175 1.111 1.060 1.022 0.9995 800 1.280 1.209 1.150 1.103 1.068 1.045 0.9912 0.9965 1.014 1.042 1.078 1.123 1.034 1.035 1.046 1.066 1.094 900 1.307 1.241 1.186 1.142 1.108 1.086 1.129 1.073 1.071 1.077 1.092 1.114 1.142 1,000 1.333 1.270 1.218 1.177 1.145 1.123 1.110 1.105 1.108 1.118 1.135 1.158 Temperature in C Pressure in bar 1 100 125 150 200 300 400 326.5 365.2 405.4 490.2 675.8 881.0 135.5 176.7 500 600 1,104 700 1,345 800 1,603 900 1,877 1,000 2,168 2,475 5 65.45 73.22 81.30 98.31 221.4 269.6 321.2 376.1 434.3 495.7 10 32.83 36.73 40.79 49.33 68.01 88.62 20 16.52 18.49 20.54 24.85 34.25 44.60 111.0 55.85 135.2 67.96 161.0 80.91 188.5 94.68 217.6 248.3 109.3 124.7 30 11.08 12.41 13.79 16.69 22.99 29.93 37.46 45.55 54.21 63.41 73.15 83.43 10.42 12.61 17.37 22.60 28.26 34.35 40.86 47.78 55.10 62.82 10.17 14.00 18.20 22.75 27.63 32.85 38.40 44.26 50.45 40 8.370 9.379 50 6.746 7.560 8.403 60 5.665 6.350 7.059 8.541 11.75 15.27 19.07 23.15 27.51 32.14 37.04 42.20 70 4.895 5.488 6.100 7.380 10.15 13.17 16.44 19.95 23.70 27.68 31.88 36.31 80 4.319 4.843 5.383 6.510 8.945 11.60 14.48 17.56 20.84 24.33 28.01 31.90 10.38 12.95 15.69 18.62 21.72 25.00 28.46 11.72 14.20 16.84 19.64 22.60 25.71 11.51 13.39 15.38 17.47 10.27 11.77 13.35 90 3.874 4.343 4.826 5.835 8.011 100 3.519 3.944 4.383 5.297 7.265 9.410 150 2.471 2.764 3.065 3.692 5.034 6.490 8.055 9.727 200 1.970 2.194 2.424 2.904 3.929 5.038 6.228 7.496 8.843 250 1.686 1.867 2.054 2.443 3.275 4.174 5.136 6.161 7.249 8.398 9.610 300 1.511 1.662 1.819 2.145 2.846 3.603 4.412 5.274 6.188 7.154 8.171 9.239 350 1.397 1.526 1.660 1.940 2.545 3.199 3.899 4.644 5.433 6.266 7.144 8.065 400 1.320 1.432 1.548 1.793 2.324 2.900 3.517 4.173 4.868 5.602 6.375 7.185 450 1.268 1.365 1.468 1.685 2.157 2.671 3.223 3.809 4.431 5.088 5.778 6.503 500 1.231 1.318 1.408 1.602 2.027 2.491 2.989 3.520 4.083 4.677 5.302 5.957 600 1.190 1.258 1.331 1.489 1.840 2.228 2.645 3.091 3.565 4.064 4.590 5.141 700 1.173 1.228 1.289 1.420 1.717 2.047 2.406 2.790 3.199 3.630 4.084 4.561 800 1.170 1.216 1.266 1.377 1.631 1.918 2.232 2.569 2.928 3.308 3.708 4.128 900 1.175 1.213 1.255 1.350 1.571 1.824 2.101 2.401 2.721 3.060 3.418 3.794 1,000 1.185 1.217 1.253 1.334 1.528 1.752 2.000 2.270 2.558 2.865 3.188 3.528 10.88 D2.3. Table 16. Prandtl number Pr of nitrogen Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 1 0.7317 0.7222 0.7189 0.7174 0.7166 0.7162 0.7159 0.7158 0.7157 0.7158 0.7159 5 0.8367 0.7568 0.7352 0.7264 0.7221 0.7197 0.7183 0.7174 0.7168 0.7165 0.7164 10 1.626 0.8218 0.7611 0.7398 0.7299 0.7246 0.7215 0.7196 0.7184 0.7176 0.7171 20 1.612 1.132 0.8368 0.7738 0.7487 0.7361 0.7290 0.7247 0.7219 0.7200 0.7188 D2.3 Properties of Nitrogen D2.3. Table 16. (continued) Temperature in C Pressure in bar 200 175 150 125 100 75 50 25 0 25 50 75 30 1.602 3.753 0.9612 0.8190 0.7717 0.7497 0.7377 0.7305 0.7259 0.7229 0.7208 40 1.595 2.137 1.168 0.8764 0.7986 0.7650 0.7473 0.7369 0.7304 0.7260 0.7231 50 1.589 1.811 1.504 0.9462 0.8291 0.7819 0.7578 0.7439 0.7352 0.7295 0.7256 60 1.586 1.657 1.921 1.026 0.8623 0.7999 0.7689 0.7513 0.7403 0.7331 0.7283 70 1.584 1.565 2.105 1.110 0.8970 0.8186 0.7804 0.7589 0.7456 0.7370 0.7311 80 1.583 1.503 1.974 1.188 0.9316 0.8375 0.7921 0.7667 0.7511 0.7409 0.7340 90 1.583 1.460 1.784 1.249 0.9646 0.8560 0.8037 0.7745 0.7566 0.7449 0.7370 100 1.584 1.428 1.634 1.286 0.9942 0.8738 0.8151 0.7822 0.7621 0.7490 0.7400 150 1.599 1.348 1.306 1.239 1.066 0.9380 0.8621 0.8165 0.7875 0.7682 0.7548 200 1.624 1.327 1.208 1.142 1.051 0.9571 0.8870 0.8391 0.8064 0.7837 0.7674 250 1.655 1.327 1.171 1.089 1.019 0.9514 0.8939 0.8501 0.8179 0.7943 0.7768 300 1.690 1.338 1.159 1.061 0.9944 0.9388 0.8915 0.8531 0.8234 0.8005 0.7831 350 1.728 1.356 1.159 1.049 0.9790 0.9272 0.8857 0.8520 0.8249 0.8035 0.7867 400 1.769 1.379 1.167 1.046 0.9708 0.9190 0.8800 0.8491 0.8243 0.8044 0.7884 450 1.812 1.404 1.179 1.049 0.9681 0.9143 0.8756 0.8461 0.8227 0.8040 0.7889 500 1.857 1.432 1.195 1.056 0.9693 0.9127 0.8730 0.8437 0.8211 0.8031 0.7886 600 1.493 1.234 1.078 0.9804 0.9165 0.8730 0.8420 0.8190 0.8014 0.7875 700 1.559 1.278 1.108 0.9991 0.9276 0.8789 0.8446 0.8197 0.8012 0.7869 800 1.630 1.328 1.142 1.023 0.9437 0.8893 0.8510 0.8235 0.8031 0.7878 900 1.705 1.381 1.181 1.051 0.9636 0.9033 0.8606 0.8299 0.8073 0.7903 1.437 1.222 1.082 0.9864 0.9201 0.8729 0.8387 0.8135 0.7946 1,000 Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 1 0.7160 0.7163 0.7167 0.7177 0.7208 0.7247 0.7288 0.7327 0.7363 0.7394 0.7422 0.7445 5 0.7164 0.7165 0.7168 0.7177 0.7206 0.7245 0.7286 0.7326 0.7362 0.7393 0.7420 0.7444 10 0.7169 0.7169 0.7170 0.7177 0.7205 0.7243 0.7284 0.7324 0.7360 0.7391 0.7419 0.7442 20 0.7181 0.7177 0.7175 0.7179 0.7203 0.7240 0.7281 0.7320 0.7356 0.7388 0.7416 0.7439 30 0.7195 0.7187 0.7182 0.7181 0.7202 0.7237 0.7277 0.7317 0.7353 0.7385 0.7413 0.7436 40 0.7212 0.7199 0.7191 0.7185 0.7201 0.7235 0.7274 0.7314 0.7350 0.7382 0.7410 0.7434 50 0.7230 0.7212 0.7200 0.7190 0.7201 0.7233 0.7272 0.7311 0.7347 0.7379 0.7407 0.7431 60 0.7249 0.7226 0.7211 0.7196 0.7202 0.7231 0.7269 0.7308 0.7344 0.7376 0.7405 0.7429 70 0.7270 0.7242 0.7223 0.7202 0.7203 0.7230 0.7267 0.7306 0.7342 0.7374 0.7402 0.7426 80 0.7292 0.7259 0.7235 0.7209 0.7205 0.7230 0.7266 0.7304 0.7339 0.7372 0.7400 0.7424 90 0.7315 0.7276 0.7248 0.7217 0.7207 0.7229 0.7264 0.7302 0.7337 0.7369 0.7398 0.7422 100 0.7338 0.7293 0.7262 0.7225 0.7209 0.7229 0.7263 0.7300 0.7335 0.7367 0.7396 0.7420 150 0.7453 0.7384 0.7333 0.7270 0.7226 0.7233 0.7261 0.7294 0.7328 0.7359 0.7387 0.7411 200 0.7556 0.7468 0.7403 0.7317 0.7248 0.7242 0.7263 0.7292 0.7324 0.7353 0.7381 0.7405 250 0.7637 0.7538 0.7463 0.7361 0.7270 0.7254 0.7267 0.7293 0.7322 0.7350 0.7376 0.7400 300 0.7696 0.7592 0.7511 0.7398 0.7293 0.7266 0.7274 0.7296 0.7322 0.7348 0.7373 0.7396 350 0.7734 0.7629 0.7546 0.7429 0.7313 0.7279 0.7281 0.7300 0.7323 0.7348 0.7372 0.7394 400 0.7756 0.7653 0.7571 0.7452 0.7330 0.7291 0.7289 0.7304 0.7326 0.7349 0.7372 0.7392 450 0.7766 0.7667 0.7587 0.7469 0.7345 0.7302 0.7297 0.7310 0.7329 0.7351 0.7372 0.7392 500 0.7769 0.7673 0.7596 0.7480 0.7357 0.7312 0.7305 0.7315 0.7333 0.7353 0.7373 0.7392 600 0.7764 0.7674 0.7600 0.7491 0.7373 0.7327 0.7318 0.7326 0.7341 0.7359 0.7377 0.7394 211 212 D2 Properties of Selected Important Pure Substances D2.3. Table 16. (continued) Temperature in C Pressure in bar 100 125 150 200 300 400 500 600 700 800 900 1,000 700 0.7758 0.7669 0.7598 0.7493 0.7381 0.7338 0.7329 0.7336 0.7349 0.7365 0.7382 0.7397 800 0.7760 0.7668 0.7596 0.7492 0.7384 0.7344 0.7337 0.7344 0.7357 0.7372 0.7387 0.7401 900 0.7775 0.7676 0.7599 0.7491 0.7384 0.7348 0.7342 0.7350 0.7363 0.7378 0.7392 0.7406 1,000 0.7803 0.7694 0.7610 0.7495 0.7384 0.7349 0.7346 0.7355 0.7369 0.7383 0.7397 0.7410 6 1. 2. Bibliography Span R, Lemmon EW, Wagner W, Jacobsen RT (1998) A reference quality equation of state for nitrogen. Int J Thermophys 19:1121–1132 Span R, Lemmon EW, Jacobsen RT, Wagner W, Yokozeki A (2000) A reference equation of state for the thermodynamic properties of nitrogen 3. for temperatures from 63.151 K to 1000 K and pressures to 2200 MPa. J Phys Chem Ref Data 29:1361–1433 Stephan K, Krauss R (1987) Viscosity and thermal conductivity of nitrogen for a wide range of fluid states. J Phys Chem Ref Data 16:993–1023 Properties of Carbon Dioxide D2.4 D2.4 Properties of Carbon Dioxide Roland Span1 . Rolf Krauss2 1 2 Ruhr-Universität Bochum, Bochum, Germany Universität Stuttgart, Stuttgart, Germany 1 Properties of Carbon Dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . 213 4 Triple Point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 2 Characteristic Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 5 Reference States of Enthalpy and Entropy . . . . . . . . . . . . . 213 3 Critical Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 6 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 1 Properties of Carbon Dioxide Tables with thermodynamic properties of carbon dioxide were calculated with the reference equation of state established by Span and Wagner [1]. The thermal conductivity and viscosity of carbon dioxide were calculated with the corresponding equations by Vesovic et al. [2]. The densities required as input to the equations by Vesovic et al. were calculated using the equation by Span and Wagner. The critical enhancement was considered for the thermal conductivity, where it significantly affects a rather large region around the critical point. p Pressure in bar n Specific volume in m3/kg r Density in kg/m3 l Thermal conductivity in mW/(m K) # Temperature in C n Kinematic viscosity n in 107m2/s h Specific enthalpy in kJ/kg Dynamic viscosity in 106 Pa·s s Specific entropy in kJ/(kg K) a Thermal diffusivity in 107 m2/s Z Compression factor Z = p/(rRT) b Isobaric expansion coefficient in 103/K b = n1·(∂n/∂T)p Pr Prandtl number Pr = cp/l cp Specific isobaric heat capacity in kJ/(kg K) ws Isentropic speed of sound in m/s cv Specific isochoric heat capacity in kJ/(kg K) 2 Characteristic Quantities Molecular mass M ~ ¼ 44:0098 g/mol, specific gas constant R = 188.9241 J/(kg K). 3 Critical Point [1] pc = 73.773 bar, Tc = 304.1282 K (#c = 30.9782 C), rc = 467.6 kg/m3. 4 Triple Point [1] pt = 5.1795 bar, Tt =216.592 K (#t = 56.558 C). 5 Reference States of Enthalpy and Entropy h = 506.78 kJ/kg, s = 2.739 kJ/(kg K) at T = 298.15 K (# = 25 C), p = 1.01325 bar corresponding to h’ = 200 kJ/kg, s’ = 1 kJ/(kg K) for saturated liquid at # = 0 C. 213 214 D2 Properties of Selected Important Pure Substances D2.4. Table 1. Properties of carbon dioxide at p = 1 bar q C kg/m3 55 2.461 440.8 2.486 0.7790 50 2.403 444.7 2.504 0.7825 40 2.296 452.6 2.538 30 2.198 460.5 20 2.109 468.5 10 2.027 476.7 h kJ/kg b 103/K ws m/s 0.5771 4.808 232.5 10.78 10.97 44.57 56.24 0.7925 0.5816 4.682 235.0 11.10 11.22 46.69 59.05 0.7907 0.7903 0.5912 4.453 239.9 11.77 11.72 51.05 64.85 0.7873 2.571 0.7988 0.6011 4.248 244.6 12.45 12.22 55.60 70.92 0.7839 2.604 0.8078 0.6113 4.063 249.2 13.17 12.72 60.32 77.28 0.7805 2.635 0.8172 0.6216 3.896 253.7 13.90 13.22 65.21 83.94 0.7769 s cp cv kJ/(kg K) kJ/(kg K) kJ/(kg K) l h n a mW/(m K) 106Pa·s 107 m2/s 107 m2/s Pr – 0 1.951 484.9 2.666 0.8267 0.6319 3.742 258.1 14.66 13.71 70.28 90.89 0.7732 10 1.880 493.2 2.696 0.8363 0.6422 3.601 262.4 15.43 14.20 75.51 98.13 0.7695 20 1.815 501.6 2.725 0.8459 0.6524 3.471 266.6 16.22 14.69 80.92 105.7 0.7659 30 1.754 510.1 2.754 0.8555 0.6624 3.351 270.7 17.03 15.17 86.49 113.5 0.7623 40 1.697 518.7 2.781 0.8650 0.6724 3.239 274.7 17.84 15.65 92.22 121.5 0.7589 50 1.644 527.4 2.809 0.8744 0.6821 3.134 278.7 18.67 16.13 98.12 129.8 0.7557 60 1.594 536.2 2.836 0.8837 0.6917 3.037 282.6 19.50 16.61 104.2 138.4 0.7526 70 1.547 545.1 2.862 0.8929 0.7011 2.945 286.4 20.34 17.08 110.4 147.2 0.7498 80 1.503 554.1 2.888 0.9018 0.7103 2.859 290.2 21.18 17.55 116.8 156.3 0.7471 90 1.461 563.1 2.913 0.9107 0.7193 2.778 294.0 22.03 18.01 123.3 165.5 0.7447 100 1.422 572.3 2.938 0.9193 0.7282 2.702 297.6 22.87 18.47 129.9 175.0 0.7425 110 1.384 581.5 2.962 0.9278 0.7368 2.630 301.3 23.72 18.93 136.8 184.7 0.7404 120 1.349 590.8 2.986 0.9361 0.7453 2.561 304.9 24.57 19.39 143.7 194.6 0.7386 130 1.315 600.2 3.010 0.9443 0.7536 2.497 308.4 25.42 19.84 150.8 204.7 0.7369 140 1.283 609.7 3.033 0.9523 0.7617 2.435 311.9 26.27 20.28 158.1 215.0 0.7353 150 1.253 619.3 3.056 0.9601 0.7696 2.377 315.3 27.12 20.73 165.5 225.4 0.7339 160 1.224 628.9 3.078 0.9678 0.7774 2.321 318.8 27.96 21.17 173.0 236.1 0.7327 170 1.196 638.6 3.101 0.9753 0.7850 2.268 322.1 28.80 21.60 180.6 246.9 0.7316 180 1.169 648.4 3.122 0.9827 0.7925 2.217 325.5 29.64 22.04 188.4 257.9 0.7306 190 1.144 658.3 3.144 0.9900 0.7998 2.168 328.8 30.48 22.47 196.4 269.1 0.7297 200 1.120 668.2 3.165 0.9971 0.8070 2.122 332.0 31.31 22.89 204.4 280.5 0.7289 220 1.074 688.3 3.207 1.011 0.8209 2.035 338.5 32.97 23.73 220.9 303.7 0.7276 240 1.032 708.7 3.247 1.024 0.8342 1.955 344.8 34.62 24.56 237.9 327.5 0.7265 260 0.9933 729.3 3.287 1.037 0.8471 1.881 350.9 36.25 25.37 255.4 351.9 0.7258 280 0.9573 750.1 3.325 1.049 0.8595 1.812 357.0 37.87 26.17 273.4 377.0 0.7252 300 0.9238 771.2 3.363 1.061 0.8714 1.749 363.0 39.47 26.96 291.8 402.6 0.7248 320 0.8926 792.6 3.399 1.072 0.8829 1.689 368.8 41.05 27.74 310.7 428.9 0.7245 340 0.8634 814.1 3.435 1.083 0.8939 1.634 374.6 42.63 28.50 330.1 455.7 0.7243 360 0.8361 835.9 3.470 1.094 0.9046 1.582 380.3 44.18 29.25 349.8 483.0 0.7242 380 0.8105 857.9 3.504 1.104 0.9149 1.533 385.9 45.73 29.99 370.0 510.9 0.7242 400 0.7864 880.1 3.537 1.114 0.9248 1.488 391.4 47.26 30.72 390.6 539.4 0.7242 425 0.7582 908.1 3.578 1.126 0.9367 1.434 398.2 49.15 31.61 416.9 575.7 0.7242 450 0.7319 936.4 3.618 1.137 0.9480 1.384 404.9 51.02 32.49 443.9 612.9 0.7242 475 0.7075 964.9 3.657 1.148 0.9589 1.338 411.4 52.87 33.35 471.4 650.9 0.7242 500 0.6846 993.8 3.695 1.159 0.9693 1.294 417.9 54.70 34.20 499.5 689.7 0.7242 550 0.6430 1,052 3.768 1.178 0.9888 1.216 430.5 58.31 35.84 557.5 769.8 0.7242 600 0.6061 1,112 3.838 1.196 1.007 1.146 442.7 61.84 37.44 617.7 853.2 0.7239 650 0.5733 1,172 3.905 1.212 1.023 1.084 454.7 65.30 38.98 680.0 939.8 0.7235 700 0.5438 1,233 3.969 1.227 1.038 1.028 466.3 68.69 40.48 744.3 1,030 0.7229 750 0.5172 1,294 4.031 1.240 1.051 0.9776 477.7 72.03 41.93 810.6 1,123 0.7221 800 0.4931 1,357 4.091 1.253 1.064 0.9320 488.8 75.30 43.34 878.9 1,219 0.7212 850 0.4712 1,420 4.148 1.264 1.075 0.8905 499.6 78.52 44.72 900 0.4511 1,483 4.203 1.275 1.086 0.8525 510.2 81.69 46.06 949.0 1,021 1,318 0.7201 1,420 0.7189 Properties of Carbon Dioxide D2.4 D2.4. Table 2. Properties of the saturated liquid q C p bar r0 kg/m3 h0 kJ/kg s0 cp 0 cv0 b0 kJ/(kg K) kJ/(kg K) kJ/(kg K) 103/K 56 5.306 1,177 81.04 0.5259 1.971 0.9851 3.100 972.3 180.1 256.1 2.176 0.7765 2.803 54 5.780 1,169 85.00 0.5439 1.973 0.9801 3.153 958.0 177.4 247.5 2.117 0.7689 2.753 52 6.286 1,162 88.96 0.5617 1.976 0.9754 3.209 943.6 174.7 239.3 2.060 0.7610 2.706 50 6.824 1,155 92.93 0.5793 1.980 0.9711 3.267 929.1 172.1 231.5 2.005 0.7529 2.663 48 7.395 1,147 96.91 0.5968 1.985 0.9671 3.330 914.7 169.5 224.1 1.954 0.7446 2.624 46 8.002 1,140 100.9 0.6142 1.990 0.9634 3.395 900.2 166.9 217.0 1.904 0.7360 2.587 44 8.645 1,132 104.9 0.6315 1.997 0.9600 3.465 885.6 164.4 210.2 1.857 0.7272 2.553 42 9.325 1,124 108.9 0.6487 2.005 0.9568 3.539 871.0 161.9 203.6 1.811 0.7181 2.522 40 10.05 1,116 112.9 0.6658 2.013 0.9539 3.617 856.4 159.4 197.3 1.768 0.7089 2.494 38 10.81 1,109 117.0 0.6828 2.023 0.9512 3.699 841.7 156.9 191.3 1.726 0.6994 2.467 36 11.61 1,101 121.1 0.6997 2.034 0.9487 3.787 826.9 154.4 185.5 1.685 0.6898 2.443 34 12.45 1,092 125.1 0.7165 2.045 0.9464 3.881 812.0 151.9 179.8 1.646 0.6799 2.421 32 13.34 1,084 129.2 0.7333 2.058 0.9444 3.980 797.1 149.5 174.4 1.609 0.6699 2.401 30 14.28 1,076 133.4 0.7500 2.072 0.9425 4.087 782.1 147.0 169.1 1.572 0.6596 2.384 28 15.26 1,067 137.5 0.7666 2.087 0.9407 4.201 767.0 144.6 164.0 1.537 0.6491 2.368 26 16.29 1,059 141.7 0.7832 2.104 0.9392 4.323 751.7 142.2 159.1 1.503 0.6384 2.354 24 17.37 1,050 145.9 0.7998 2.122 0.9379 4.454 736.4 139.8 154.3 1.470 0.6274 2.343 22 18.51 1,041 150.2 0.8164 2.142 0.9367 4.595 721.0 137.4 149.6 1.438 0.6162 2.333 20 19.70 1,032 154.5 0.8329 2.164 0.9357 4.747 705.4 135.0 145.1 1.406 0.6048 2.325 18 20.94 1,022 158.8 0.8495 2.187 0.9349 4.913 689.7 132.6 140.7 1.376 0.5930 2.320 16 22.24 1,013 163.2 0.8660 2.213 0.9342 5.092 673.9 130.2 136.3 1.346 0.5810 2.317 14 23.59 1,003 167.6 0.8825 2.241 0.9338 5.288 657.9 127.8 132.1 1.317 0.5687 2.316 ws0 m/s h0 l0 n0 a0 mW/(m K) 106 Pa·s 107 m2/s 107 m2/s Pr0 – 12 25.01 993.1 172.0 0.8991 2.272 0.9335 5.503 641.7 125.4 128.0 1.289 0.5560 2.318 10 26.49 982.9 176.5 0.9157 2.306 0.9335 5.740 625.3 123.0 123.9 1.261 0.5429 2.323 8 28.03 972.4 181.1 0.9324 2.343 0.9337 6.001 608.7 120.7 120.0 1.234 0.5294 2.330 6 29.63 961.7 185.7 0.9492 2.385 0.9343 6.292 591.8 118.3 116.1 1.207 0.5156 2.341 4 31.30 950.6 190.4 0.9660 2.432 0.9353 6.617 574.5 115.9 112.2 1.181 0.5012 2.356 2 33.04 939.2 195.2 0.9829 2.484 0.9368 6.983 556.9 113.5 108.5 1.155 0.4864 2.374 0 34.85 927.4 200.0 1.000 2.542 0.9390 7.397 538.9 111.0 104.7 1.129 0.4710 2.398 2 36.73 915.2 204.9 1.017 2.608 0.9420 7.869 520.4 108.6 101.0 1.104 0.4550 2.427 4 38.69 902.5 209.9 1.035 2.684 0.9459 8.412 501.6 106.2 97.38 1.079 0.4383 2.462 6 40.72 889.3 215.1 1.052 2.772 0.9509 9.042 482.3 103.7 93.75 1.054 0.4209 2.505 8 42.83 875.5 220.3 1.070 2.874 0.9569 9.783 462.6 101.3 90.14 1.030 0.4026 2.558 10 45.02 861.0 225.7 1.088 2.996 0.9639 10.67 442.7 98.86 86.54 1.005 0.3832 2.622 12 47.30 845.8 231.3 1.107 3.143 0.9720 11.75 422.4 96.42 82.93 0.9804 0.3627 2.703 14 49.66 829.6 237.0 1.126 3.325 0.9809 13.09 401.8 94.00 79.30 0.9558 0.3408 2.805 16 52.11 812.4 243.0 1.146 3.555 0.9908 14.81 380.8 91.61 75.63 0.9309 0.3172 2.935 18 54.65 793.8 249.2 1.166 3.856 1.002 17.09 359.4 89.28 71.89 0.9057 0.2917 3.105 20 57.29 773.4 255.8 1.188 4.266 1.015 20.26 337.1 87.07 68.07 0.8801 0.2639 3.335 22 60.03 750.8 262.9 1.210 4.855 1.030 24.90 313.8 85.06 64.09 0.8536 0.2333 3.659 24 62.88 725.0 270.6 1.235 5.778 1.052 32.35 289.0 83.39 59.87 0.8259 0.1991 4.149 26 65.84 694.4 279.3 1.263 7.448 1.085 46.22 261.5 82.37 55.26 0.7958 0.1593 4.997 28 68.92 655.3 289.6 1.296 11.50 1.148 81.20 228.7 83.06 50.05 0.7637 0.1102 30 72.14 593.3 304.6 1.343 35.11 1.354 180.8 94.73 43.73 0.7371 0.04548 297.2 6.932 16.21 215 216 D2 Properties of Selected Important Pure Substances D2.4. Table 3. Properties of the saturated vapor r00 kg/m3 s00 cp00 h00 cv00 b00 kJ/kg kJ/(kg K) kJ/(kg K) kJ/(kg K) 103/K h00 l00 n00 a00 mW/(m K) 106 Pa·s 107 m2/s 107 m2/s Pr00 – q C p bar 56 5.306 14.08 430.6 2.136 0.9176 0.6346 6.162 222.8 11.11 10.97 7.793 8.597 0.9065 54 5.780 15.28 431.4 2.124 0.9308 0.6407 6.219 223.0 11.28 11.08 7.251 7.932 0.9142 52 6.286 16.56 432.0 2.113 0.9447 0.6469 6.283 223.2 11.46 11.19 6.756 7.327 0.9221 50 6.824 17.93 432.7 2.102 0.9592 0.6533 6.353 223.3 11.65 11.30 6.303 6.775 0.9304 48 7.395 19.37 433.3 2.091 0.9744 0.6599 6.429 223.4 11.84 11.41 5.889 6.272 0.9389 46 8.002 20.91 433.9 2.080 0.9903 0.6665 6.513 223.4 12.04 11.52 5.508 5.812 0.9477 44 8.645 22.55 434.4 2.069 1.007 0.6734 6.605 223.5 12.24 11.63 5.158 5.391 0.9568 42 9.325 24.28 434.9 2.059 1.025 0.6803 6.705 223.4 12.45 11.74 4.836 5.005 0.9663 ws00 m/s 40 10.05 26.12 435.3 2.048 1.043 0.6875 6.813 223.4 12.67 11.86 4.539 4.650 0.9762 38 10.81 28.07 435.7 2.038 1.063 0.6947 6.931 223.2 12.90 11.97 4.265 4.324 0.9864 36 11.61 30.14 436.1 2.028 1.083 0.7022 7.059 223.1 13.14 12.09 4.011 4.023 0.9970 34 12.45 32.33 436.4 2.018 1.105 0.7098 7.199 222.9 13.38 12.21 3.776 3.746 1.008 32 13.34 34.65 436.6 2.008 1.128 0.7175 7.350 222.6 13.64 12.33 3.558 3.490 1.020 30 14.28 37.10 436.8 1.998 1.153 0.7255 7.514 222.4 13.91 12.45 3.355 3.253 1.032 28 15.26 39.70 436.9 1.988 1.179 0.7336 7.692 222.0 14.19 12.57 3.167 3.033 1.044 26 16.29 42.45 437.0 1.978 1.206 0.7418 7.886 221.6 14.49 12.70 2.992 2.829 1.057 24 17.37 45.36 437.0 1.968 1.236 0.7503 8.097 221.2 14.80 12.83 2.828 2.640 1.071 22 18.51 48.44 437.0 1.958 1.267 0.7589 8.328 220.7 15.12 12.96 2.675 2.464 1.086 20 19.70 51.70 436.9 1.949 1.301 0.7677 8.580 220.2 15.47 13.09 2.533 2.300 1.101 18 20.94 55.16 436.7 1.939 1.337 0.7767 8.856 219.6 15.83 13.23 2.399 2.146 1.118 16 22.24 58.82 436.4 1.929 1.377 0.7861 9.160 219.0 16.22 13.38 2.274 2.003 1.136 14 23.59 62.70 436.1 1.919 1.420 0.7958 9.495 218.4 16.63 13.52 2.157 1.868 1.155 12 25.01 66.82 435.7 1.909 1.467 0.8059 9.864 217.6 17.07 13.68 2.047 1.741 1.175 10 26.49 71.19 435.1 1.898 1.519 0.8166 10.27 216.8 17.54 13.83 1.943 1.622 1.198 8 28.03 75.83 434.5 1.888 1.576 0.8277 10.73 216.0 18.04 14.00 1.846 1.510 1.223 6 29.63 80.77 433.8 1.878 1.639 0.8394 11.24 215.1 18.58 14.17 1.755 1.403 1.250 4 31.30 86.04 432.9 1.867 1.710 0.8517 11.82 214.1 19.16 14.35 1.668 1.303 1.280 2 33.04 91.65 432.0 1.856 1.789 0.8647 12.46 213.0 19.80 14.55 1.587 1.208 1.314 0 34.85 1.845 1.878 0.8783 13.20 211.9 20.49 14.75 1.510 1.117 1.352 2 36.73 104.1 429.6 1.834 1.979 0.8927 14.04 210.7 21.24 14.96 1.438 1.031 1.395 4 38.69 111.0 428.2 1.822 2.096 0.9078 15.02 209.4 22.07 15.20 1.369 0.9488 1.443 6 40.72 118.4 426.7 1.810 2.230 0.9238 16.15 208.1 22.98 15.45 1.304 0.8702 1.499 8 42.83 126.4 424.9 1.798 2.388 0.9408 17.50 206.7 24.00 15.72 1.243 0.7947 1.564 10 45.02 135.2 422.9 1.785 2.577 0.9590 19.10 205.1 25.15 16.01 1.185 0.7220 1.641 12 47.30 144.7 420.6 1.771 2.805 0.9786 21.06 203.5 26.44 16.34 1.130 0.6515 1.734 14 49.66 155.1 418.0 1.756 3.088 0.9999 23.48 201.8 27.92 16.71 1.077 0.5830 1.848 16 52.11 166.7 415.1 1.741 3.448 1.023 26.58 199.9 29.65 17.12 1.028 0.5159 1.992 18 54.65 179.6 411.8 1.724 3.922 1.050 30.67 197.9 31.68 17.60 0.9802 0.4499 2.178 20 57.29 194.2 407.9 1.706 4.574 1.080 36.30 195.7 34.16 18.16 0.9351 0.3846 2.431 22 60.03 211.0 403.3 1.686 5.531 1.117 44.54 193.2 37.27 18.83 0.8920 0.3193 2.794 24 62.88 231.0 397.8 1.663 7.065 1.162 57.73 190.4 41.39 19.66 0.8509 0.2536 3.356 26 65.84 255.8 390.8 1.635 9.918 1.224 82.17 186.8 47.35 20.76 0.8114 0.1866 4.348 28 68.92 289.1 381.2 1.600 16.96 1.321 142.2 181.6 57.59 22.37 0.7737 0.1174 30 72.14 345.3 365.0 1.543 57.48 1.550 485.1 170.5 93.37 25.67 0.7434 0.04705 97.65 430.9 6.589 15.80 Properties of Carbon Dioxide D2.4 D2.4. Table 4. Density r of carbon dioxide in kg/m3 Temperature in C Pressure in bar 1 5 55 2.461 13.12 50 2.403 12.74 40 2.296 12.06 25.99 30 2.198 11.47 24.38 20 2.109 10 2.027 0 10 20 30 40 50 1.951 1.880 1.815 1.754 1.697 1.644 9.637 9.276 8.944 8.636 8.350 10.94 10.46 10.03 23.03 21.86 20.84 19.92 19.10 18.35 17.67 48.76 45.61 43.00 40.77 38.84 37.13 35.60 77.33 71.01 66.16 62.21 58.89 56.03 10 1,174 1,155 20 1,176 1,158 1,119 1,078 1,032 30 1,178 1,160 1,122 1,081 1,036 985.1 40 1,180 1,162 1,125 1,085 1,041 991.1 932.1 108.4 50 1,182 1,164 1,127 1,088 1,045 996.7 940.5 868.5 140.6 124.0 113.0 104.8 60 1,184 1,167 1,130 1,091 1,049 1,002 948.2 881.7 782.7 171.5 149.3 135.2 70 1,186 1,169 1,133 1,094 1,053 1,007 955.3 893.1 808.6 266.5 198.0 172.0 80 1,188 1,171 1,135 1,097 1,057 1,012 962.0 903.1 827.7 701.7 277.9 219.2 97.49 89.76 83.76 17.04 78.86 90 1,190 1,173 1,138 1,100 1,060 1,017 968.2 912.2 843.2 744.3 485.6 285.0 100 1,192 1,175 1,140 1,103 1,064 1,021 974.1 920.5 856.3 771.5 628.7 384.4 150 1,201 1,185 1,151 1,117 1,080 1,041 999.6 954.3 904.0 847.0 780.3 699.8 200 1,209 1,194 1,162 1,129 1,094 1,058 1,021 980.3 937.2 890.6 839.9 784.4 250 1,217 1,202 1,172 1,140 1,107 1,074 1,038 1,002 963.1 922.5 879.6 834.4 300 1,225 1,210 1,181 1,150 1,119 1,087 1,054 1,020 984.7 948.1 910.0 870.6 350 1,232 1,218 1,189 1,160 1,130 1,100 1,068 1,036 1,003 969.6 934.9 899.4 400 1,239 1,225 1,197 1,169 1,140 1,111 1,081 1,051 1,020 988.3 956.1 923.4 450 1,246 1,232 1,205 1,178 1,150 1,122 1,093 1,064 1,035 1,005 974.6 944.1 500 1,252 1,239 1,213 1,186 1,159 1,132 1,104 1,076 1,048 1,020 991.2 962.4 600 1,264 1,252 1,226 1,201 1,176 1,150 1,124 1,098 1,072 1,046 1,020 700 1,275 1,263 1,239 1,215 1,191 1,166 1,142 1,117 1,093 1,069 1,044 1,020 800 1,286 1,274 1,251 1,228 1,204 1,181 1,158 1,135 1,112 1,089 1,066 1,043 900 1,296 1,284 1,262 1,240 1,217 1,195 1,173 1,150 1,128 1,107 1,085 1,063 1,000 1,305 1,294 1,272 1,251 1,229 1,208 1,186 1,165 1,144 1,123 1,102 1,082 2,000 1,380 1,371 1,354 1,336 1,319 1,302 1,286 1,269 1,253 1,237 1,222 1,207 993.7 Temperature in C Pressure in bar 1 5 60 80 1.594 1.503 8.084 7.602 100 1.422 7.176 150 1.253 6.300 200 300 400 500 600 700 800 900 1.120 0.9238 0.7864 0.6846 0.6061 0.5438 0.4931 0.4511 5.619 4.626 3.933 3.422 3.029 2.717 2.463 2.253 9.267 7.868 6.841 6.052 5.428 4.921 4.501 9.821 8.982 10 16.46 15.43 14.52 12.69 11.29 20 34.22 31.81 29.77 25.77 22.79 18.59 15.75 13.67 12.09 10.83 30 53.52 49.29 45.82 39.24 34.50 27.98 23.63 20.49 18.10 16.22 14.70 13.44 40 74.73 68.03 62.75 53.13 46.42 37.42 31.52 27.29 24.09 21.58 19.55 17.88 88.24 80.66 67.43 58.55 46.92 39.41 34.08 30.06 26.92 24.39 22.30 99.64 82.18 70.89 56.46 47.30 40.85 36.01 32.24 29.20 26.69 97.37 83.43 66.04 55.19 47.60 41.94 37.53 33.99 31.07 96.16 50 98.30 60 124.9 110.1 70 155.5 134.1 119.8 80 191.6 160.3 141.3 113.0 75.67 63.08 54.34 47.85 42.80 38.76 35.43 90 235.4 189.4 164.2 129.1 109.1 85.32 70.96 61.06 53.73 48.05 43.50 39.76 100 290.0 221.6 188.6 145.6 122.2 95.00 78.82 67.76 59.59 53.28 48.22 44.08 150 603.9 426.8 332.2 234.0 189.8 143.6 117.9 100.9 79.03 71.50 65.34 200 723.8 594.1 480.4 327.1 259.0 192.0 156.3 133.3 94.19 86.08 88.51 116.7 104.2 217 218 D2 Properties of Selected Important Pure Substances D2.4. Table 4. (continued) Temperature in C Pressure in bar 60 80 100 150 200 250 786.8 686.6 589.0 415.1 326.6 239.2 193.8 164.8 144.2 128.6 116.3 106.3 300 830.0 746.0 662.3 492.2 389.6 284.7 230.0 195.3 170.8 152.3 137.8 126.0 350 863.2 789.4 715.7 555.8 446.7 327.8 264.7 224.7 196.5 175.3 158.6 145.1 400 890.3 823.5 757.1 607.4 497.4 368.3 297.9 253.0 221.4 197.6 178.9 163.7 450 913.4 851.7 790.7 650.4 541.8 406.0 329.4 280.1 245.3 219.1 198.5 181.7 500 933.5 875.8 819.0 687.0 580.5 441.0 359.4 306.1 268.3 239.9 217.5 199.3 600 967.6 915.8 865.0 746.3 645.3 503.2 414.4 354.7 311.9 279.3 253.7 232.8 700 996.0 948.3 901.8 792.9 697.7 556.3 463.5 399.2 352.1 316.2 287.7 264.4 975.9 932.6 831.1 741.3 602.2 507.2 439.7 389.4 350.6 319.6 294.2 800 1,020 300 400 500 600 700 800 900 900 1,042 1,000 959.1 863.5 778.4 642.4 546.4 476.7 423.9 382.7 349.6 322.4 1,000 1,061 1,021 982.6 891.7 810.5 678.1 581.7 510.6 456.0 412.9 378.0 349.1 2,000 1,192 1,162 901.3 814.9 743.5 684.1 634.1 591.6 554.9 1,134 1,067 1,007 D2.4. Table 5. Compression factor Z of carbon dioxide Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 1 0.9859 0.9870 0.9888 0.9902 0.9915 0.9925 0.9934 0.9941 0.9948 0.9953 0.9958 0.9962 5 0.9250 0.9310 0.9411 0.9493 0.9559 0.9614 0.9660 0.9699 0.9733 0.9761 0.9786 0.9808 10 0.02067 0.02053 0.8737 0.8928 0.9079 0.9200 0.9300 0.9384 0.9454 0.9515 0.9566 0.9611 20 0.04127 0.04098 0.04057 0.04040 0.04053 0.8250 0.8498 0.8695 0.8857 0.8992 0.9105 0.9203 30 0.06179 0.06135 0.06070 0.06040 0.06053 0.06126 0.7518 0.7898 0.8188 0.8420 0.8611 0.8770 40 0.08224 0.08164 0.08074 0.08028 0.08037 0.08118 0.08316 0.6898 0.7409 0.7781 0.8072 0.8309 50 0.1026 0.1019 0.1007 0.1001 0.1001 0.1009 0.1030 0.1076 0.6419 0.7040 0.7476 0.7812 60 0.1229 0.1220 0.1205 0.1197 0.1196 0.1204 0.1226 0.1272 0.1384 0.6110 0.6795 0.7269 70 0.1432 0.1421 0.1403 0.1393 0.1390 0.1398 0.1420 0.1465 0.1563 0.4586 0.5975 0.6666 80 0.1534 0.1621 0.1600 0.1587 0.1583 0.1590 0.1612 0.1656 0.1745 0.1991 0.4866 0.5978 90 0.1835 0.1820 0.1796 0.1781 0.1775 0.1781 0.1801 0.1844 0.1927 0.2111 0.3133 0.5173 100 0.2036 0.2019 0.1992 0.1974 0.1966 0.1970 0.1989 0.2031 0.2109 0.2263 0.2689 0.4262 150 0.3031 0.3004 0.2958 0.2924 0.2904 0.2898 0.2908 0.2938 0.2996 0.3092 0.3250 0.3511 200 0.4013 0.3974 0.3908 0.3857 0.3821 0.3801 0.3798 0.3814 0.3853 0.3921 0.4025 0.4176 250 0.4983 0.4932 0.4845 0.4774 0.4720 0.4684 0.4665 0.4666 0.4687 0.4732 0.4804 0.4908 300 0.5943 0.5879 0.5768 0.5677 0.5604 0.5550 0.5514 0.5498 0.5501 0.5525 0.5572 0.5644 350 0.6892 0.6816 0.6681 0.6568 0.6475 0.6402 0.6348 0.6313 0.6298 0.6303 0.6328 0.6374 400 0.7833 0.7743 0.7584 0.7448 0.7334 0.7241 0.7168 0.7115 0.7082 0.7067 0.7072 0.7096 450 0.8765 0.8662 0.8477 0.8318 0.8182 0.8069 0.7977 0.7905 0.7853 0.7819 0.7805 0.7808 500 0.9690 0.9573 0.9362 0.9178 0.9021 0.8887 0.8775 0.8684 0.8613 0.8561 0.8527 0.8510 600 1.152 1.137 1.111 1.088 1.067 1.050 1.034 1.021 1.010 1.002 0.9944 0.9890 700 1.332 1.314 1.283 1.254 1.229 1.207 1.188 1.171 1.156 1.144 1.133 1.124 800 1.510 1.489 1.452 1.419 1.389 1.362 1.339 1.318 1.299 1.283 1.269 1.256 900 1.685 1.662 1.619 1.581 1.546 1.515 1.487 1.462 1.440 1.420 1.402 1.386 1,000 1.859 1.833 1.784 1.741 1.701 1.666 1.634 1.605 1.579 1.555 1.534 1.514 2,000 3.516 3.459 3.354 3.258 3.170 3.089 3.014 2.945 2.882 2.822 2.767 2.715 D2.4 Properties of Carbon Dioxide D2.4. Table 5. (continued) Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 1 0.9966 0.9972 0.9977 0.9986 0.9991 0.9997 1.000 1.000 1.000 1.000 1.000 1.000 5 0.9827 0.9859 0.9884 0.9927 0.9954 0.9983 0.9997 1.000 1.001 1.001 1.001 1.001 10 0.9651 0.9716 0.9767 0.9854 0.9908 0.9966 0.9994 1.001 1.002 1.002 1.002 1.002 20 0.9287 0.9423 0.9529 0.9709 0.9817 0.9933 0.9988 1.002 1.003 1.004 1.005 1.005 30 0.8905 0.9122 0.9288 0.9563 0.9727 0.9902 0.9984 1.003 1.005 1.006 1.007 1.007 40 0.8505 0.8813 0.9042 0.9419 0.9639 0.9871 0.9980 1.004 1.007 1.008 1.009 1.009 50 0.8082 0.8493 0.8794 0.9275 0.9553 0.9842 0.9977 1.005 1.008 1.010 1.011 1.012 60 0.7632 0.8165 0.8542 0.9133 0.9469 0.9815 0.9974 1.006 1.010 1.012 1.014 1.014 70 0.7151 0.7826 0.8288 0.8993 0.9387 0.9789 0.9973 1.007 1.012 1.014 1.016 1.017 80 0.6633 0.7479 0.8032 0.8856 0.9307 0.9764 0.9973 1.008 1.014 1.017 1.018 1.019 90 0.6075 0.7124 0.7776 0.8721 0.9231 0.9742 0.9974 1.009 1.015 1.019 1.020 1.021 100 0.5479 0.6764 0.7522 0.8591 0.9157 0.9721 0.9976 1.010 1.017 1.021 1.023 1.024 150 0.3946 0.5268 0.6405 0.8017 0.8843 0.9646 1.000 1.018 1.027 1.032 1.035 1.036 200 0.4390 0.5046 0.5906 0.7648 0.8639 0.9622 1.006 1.027 1.039 1.045 1.047 1.048 250 0.5048 0.5458 0.6021 0.7533 0.8563 0.9652 1.014 1.039 1.051 1.058 1.060 1.061 300 0.5743 0.6027 0.6426 0.7624 0.8614 0.9732 1.026 1.052 1.065 1.071 1.074 1.075 350 0.6442 0.6646 0.6937 0.7877 0.8766 0.9860 1.040 1.066 1.080 1.086 1.088 1.088 400 0.7138 0.7280 0.7495 0.8237 0.8997 1.003 1.056 1.082 1.095 1.101 1.103 1.103 450 0.7828 0.7919 0.8073 0.8655 0.9292 1.024 1.074 1.100 1.112 1.117 1.118 1.117 500 0.8510 0.8557 0.8660 0.9105 0.9635 1.047 1.094 1.118 1.130 1.134 1.134 1.132 600 0.9853 0.9820 0.9839 1.006 1.040 1.101 1.138 1.158 1.166 1.168 1.167 1.163 700 1.117 1.106 1.101 1.104 1.122 1.162 1.188 1.201 1.205 1.204 1.200 1.194 800 1.246 1.229 1.217 1.204 1.207 1.227 1.240 1.246 1.245 1.241 1.235 1.227 900 1.372 1.349 1.331 1.304 1.293 1.294 1.295 1.293 1.287 1.279 1.270 1.259 1,000 1.497 1.468 1.444 1.403 1.380 1.362 1.352 1.341 1.329 1.317 1.305 1.292 2,000 2.667 2.579 2.502 2.344 2.223 2.049 1.930 1.842 1.772 1.715 1.667 1.626 D2.4. Table 6. Specific enthalpy h of carbon dioxide in kJ/kg Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 1 440.8 444.7 452.6 460.5 468.5 476.7 484.9 493.2 501.6 510.1 518.7 527.4 5 432.3 436.7 445.6 454.3 462.9 471.6 480.2 488.9 497.7 506.5 515.3 524.3 10 83.14 93.01 435.4 445.5 455.2 464.7 474.0 483.3 492.5 501.7 510.9 520.2 20 83.42 93.25 113.1 133.4 154.5 448.6 460.0 470.8 481.3 491.5 501.6 511.6 30 83.71 93.50 113.2 133.4 154.3 176.4 442.2 456.0 468.5 480.2 491.4 502.4 40 84.00 93.75 113.4 133.5 154.2 175.9 199.5 436.6 453.0 467.1 480.1 492.3 50 84.29 94.02 113.6 133.5 154.0 175.5 198.5 224.6 432.4 451.4 467.1 481.1 60 84.59 94.29 113.8 133.6 154.0 175.2 197.7 222.8 254.3 430.7 451.7 468.5 70 84.90 94.57 114.0 133.7 153.9 174.9 197.1 221.3 249.9 392.7 432.1 453.9 80 85.21 94.85 114.2 133.8 153.9 174.7 196.5 220.0 246.9 284.1 402.8 436.3 90 85.53 95.14 114.4 134.0 153.9 174.5 196.0 219.0 244.6 276.3 343.7 413.8 219 220 D2 Properties of Selected Important Pure Substances D2.4. Table 6. (continued) Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 100 85.85 95.44 114.7 134.1 153.9 174.3 195.5 218.0 242.7 271.6 313.0 384.0 150 87.53 97.00 115.9 135.0 154.3 173.9 194.1 215.0 236.8 260.1 285.5 313.9 200 89.31 98.67 117.4 136.1 155.0 174.1 193.5 213.4 233.9 255.0 277.0 300.1 250 91.18 100.4 118.9 137.4 156.0 174.7 193.6 212.8 232.3 252.2 272.6 293.5 300 93.11 102.3 120.6 138.9 157.1 175.5 194.0 212.7 231.6 250.8 270.2 289.8 350 95.11 104.2 122.4 140.4 158.5 176.6 194.8 213.1 231.5 250.1 268.8 287.7 400 97.17 106.2 124.2 142.1 160.0 177.9 195.8 213.8 231.8 250.0 268.2 286.5 450 99.28 108.3 126.2 143.9 161.6 179.3 197.0 214.7 232.5 250.3 268.1 286.0 500 101.4 110.4 128.2 145.8 163.3 180.8 198.3 215.8 233.3 250.9 268.4 285.9 600 105.8 114.7 132.3 149.7 167.0 184.3 201.4 218.6 235.7 252.8 269.9 286.9 700 110.4 119.2 136.6 153.9 171.0 188.0 204.9 221.8 238.6 255.4 272.1 288.8 800 115.0 123.8 141.1 158.2 175.1 192.0 208.7 225.4 242.0 258.5 275.0 291.4 900 119.8 128.5 145.7 162.6 179.4 196.1 212.7 229.2 245.7 262.0 278.3 294.5 1,000 124.6 133.3 150.3 167.2 183.9 200.5 216.9 233.3 249.6 265.8 281.9 297.9 2,000 175.3 183.7 200.2 216.5 232.7 248.7 264.6 280.3 296.0 311.5 327.0 342.3 Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 1 536.2 554.1 572.3 619.3 668.2 771.2 880.1 993.8 1,112 1,233 1,357 1,483 5 533.2 551.4 569.9 617.5 666.8 770.3 879.4 993.3 1,111 1,232 1,357 1,483 10 529.4 548.1 567.0 615.2 665.0 769.1 878.6 992.7 1,111 1,232 1,356 1,483 20 521.5 541.2 560.9 610.6 661.4 766.7 876.9 991.6 1,110 1,232 1,356 1,483 30 513.1 534.0 554.7 606.0 657.8 764.3 875.3 990.4 1,109 1,231 1,356 1,483 40 504.0 526.5 548.2 601.3 654.1 761.9 873.6 989.3 1,108 1,231 1,355 1,483 50 494.2 518.5 541.5 596.5 650.5 759.6 872.0 988.1 1,108 1,230 1,355 1,482 60 483.4 510.1 534.5 591.7 646.8 757.3 870.5 987.0 1,107 1,230 1,355 1,482 70 471.5 501.2 527.3 586.8 643.2 755.0 868.9 985.9 1,106 1,229 1,354 1,482 80 458.1 491.7 519.9 581.9 639.5 752.7 867.3 984.9 1,105 1,229 1,354 1,482 90 442.7 481.6 512.1 576.9 635.9 750.4 865.8 983.8 1,105 1,228 1,354 1,482 100 425.0 470.9 504.1 571.9 632.2 748.1 864.3 982.8 1,104 1,228 1,354 1,482 150 346.5 412.8 462.1 546.8 614.4 737.3 857.0 977.8 1,101 1,225 1,352 1,481 200 324.4 376.1 426.2 523.3 597.6 727.2 850.4 973.3 1,098 1,223 1,351 1,481 250 315.0 359.5 404.3 503.7 582.7 718.0 844.3 969.2 1,095 1,222 1,350 1,480 300 309.8 350.5 391.7 488.3 570.2 709.8 838.9 965.6 1,092 1,220 1,350 1,480 350 306.7 345.2 383.9 477.1 559.9 702.7 834.0 962.4 1,090 1,219 1,349 1,481 400 304.9 341.8 378.9 469.1 551.6 696.5 829.8 959.6 1,089 1,218 1,349 1,481 450 303.9 339.7 375.5 463.4 545.1 691.3 826.1 957.2 1,087 1,218 1,349 1,481 500 303.5 338.5 373.4 459.1 540.1 687.0 823.0 955.1 1,086 1,217 1,349 1,482 600 303.9 337.7 371.4 454.0 533.5 680.6 818.2 952.1 1,085 1,217 1,350 1,484 700 305.4 338.5 371.2 451.7 529.8 676.7 815.2 950.2 1,084 1,217 1,351 1,486 800 307.7 340.2 372.4 451.3 528.1 674.6 813.6 949.4 1,084 1,218 1,353 1,488 900 310.6 342.6 374.3 452.1 527.9 673.8 813.2 949.5 1,085 1,220 1,355 1,491 1,000 313.9 345.5 376.9 453.8 528.9 674.1 813.7 950.4 1,086 1,222 1,358 1,494 2,000 357.5 387.7 417.6 491.1 563.2 704.6 843.9 982.3 1,121 1,259 1,398 1,537 D2.4 Properties of Carbon Dioxide D2.4. Table 7. Specific entropy s of carbon dioxide in kJ/(kg K) Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 1 2.486 2.504 2.538 2.571 2.604 2.635 2.666 2.696 2.725 2.754 2.781 2.809 5 2.154 2.174 2.213 2.249 2.284 2.318 2.350 2.381 2.411 2.441 2.470 2.498 10 0.5337 0.5784 2.050 2.092 2.131 2.168 2.203 2.236 2.268 2.299 2.329 2.358 20 0.5311 0.5756 0.6626 0.7478 0.8328 1.992 2.034 2.073 2.109 2.144 2.176 2.208 30 0.5285 0.5729 0.6594 0.7441 0.8283 0.9137 1.907 1.957 2.000 2.039 2.076 2.110 40 0.5259 0.5702 0.6564 0.7405 0.8239 0.9081 0.9960 1.848 1.905 1.952 1.994 2.033 50 0.5234 0.5675 0.6533 0.7370 0.8197 0.9028 0.9887 1.082 1.805 1.869 1.920 1.964 60 0.5209 0.5649 0.6504 0.7336 0.8156 0.8978 0.9819 1.072 1.181 1.778 1.846 1.899 70 0.5185 0.5623 0.6474 0.7302 0.8117 0.8929 0.9756 1.063 1.162 1.637 1.765 1.834 80 0.5160 0.5597 0.6446 0.7269 0.8078 0.8882 0.9696 1.054 1.148 1.272 1.658 1.763 90 0.5136 0.5572 0.6417 0.7237 0.8041 0.8837 0.9639 1.047 1.136 1.242 1.460 1.681 100 0.5113 0.5547 0.6390 0.7206 0.8004 0.8794 0.9586 1.040 1.125 1.222 1.356 1.579 150 0.4998 0.5427 0.6257 0.7057 0.7834 0.8596 0.9348 1.010 1.086 1.164 1.246 1.335 200 0.4889 0.5314 0.6133 0.6919 0.7680 0.8421 0.9147 0.9862 1.057 1.128 1.199 1.272 250 0.4786 0.5206 0.6016 0.6792 0.7540 0.8265 0.8970 0.9660 1.034 1.101 1.167 1.233 300 0.4687 0.5104 0.5906 0.6672 0.7409 0.8121 0.8812 0.9484 1.014 1.078 1.141 1.203 350 0.4592 0.5006 0.5801 0.6560 0.7288 0.7989 0.8667 0.9325 0.9964 1.059 1.120 1.179 400 0.4501 0.4912 0.5701 0.6453 0.7173 0.7865 0.8533 0.9180 0.9806 1.041 1.101 1.158 450 0.4413 0.4822 0.5605 0.6351 0.7064 0.7749 0.8409 0.9046 0.9662 1.026 1.084 1.140 500 0.4328 0.4734 0.5513 0.6254 0.6961 0.7639 0.8292 0.8921 0.9529 1.012 1.069 1.124 600 0.4166 0.4569 0.5339 0.6071 0.6768 0.7436 0.8077 0.8693 0.9287 0.9861 1.041 1.095 700 0.4014 0.4413 0.5177 0.5901 0.6590 0.7249 0.7881 0.8488 0.9072 0.9635 1.018 1.070 800 0.3869 0.4266 0.5024 0.5741 0.6424 0.7077 0.7701 0.8301 0.8877 0.9432 0.9966 1.048 900 0.3732 0.4126 0.4879 0.5591 0.6269 0.6916 0.7535 0.8128 0.8698 0.9246 0.9774 1.028 1,000 0.3600 0.3992 0.4741 0.5449 0.6122 0.6764 0.7378 0.7967 0.8532 0.9075 0.9597 1.010 2,000 0.2515 0.2894 0.3619 0.4305 0.4956 0.5576 0.6168 0.6735 0.7278 0.7799 0.8300 0.8782 Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 1 2.836 2.888 2.938 3.056 3.165 3.363 3.537 3.695 3.838 3.969 4.091 4.203 5 2.525 2.578 2.629 2.749 2.859 3.057 3.232 3.390 3.533 3.665 3.786 3.899 10 2.386 2.441 2.493 2.614 2.725 2.924 3.100 3.258 3.402 3.534 3.655 3.768 20 2.238 2.296 2.350 2.475 2.588 2.790 2.967 3.126 3.270 3.402 3.523 3.636 30 2.143 2.204 2.261 2.390 2.506 2.710 2.888 3.047 3.192 3.324 3.446 3.559 40 2.068 2.134 2.194 2.327 2.445 2.652 2.831 2.991 3.136 3.269 3.391 3.504 50 2.004 2.075 2.138 2.276 2.397 2.606 2.787 2.948 3.093 3.226 3.348 3.461 60 1.944 2.022 2.090 2.233 2.357 2.568 2.750 2.912 3.057 3.190 3.313 3.426 70 1.887 1.974 2.046 2.195 2.321 2.536 2.719 2.881 3.027 3.160 3.283 3.397 80 1.829 1.927 2.005 2.161 2.290 2.507 2.691 2.854 3.001 3.134 3.257 3.371 90 1.769 1.883 1.967 2.130 2.262 2.481 2.667 2.830 2.977 3.111 3.234 3.348 100 1.704 1.838 1.930 2.101 2.236 2.458 2.645 2.809 2.956 3.090 3.214 3.328 150 1.435 1.628 1.764 1.978 2.129 2.365 2.558 2.725 2.874 3.009 3.134 3.248 200 1.346 1.497 1.635 1.880 2.046 2.295 2.493 2.663 2.814 2.951 3.076 3.191 250 1.298 1.428 1.551 1.802 1.979 2.238 2.442 2.615 2.767 2.905 3.031 3.147 221 222 D2 Properties of Selected Important Pure Substances D2.4. Table 7. (continued) Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 300 1.264 1.383 1.496 1.739 1.922 2.191 2.398 2.574 2.728 2.867 2.993 3.110 350 1.237 1.349 1.456 1.690 1.875 2.150 2.361 2.539 2.695 2.834 2.962 3.078 400 1.214 1.322 1.424 1.651 1.835 2.114 2.328 2.508 2.665 2.806 2.934 3.051 450 1.195 1.299 1.398 1.619 1.801 2.082 2.299 2.481 2.639 2.781 2.909 3.027 500 1.177 1.279 1.375 1.591 1.772 2.054 2.273 2.456 2.615 2.758 2.887 3.005 600 1.147 1.245 1.338 1.546 1.724 2.006 2.228 2.413 2.574 2.718 2.848 2.967 700 1.121 1.217 1.307 1.510 1.684 1.966 2.189 2.376 2.539 2.684 2.815 2.934 800 1.098 1.193 1.281 1.480 1.651 1.933 2.156 2.344 2.508 2.654 2.786 2.906 900 1.077 1.171 1.258 1.454 1.623 1.903 2.127 2.316 2.481 2.627 2.760 2.881 1,000 1.059 1.151 1.237 1.431 1.599 1.877 2.102 2.291 2.456 2.604 2.737 2.858 2,000 0.9246 1.013 1.095 1.280 1.441 1.712 1.936 2.128 2.296 2.446 2.582 2.706 D2.4. Table 8. Specific isobaric heat capacity cp of carbon dioxide in kJ/(kg K) Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 1 0.7790 0.7825 0.7903 0.7988 0.8078 0.8172 0.8267 0.8363 0.8459 0.8555 0.8650 0.8744 5 0.9013 0.8890 0.8743 0.8673 0.8648 0.8653 0.8679 0.8719 0.8769 0.8828 0.8891 0.8959 10 1.969 1.977 1.041 0.9864 0.9567 0.9393 0.9291 0.9234 0.9210 0.9208 0.9224 0.9252 20 1.962 1.969 2.002 2.063 2.163 1.180 1.107 1.063 1.034 1.015 1.002 0.9936 30 1.956 1.962 1.992 2.047 2.137 2.289 1.473 1.298 1.204 1.146 1.107 1.080 40 1.950 1.955 1.981 2.032 2.113 2.247 2.495 1.833 1.501 1.344 1.252 1.192 50 1.944 1.948 1.972 2.018 2.092 2.210 2.417 2.879 2.210 1.690 1.469 1.346 60 1.938 1.941 1.963 2.005 2.072 2.177 2.353 2.703 3.945 2.490 1.834 1.567 70 1.933 1.935 1.954 1.992 2.054 2.148 2.299 2.577 3.299 7.929 2.582 1.913 80 1.927 1.929 1.946 1.981 2.037 2.121 2.253 2.480 2.974 5.229 4.946 2.515 90 1.922 1.923 1.938 1.970 2.021 2.097 2.213 2.403 2.768 3.802 12.87 3.701 100 1.917 1.917 1.930 1.959 2.006 2.075 2.178 2.339 2.623 3.260 5.660 5.813 150 1.895 1.891 1.897 1.915 1.945 1.989 2.049 2.132 2.248 2.417 2.672 3.044 200 1.875 1.870 1.869 1.879 1.899 1.927 1.965 2.014 2.075 2.153 2.251 2.369 250 1.859 1.851 1.846 1.850 1.862 1.881 1.905 1.935 1.972 2.015 2.064 2.118 300 1.844 1.835 1.826 1.826 1.832 1.844 1.859 1.879 1.902 1.927 1.954 1.983 350 1.831 1.821 1.809 1.805 1.807 1.814 1.824 1.836 1.850 1.865 1.880 1.896 400 1.819 1.808 1.794 1.787 1.786 1.789 1.794 1.801 1.810 1.818 1.827 1.835 450 1.809 1.797 1.780 1.772 1.768 1.768 1.770 1.773 1.778 1.782 1.786 1.790 500 1.800 1.786 1.768 1.758 1.752 1.750 1.749 1.750 1.751 1.753 1.754 1.754 600 1.783 1.769 1.748 1.735 1.726 1.720 1.716 1.713 1.711 1.708 1.705 1.702 700 1.769 1.754 1.732 1.717 1.706 1.697 1.691 1.685 1.680 1.675 1.670 1.665 800 1.757 1.741 1.718 1.701 1.689 1.679 1.671 1.663 1.657 1.650 1.644 1.637 900 1.747 1.731 1.706 1.688 1.675 1.664 1.655 1.646 1.638 1.631 1.623 1.616 1,000 1.738 1.721 1.696 1.678 1.663 1.652 1.641 1.632 1.623 1.615 1.607 1.599 2,000 1.685 1.668 1.642 1.623 1.608 1.594 1.582 1.570 1.559 1.548 1.538 1.528 Properties of Carbon Dioxide D2.4 D2.4. Table 8. (continued) Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 1 0.8837 0.9018 0.9193 0.9601 0.9971 1.061 1.114 1.159 1.196 1.227 1.253 1.275 5 0.9030 0.9175 0.9323 0.9688 1.003 1.065 1.117 1.160 1.197 1.228 1.254 1.276 10 0.9289 0.9383 0.9494 0.9800 1.011 1.069 1.119 1.162 1.198 1.229 1.255 1.276 20 0.9885 0.9847 0.9865 1.003 1.027 1.078 1.125 1.166 1.202 1.231 1.256 1.278 30 1.061 1.038 1.028 1.028 1.044 1.088 1.131 1.170 1.205 1.234 1.258 1.279 40 1.152 1.102 1.075 1.055 1.062 1.097 1.137 1.175 1.207 1.236 1.260 1.281 50 1.267 1.176 1.128 1.083 1.080 1.106 1.143 1.179 1.210 1.238 1.262 1.282 60 1.421 1.266 1.189 1.114 1.098 1.116 1.149 1.183 1.213 1.240 1.264 1.284 70 1.631 1.374 1.257 1.145 1.117 1.125 1.155 1.187 1.216 1.243 1.265 1.285 80 1.931 1.505 1.334 1.179 1.137 1.135 1.160 1.190 1.219 1.245 1.267 1.286 90 2.376 1.666 1.422 1.215 1.157 1.144 1.166 1.194 1.222 1.247 1.269 1.288 100 3.032 1.859 1.521 1.252 1.178 1.154 1.172 1.198 1.225 1.249 1.270 1.289 150 3.433 2.920 2.103 1.452 1.283 1.201 1.200 1.217 1.238 1.259 1.279 1.296 200 2.497 2.603 2.367 1.632 1.383 1.246 1.226 1.234 1.251 1.269 1.286 1.302 250 2.175 2.259 2.197 1.744 1.463 1.286 1.250 1.251 1.263 1.278 1.293 1.308 300 2.011 2.057 2.050 1.790 1.515 1.321 1.272 1.266 1.274 1.286 1.300 1.313 350 1.911 1.933 1.934 1.765 1.551 1.348 1.291 1.279 1.284 1.294 1.306 1.318 400 1.842 1.851 1.849 1.733 1.568 1.369 1.308 1.292 1.293 1.301 1.312 1.323 450 1.792 1.792 1.787 1.705 1.568 1.385 1.322 1.303 1.302 1.308 1.318 1.327 500 1.753 1.749 1.739 1.678 1.561 1.397 1.334 1.313 1.310 1.315 1.323 1.332 600 1.698 1.687 1.673 1.627 1.548 1.411 1.351 1.329 1.324 1.326 1.332 1.340 700 1.659 1.646 1.630 1.588 1.532 1.416 1.362 1.341 1.335 1.336 1.341 1.347 800 1.631 1.616 1.600 1.558 1.514 1.419 1.369 1.350 1.344 1.345 1.348 1.353 900 1.608 1.593 1.577 1.536 1.498 1.420 1.373 1.356 1.351 1.352 1.355 1.359 1,000 1.591 1.575 1.559 1.519 1.484 1.421 1.377 1.361 1.357 1.358 1.361 1.365 2,000 1.519 1.501 1.486 1.455 1.431 1.401 1.387 1.383 1.382 1.385 1.389 1.393 D2.4. Table 9. Specific isochoric heat capacity cv of carbon dioxide in kJ/(kg K) Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 1 0.5771 0.5816 0.5912 0.6011 0.6113 0.6216 0.6319 0.6422 0.6524 0.6624 0.6724 0.6821 5 0.6282 0.6254 0.6248 0.6279 0.6331 0.6396 0.6470 0.6549 0.6632 0.6717 0.6804 0.6891 10 0.9832 0.9715 0.6867 0.6704 0.6651 0.6650 0.6677 0.6720 0.6776 0.6839 0.6908 0.6981 20 0.9846 0.9727 0.9549 0.9428 0.9357 0.7353 0.7194 0.7125 0.7103 0.7111 0.7137 0.7176 30 0.9859 0.9740 0.9558 0.9435 0.9358 0.9332 0.8037 0.7678 0.7512 0.7431 0.7397 0.7392 40 0.9873 0.9752 0.9568 0.9441 0.9360 0.9325 0.9372 0.8621 0.8075 0.7829 0.7701 0.7635 50 0.9886 0.9764 0.9577 0.9448 0.9363 0.9320 0.9344 0.9568 0.9014 0.8363 0.8071 0.7915 60 0.9899 0.9776 0.9587 0.9455 0.9366 0.9317 0.9324 0.9465 1.003 0.9196 0.8544 0.8242 70 0.9912 0.9787 0.9596 0.9462 0.9369 0.9315 0.9308 0.9397 0.9717 1.141 0.9208 0.8637 80 0.9925 0.9799 0.9606 0.9469 0.9373 0.9314 0.9297 0.9351 0.9541 1.031 1.032 0.9128 90 0.9937 0.9810 0.9615 0.9476 0.9378 0.9314 0.9288 0.9319 0.9437 0.9792 1.147 0.9745 100 0.9950 0.9821 0.9624 0.9483 0.9382 0.9315 0.9282 0.9295 0.9370 0.9569 1.025 1.035 223 224 D2 Properties of Selected Important Pure Substances D2.4. Table 9. (continued) Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 150 1.001 0.9875 0.9669 0.9519 0.9407 0.9326 0.9270 0.9239 0.9233 0.9254 0.9313 0.9423 200 1.007 0.9926 0.9711 0.9554 0.9435 0.9345 0.9276 0.9227 0.9196 0.9181 0.9183 0.9201 250 1.012 0.9975 0.9752 0.9589 0.9464 0.9367 0.9291 0.9232 0.9188 0.9157 0.9138 0.9131 300 1.017 1.002 0.9791 0.9622 0.9493 0.9392 0.9310 0.9245 0.9193 0.9153 0.9124 0.9104 350 1.022 1.006 0.9828 0.9655 0.9522 0.9417 0.9332 0.9262 0.9206 0.9160 0.9124 0.9097 400 1.026 1.010 0.9864 0.9687 0.9551 0.9443 0.9355 0.9283 0.9223 0.9173 0.9133 0.9102 450 1.030 1.014 0.9898 0.9718 0.9580 0.9470 0.9380 0.9305 0.9243 0.9190 0.9147 0.9113 500 1.034 1.018 0.9932 0.9748 0.9608 0.9496 0.9405 0.9328 0.9264 0.9210 0.9165 0.9128 600 1.042 1.025 0.9994 0.9806 0.9662 0.9549 0.9455 0.9377 0.9311 0.9255 0.9207 0.9167 700 1.049 1.032 1.005 0.9861 0.9715 0.9600 0.9506 0.9427 0.9360 0.9303 0.9254 0.9213 800 1.056 1.038 1.011 0.9914 0.9767 0.9651 0.9556 0.9478 0.9410 0.9353 0.9304 0.9262 900 1.062 1.044 1.016 0.9964 0.9816 0.9700 0.9606 0.9528 0.9461 0.9404 0.9355 0.9312 1,000 1.067 1.049 1.021 1.001 0.9864 0.9748 0.9655 0.9578 0.9512 0.9455 0.9406 0.9364 2,000 1.108 1.089 1.060 1.041 1.028 1.018 1.010 1.004 0.9985 0.9940 0.9900 0.9864 Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 1 0.6917 0.7103 0.7282 0.7696 0.8070 0.8714 0.9248 0.9693 1.007 1.038 1.064 1.086 5 0.6978 0.7150 0.7319 0.7719 0.8085 0.8721 0.9252 0.9696 1.007 1.038 1.064 1.086 10 0.7056 0.7211 0.7367 0.7747 0.8103 0.8731 0.9258 0.9700 1.007 1.038 1.064 1.086 20 0.7224 0.7338 0.7466 0.7805 0.8140 0.8750 0.9269 0.9708 1.008 1.039 1.065 1.087 30 0.7406 0.7472 0.7568 0.7864 0.8177 0.8768 0.9281 0.9715 1.008 1.039 1.065 1.087 40 0.7607 0.7615 0.7676 0.7923 0.8215 0.8787 0.9292 0.9723 1.009 1.039 1.065 1.087 50 0.7828 0.7768 0.7787 0.7983 0.8252 0.8805 0.9303 0.9730 1.009 1.040 1.066 1.087 60 0.8076 0.7929 0.7903 0.8043 0.8289 0.8823 0.9313 0.9738 1.010 1.040 1.066 1.088 70 0.8356 0.8101 0.8022 0.8104 0.8325 0.8841 0.9324 0.9745 1.010 1.041 1.066 1.088 80 0.8671 0.8282 0.8144 0.8164 0.8362 0.8858 0.9335 0.9752 1.011 1.041 1.067 1.088 90 0.9024 0.8470 0.8268 0.8224 0.8397 0.8875 0.9345 0.9759 1.011 1.042 1.067 1.089 100 0.9393 0.8662 0.8393 0.8284 0.8432 0.8892 0.9355 0.9766 1.012 1.042 1.067 1.089 150 0.9521 0.9300 0.8935 0.8558 0.8595 0.8971 0.9403 0.9800 1.014 1.044 1.069 1.090 200 0.9234 0.9255 0.9152 0.8768 0.8729 0.9040 0.9447 0.9830 1.017 1.046 1.070 1.091 250 0.9133 0.9151 0.9133 0.8912 0.8831 0.9099 0.9486 0.9859 1.019 1.048 1.072 1.093 300 0.9093 0.9089 0.9085 0.8988 0.8906 0.9147 0.9520 0.9885 1.021 1.049 1.073 1.094 350 0.9078 0.9060 0.9053 0.9008 0.8960 0.9187 0.9551 0.9909 1.023 1.051 1.075 1.095 400 0.9078 0.9049 0.9038 0.9013 0.8999 0.9220 0.9578 0.9931 1.025 1.052 1.076 1.096 450 0.9085 0.9050 0.9034 0.9020 0.9028 0.9247 0.9602 0.9951 1.026 1.054 1.077 1.097 500 0.9098 0.9058 0.9038 0.9030 0.9052 0.9272 0.9624 0.9970 1.028 1.055 1.078 1.098 600 0.9135 0.9088 0.9062 0.9057 0.9097 0.9318 0.9662 1.000 1.031 1.058 1.081 1.100 700 0.9178 0.9128 0.9098 0.9091 0.9141 0.9364 0.9697 1.003 1.034 1.060 1.083 1.102 800 0.9226 0.9173 0.9141 0.9131 0.9184 0.9409 0.9731 1.006 1.036 1.062 1.085 1.104 900 0.9277 0.9222 0.9188 0.9174 0.9229 0.9453 0.9765 1.009 1.039 1.064 1.087 1.106 1,000 0.9328 0.9273 0.9237 0.9220 0.9273 0.9495 0.9799 1.012 1.041 1.066 1.088 1.107 2,000 0.9832 0.9780 0.9740 0.9694 0.9711 0.9872 1.011 1.037 1.062 1.084 1.104 1.121 D2.4 Properties of Carbon Dioxide D2.4. Table 10. Isobaric expansion coefficient b of carbon dioxide in 103/K Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 1 4.808 4.682 4.453 4.248 4.063 3.896 3.742 3.601 3.471 3.351 3.239 3.134 5 5.979 5.701 5.247 4.883 4.580 4.323 4.100 3.904 3.729 3.573 3.431 3.302 10 3.108 3.253 6.794 5.997 5.429 4.993 4.641 4.348 4.100 3.886 3.698 3.531 20 3.070 3.208 3.553 4.032 4.743 7.199 6.244 5.575 5.070 4.671 4.346 4.074 30 3.034 3.166 3.493 3.941 4.592 5.641 9.564 7.684 6.556 5.782 5.209 4.764 40 2.998 3.124 3.436 3.856 4.455 5.387 7.095 7.489 6.421 5.673 50 2.964 3.085 3.381 3.777 4.330 5.165 6.603 9.863 15.50 10.50 8.249 6.920 60 2.931 3.047 3.329 3.702 4.215 4.969 6.203 8.681 17.85 17.49 11.34 70 2.899 3.010 3.280 3.632 4.109 4.794 5.869 7.844 13.12 64.86 17.68 11.55 80 2.868 2.975 3.232 3.566 4.011 4.637 5.584 7.210 10.81 28.61 37.61 16.45 25.95 12.50 9.185 8.728 90 2.838 2.941 3.187 3.503 3.920 4.494 5.338 6.708 9.383 17.36 99.50 100 2.809 2.908 3.144 3.443 3.834 4.364 5.121 6.297 8.393 13.27 33.46 150 2.677 2.759 2.951 3.187 3.480 3.851 4.333 4.981 5.890 7.237 9.345 200 2.562 2.632 2.791 2.981 3.209 3.486 3.824 4.244 4.772 5.445 6.310 7.404 250 2.461 2.520 2.654 2.811 2.994 3.209 3.461 3.758 4.108 4.521 5.006 5.566 300 2.371 2.422 2.537 2.668 2.818 2.989 3.185 3.407 3.658 3.940 4.255 4.598 350 2.291 2.335 2.433 2.545 2.670 2.810 2.966 3.138 3.328 3.534 3.755 3.988 400 2.218 2.257 2.342 2.437 2.543 2.659 2.786 2.924 3.073 3.230 3.394 3.563 450 2.152 2.186 2.261 2.343 2.433 2.531 2.636 2.749 2.868 2.991 3.118 3.246 500 2.091 2.122 2.187 2.259 2.336 2.419 2.508 2.601 2.698 2.798 2.899 2.999 600 1.984 2.009 2.060 2.115 2.173 2.235 2.299 2.365 2.433 2.501 2.568 2.633 700 1.893 1.912 1.953 1.996 2.041 2.087 2.135 2.184 2.232 2.281 2.328 2.373 800 1.813 1.829 1.862 1.896 1.930 1.966 2.002 2.038 2.074 2.109 2.143 2.175 900 1.742 1.755 1.782 1.809 1.836 1.864 1.891 1.918 1.945 1.971 1.995 2.018 1,000 1.679 1.691 1.713 1.734 1.755 1.776 1.797 1.817 1.837 1.856 1.874 1.890 2,000 1.289 1.292 1.294 1.294 1.292 1.288 1.284 1.278 1.273 1.267 1.261 1.255 41.90 12.64 Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 1 3.037 2.859 2.702 2.377 2.122 1.749 1.488 1.294 1.146 1.028 0.9320 0.8525 5 3.183 2.974 2.793 2.430 2.156 1.764 1.495 1.299 1.148 1.029 0.9326 0.8528 10 3.382 3.126 2.912 2.500 2.199 1.783 1.505 1.304 1.151 1.031 0.9334 0.8531 20 3.842 3.466 3.171 2.644 2.288 1.822 1.524 1.314 1.156 1.034 0.9349 0.8537 30 4.406 3.861 3.461 2.797 2.378 1.860 1.543 1.324 1.162 1.036 0.9364 0.8543 40 5.115 4.326 3.788 2.959 2.471 1.899 1.561 1.333 1.167 1.039 0.9377 0.8549 50 6.025 4.875 4.155 3.129 2.565 1.936 1.579 1.343 1.172 1.042 0.9390 0.8554 60 7.231 5.532 4.569 3.307 2.661 1.973 1.597 1.352 1.177 1.044 0.9403 0.8559 70 8.882 6.320 5.035 3.493 2.758 2.010 1.614 1.360 1.181 1.047 0.9414 0.8563 80 11.23 7.272 5.558 3.687 2.856 2.046 1.630 1.368 1.186 1.049 0.9425 0.8567 90 14.66 8.416 6.140 3.887 2.954 2.081 1.646 1.376 1.190 1.051 0.9435 0.8570 100 19.59 9.772 6.781 4.092 3.051 2.116 1.661 1.384 1.194 1.053 0.9444 0.8573 150 16.72 200 8.693 15.53 10.05 5.099 3.512 2.271 1.729 1.417 1.210 1.061 0.9476 0.8578 10.69 10.15 5.733 3.858 2.391 1.781 1.442 1.222 1.066 0.9488 0.8569 225 226 D2 Properties of Selected Important Pure Substances D2.4. Table 10. (continued) Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 250 6.187 7.387 7.758 5.787 4.012 2.470 1.817 1.458 1.229 1.068 0.9481 0.8547 300 4.964 5.687 6.140 5.451 3.985 2.507 1.836 1.466 1.231 1.067 0.9456 0.8514 350 4.229 4.702 5.062 4.825 3.864 2.505 1.842 1.467 1.229 1.064 0.9416 0.8470 400 3.733 4.061 4.330 4.289 3.663 2.471 1.835 1.463 1.224 1.059 0.9363 0.8417 450 3.372 3.611 3.810 3.872 3.411 2.415 1.818 1.454 1.217 1.052 0.9299 0.8358 500 3.096 3.275 3.424 3.523 3.174 2.347 1.792 1.441 1.208 1.044 0.9228 0.8292 600 2.695 2.804 2.892 2.979 2.793 2.189 1.723 1.406 1.184 1.025 0.9068 0.8151 700 2.414 2.486 2.539 2.591 2.492 2.029 1.642 1.361 1.156 1.005 0.8897 0.8002 800 2.204 2.252 2.286 2.309 2.245 1.890 1.559 1.312 1.125 0.9822 0.8719 0.7851 900 2.039 2.072 2.093 2.097 2.044 1.770 1.480 1.261 1.092 0.9587 0.8538 0.7701 1,000 1.905 1.928 1.941 1.932 1.881 1.664 1.409 1.210 1.057 0.9344 0.8354 0.7552 2,000 1.249 1.238 1.226 1.193 1.153 1.056 0.9612 0.8738 0.7939 0.7244 0.6658 0.6164 D2.4. Table 11. Isentropic speed of sound ws in carbon dioxide in m/s Temperature in C Pressure in bar 55 50 40 30 20 10 1 232.5 235.0 239.9 244.6 249.2 253.7 5 224.2 227.3 233.2 238.8 244.1 249.2 10 967.7 931.1 223.5 230.6 237.1 20 973.4 937.3 863.8 787.2 705.7 30 978.9 943.4 871.0 796.0 40 984.4 949.3 878.1 804.5 50 989.8 955.2 885.0 812.8 60 995.2 0 10 20 30 40 50 258.1 262.4 266.6 270.7 274.7 278.7 254.0 258.7 263.3 267.7 272.1 276.3 243.1 248.7 254.0 259.1 264.0 268.7 273.3 228.8 236.6 243.6 250.0 256.0 261.7 267.0 716.7 630.4 221.5 231.5 240.0 247.4 254.2 260.5 727.3 644.1 549.1 216.1 228.3 238.0 246.3 253.8 737.4 657.0 567.4 458.1 213.4 227.2 237.8 246.8 961.0 891.8 820.9 747.2 669.3 584.0 484.9 351.9 214.1 228.6 239.6 70 1,000 966.7 898.5 828.8 756.6 680.9 599.4 507.7 395.8 192.3 218.2 232.1 80 1,006 972.3 905.0 836.4 765.8 692.1 613.7 527.7 428.7 293.0 205.8 224.7 90 1,011 977.8 911.4 843.9 774.7 702.8 627.1 545.7 455.4 346.5 205.9 218.2 100 1,016 983.3 917.7 851.2 783.3 713.1 639.8 562.1 478.1 383.3 270.2 217.5 150 1,040 1,009 947.7 885.7 823.1 759.7 695.3 629.8 563.0 495.3 427.3 362.7 200 1,063 1,034 975.5 917.1 858.6 800.2 741.7 683.3 625.2 567.8 511.9 458.9 250 1,085 1,057 1,001 946.1 890.9 836.2 782.1 728.6 676.0 624.7 575.2 528.4 300 1,106 1,079 1,026 973.1 920.7 869.0 818.2 768.3 719.7 672.6 627.4 584.6 350 1,126 1,100 1,049 998.5 948.5 899.2 851.0 804.0 758.3 714.3 672.2 632.3 400 1,145 1,120 1,071 1,023 974.5 927.3 881.3 836.5 793.2 751.6 711.9 674.2 450 1,163 1,140 1,092 1,045 999.0 953.7 909.4 866.6 825.2 785.5 747.6 711.8 500 1,181 1,158 1,112 1,067 1,022 978.5 935.9 894.5 854.8 816.6 780.3 745.9 600 1,215 1,194 1,151 1,108 1,066 1,024 984.4 945.6 908.3 872.6 838.7 806.5 700 1,247 1,227 1,186 1,146 1,106 1,066 1,028 991.6 956.2 922.3 890.1 859.5 800 1,277 1,258 1,219 1,181 1,143 1,105 1,069 1,034 999.6 967.2 936.3 907.0 900 1,305 1,287 1,251 1,214 1,177 1,141 1,106 1,072 1,040 1,008 978.5 950.1 1,000 1,332 1,315 1,280 1,245 1,210 1,175 1,141 1,108 1,077 1,046 1,017 2,000 1,554 1,543 1,519 1,493 1,466 1,438 1,411 1,384 1,358 1,332 1,308 989.9 1,284 D2.4 Properties of Carbon Dioxide D2.4. Table 11. (continued) Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 1 282.6 290.2 297.6 315.3 5 280.4 288.4 296.2 314.5 332.0 363.0 391.4 417.9 442.7 466.3 488.8 510.2 331.5 362.9 391.6 418.2 443.2 466.8 489.3 510.8 10 277.7 286.2 294.3 20 272.1 281.7 290.7 313.4 330.9 362.9 391.9 418.7 443.8 467.5 490.0 511.5 311.2 329.8 362.9 392.5 419.6 444.9 468.8 491.4 30 266.4 277.2 512.9 287.2 309.2 328.7 363.0 393.1 420.6 446.1 470.1 492.7 514.4 40 260.6 50 254.7 272.8 283.7 307.4 327.8 363.1 393.8 421.6 447.3 471.4 494.1 515.8 268.5 280.4 305.7 327.0 363.3 394.6 422.6 448.5 472.7 495.5 517.2 60 70 248.8 264.3 277.3 304.2 326.4 363.6 395.4 423.7 449.7 474.0 496.9 518.7 243.0 260.3 274.4 302.8 325.9 364.0 396.2 424.8 451.0 475.4 498.3 80 520.1 237.5 256.7 271.9 301.8 325.6 364.5 397.1 426.0 452.3 476.7 499.7 521.6 90 232.7 253.6 269.8 300.9 325.5 365.1 398.1 427.2 453.6 478.1 501.2 523.0 100 229.9 251.4 268.2 300.4 325.5 365.9 399.1 428.4 454.9 479.5 502.6 524.5 150 310.0 270.8 274.9 303.3 329.1 371.1 405.4 435.2 462.1 486.9 510.1 531.9 200 411.2 341.9 312.7 317.9 338.9 379.2 413.3 443.1 470.0 494.8 517.9 539.7 250 485.3 415.0 370.7 343.2 355.0 390.0 422.8 452.1 478.7 503.2 526.2 547.8 300 544.8 476.9 427.8 375.6 376.2 403.3 433.8 462.1 488.1 512.2 534.8 556.2 350 595.1 529.9 479.5 414.7 400.6 418.7 446.0 472.9 498.1 521.7 543.9 564.9 400 639.0 576.4 525.9 453.2 428.3 435.7 459.3 484.4 508.7 531.6 553.2 573.9 450 678.1 617.9 567.9 489.3 458.0 454.0 473.3 496.5 519.6 541.7 562.9 583.1 500 713.6 655.3 606.2 523.7 487.4 473.2 487.9 508.9 530.8 552.2 572.7 592.5 600 776.2 721.2 673.9 587.8 542.2 513.7 518.7 534.7 553.9 573.5 592.8 611.6 700 830.7 778.2 732.5 645.7 593.5 554.5 550.8 561.5 577.5 595.2 613.2 631.0 800 879.2 828.7 784.3 698.1 641.8 593.5 583.4 588.8 601.4 617.0 633.6 650.4 900 923.3 874.2 830.9 745.7 687.3 630.6 615.4 616.4 625.6 638.9 654.0 669.7 729.7 666.2 646.4 643.8 649.8 660.8 674.3 688.8 958.2 910.3 883.0 870.3 866.2 867.1 870.9 1,000 2,000 963.8 1,261 915.8 1,219 873.5 1,180 789.2 1,100 1,039 D2.4. Table 12. Thermal conductivity l of carbon dioxide in mW/(m K) Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 1 10.78 11.10 11.77 12.45 13.17 13.90 14.66 15.43 16.22 17.03 17.84 18.67 5 11.13 11.44 12.07 12.73 13.42 14.14 14.88 15.64 16.42 17.22 18.03 18.84 12.67 13.24 13.86 14.53 15.24 15.97 16.72 17.50 18.29 19.09 15.86 16.34 16.91 17.55 18.24 18.96 19.71 18.48 18.53 18.86 19.33 19.91 20.54 21.74 21.04 21.00 21.25 21.67 10 179.1 172.4 20 179.9 173.2 160.3 147.6 135.0 30 180.7 174.1 161.2 148.7 136.3 123.6 40 181.5 174.9 162.1 149.7 137.5 125.0 112.0 50 182.3 175.7 163.0 150.8 138.6 126.5 113.8 100.1 25.36 23.70 23.23 23.23 60 183.1 176.6 163.9 151.7 139.8 127.8 115.5 102.5 87.89 28.76 26.28 25.42 70 183.9 177.4 164.8 152.7 140.9 129.1 117.1 104.6 90.88 46.34 31.43 28.58 80 184.6 178.2 165.7 153.7 142.0 130.4 118.7 106.5 93.59 80.14 42.57 33.34 90 185.4 179.0 166.5 154.6 143.0 131.6 120.1 108.4 96.03 82.96 70.37 41.03 227 228 D2 Properties of Selected Important Pure Substances D2.4. Table 12. (continued) Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 100 186.2 179.7 167.4 155.6 144.1 132.8 121.5 110.1 150 189.9 183.6 171.5 160.0 149.0 138.3 127.8 117.5 107.3 98.25 85.85 73.49 53.06 97.08 86.92 200 193.4 187.2 175.4 164.2 153.5 143.2 133.3 123.7 114.3 105.2 76.97 96.33 87.81 250 196.9 190.7 179.1 168.1 157.7 147.7 138.2 129.0 120.2 111.8 103.7 300 200.2 194.2 182.7 171.9 161.7 152.0 142.7 133.9 125.5 117.4 109.8 102.5 350 203.5 197.5 186.1 175.5 165.4 155.9 146.9 138.4 130.2 122.5 115.2 108.3 400 206.7 200.7 189.4 178.9 169.0 159.7 150.9 142.5 134.6 127.1 120.0 113.4 450 209.8 203.8 192.7 182.3 172.5 163.3 154.7 146.5 138.7 131.4 124.5 118.0 500 212.8 206.9 195.8 185.5 175.9 166.8 158.2 150.2 142.6 135.4 128.6 122.3 600 218.6 212.8 201.9 191.7 182.2 173.4 165.0 157.1 149.7 142.8 136.2 130.1 700 224.3 218.5 207.7 197.6 188.3 179.5 171.3 163.6 156.4 149.5 143.1 137.1 800 229.7 224.0 213.2 203.3 194.0 185.4 177.3 169.7 162.5 155.8 149.5 143.6 900 235.0 229.3 218.6 208.7 199.5 190.9 182.9 175.4 168.3 161.7 155.5 149.6 1,000 240.1 234.4 223.7 213.9 204.8 196.3 188.3 180.8 173.8 167.3 161.1 155.3 95.91 Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 1 19.50 21.18 22.87 27.12 31.31 39.47 47.26 54.70 61.84 68.69 75.30 81.69 5 19.67 21.34 23.02 27.24 31.43 39.56 47.34 54.77 61.90 68.75 75.35 81.73 10 19.90 21.55 23.22 27.41 31.57 39.68 47.44 54.86 61.97 68.81 75.41 81.79 20 20.48 22.06 23.67 27.78 31.89 39.93 47.65 55.04 62.13 68.95 75.54 81.90 30 21.22 22.68 24.21 28.19 32.23 40.20 47.86 55.22 62.29 69.10 75.67 82.02 40 22.20 23.45 24.85 28.66 32.60 40.48 48.09 55.42 62.46 69.25 75.80 82.14 50 23.48 24.39 25.60 29.17 33.01 40.78 48.33 55.62 62.63 69.40 75.94 82.26 60 25.18 25.56 26.49 29.74 33.44 41.09 48.58 55.83 62.81 69.56 76.08 82.39 70 27.46 27.00 27.54 30.37 33.90 41.42 48.84 56.04 63.00 69.72 76.22 82.52 80 30.53 28.77 28.76 31.06 34.39 41.77 49.11 56.26 63.18 69.88 76.36 82.65 90 34.71 30.93 30.19 31.81 34.92 42.13 49.39 56.49 63.38 70.05 76.51 82.78 100 40.35 33.53 31.82 32.63 35.48 42.50 49.68 56.72 63.58 70.22 76.66 82.92 150 67.48 51.61 43.04 37.75 38.72 44.59 51.24 57.98 64.63 71.13 77.46 83.63 200 79.73 65.70 55.48 44.25 42.66 46.98 52.98 59.36 65.77 72.10 78.31 84.38 250 88.61 75.67 65.45 51.27 47.10 49.62 54.88 60.84 66.99 73.14 79.22 85.19 300 95.73 83.56 73.58 58.02 51.79 52.42 56.88 62.40 68.28 74.23 80.16 86.02 90.15 80.44 64.23 56.49 55.33 58.96 64.03 69.61 75.36 81.14 86.89 95.88 350 101.8 400 107.1 86.40 69.86 61.07 58.28 61.10 65.70 70.98 76.52 82.15 87.78 450 111.9 101.0 91.69 74.99 65.46 61.23 63.26 67.40 72.38 77.71 83.18 88.68 500 116.4 105.6 96.49 79.71 69.64 64.16 65.44 69.12 73.80 78.92 84.23 89.61 600 124.3 114.0 105.0 88.15 77.36 69.84 69.76 72.58 76.67 81.37 86.36 91.50 700 131.5 121.3 112.5 95.59 84.34 75.26 74.00 76.01 79.54 83.84 88.53 93.42 800 138.0 128.0 119.3 102.3 90.73 80.40 78.11 79.40 82.40 86.31 90.70 95.35 900 144.1 134.2 125.5 108.5 96.63 85.29 82.10 82.71 85.23 88.76 92.86 97.29 1,000 149.8 140.0 131.3 114.2 89.93 85.95 85.95 88.01 91.19 95.01 99.22 102.1 Properties of Carbon Dioxide D2.4 D2.4. Table 13. Dynamic viscosity of carbon dioxide in 106 Pa·s Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 1 10.97 11.22 11.72 12.22 12.72 13.22 13.71 14.20 14.69 15.17 15.65 16.13 5 11.02 11.27 11.77 12.27 12.76 13.25 13.75 14.23 14.72 15.20 15.69 16.16 12.83 13.32 13.81 14.29 14.78 15.26 15.73 16.21 13.56 14.02 14.48 14.95 15.42 15.88 16.35 14.42 14.81 15.24 15.67 16.11 16.56 10 252.7 232.2 20 254.8 234.2 199.3 11.86 170.2 12.35 145.1 30 257.0 236.3 201.2 172.1 147.1 124.7 40 259.1 238.3 203.1 174.0 149.0 126.8 106.1 15.44 15.72 16.07 16.46 16.86 50 261.3 240.4 205.0 175.8 150.9 128.9 108.5 88.26 16.63 16.73 16.98 17.30 60 263.4 242.4 206.9 177.7 152.8 130.9 110.8 91.39 69.72 17.92 17.80 17.93 70 265.6 244.4 208.8 179.5 154.6 132.8 113.0 94.20 74.54 21.40 19.21 18.89 80 267.7 246.5 210.6 181.2 156.4 134.7 115.1 96.76 78.33 55.98 22.30 20.40 99.14 90 269.9 248.5 212.5 183.0 158.1 136.5 117.1 81.56 61.94 34.93 23.06 100 272.0 250.5 214.3 184.8 159.9 138.3 119.1 101.4 84.42 66.16 47.84 28.34 150 282.8 260.6 223.4 193.3 168.2 146.7 127.9 111.1 95.73 79.98 67.79 56.54 200 293.6 270.6 232.4 201.7 176.2 154.5 135.8 119.3 104.6 89.63 78.58 68.93 250 304.5 280.7 241.3 209.8 183.8 161.9 143.1 126.7 112.2 97.65 87.06 77.95 300 315.5 290.9 250.2 217.9 191.3 169.0 150.0 133.5 119.0 104.7 94.39 85.50 350 326.6 301.1 259.1 225.8 198.6 175.9 156.6 139.9 125.4 111.3 101.0 92.20 400 338.0 311.4 268.0 233.7 205.9 182.7 163.0 146.1 131.4 117.4 107.2 98.36 450 349.5 321.9 277.0 241.7 213.0 189.3 169.2 152.0 137.1 123.2 113.0 104.1 500 361.2 332.6 286.0 249.6 220.1 195.8 175.3 157.8 142.6 128.7 118.6 109.6 600 385.4 354.4 304.3 265.5 234.3 208.7 187.2 168.9 153.2 139.3 129.1 120.0 700 410.7 377.1 323.1 281.6 248.5 221.5 198.9 179.8 163.3 149.4 139.1 129.7 800 437.3 400.7 342.5 298.0 262.9 234.3 210.5 190.4 173.2 159.2 148.8 139.1 900 465.3 425.4 362.5 314.8 277.4 247.1 222.1 201.0 183.0 168.7 158.1 148.2 1,000 495.0 451.4 383.2 332.1 292.2 260.1 233.7 211.5 192.6 178.0 167.2 157.0 Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 1 16.61 17.55 18.47 20.73 22.89 26.96 30.72 34.20 37.44 40.48 43.34 46.06 5 16.64 17.57 18.50 20.75 22.91 26.98 30.73 34.21 37.45 40.48 43.35 46.06 10 16.68 17.62 18.54 20.78 22.94 27.00 30.75 34.22 37.46 40.50 43.36 46.07 20 16.81 17.73 18.64 20.86 23.01 27.05 30.79 34.26 37.49 40.52 43.38 46.09 30 17.00 17.90 18.79 20.98 23.10 27.12 30.84 34.30 37.53 40.55 43.41 46.12 40 17.28 18.12 18.98 21.12 23.21 27.19 30.90 34.35 37.57 40.59 43.44 46.14 50 17.65 18.42 19.23 21.30 23.35 27.29 30.97 34.40 37.61 40.62 43.47 46.17 60 18.18 18.82 19.55 21.51 23.51 27.39 31.05 34.46 37.66 40.67 43.51 46.20 70 18.91 19.32 19.94 21.76 23.69 27.51 31.13 34.53 37.71 40.71 43.55 46.24 80 19.95 19.98 20.42 22.05 23.90 27.65 31.23 34.60 37.77 40.76 43.59 46.27 90 21.46 20.82 21.01 22.39 24.14 27.79 31.33 34.68 37.84 40.82 43.63 46.31 100 23.74 21.89 21.72 22.78 24.41 27.95 31.45 34.77 37.91 40.87 43.68 46.35 150 46.09 32.39 27.67 25.53 26.18 28.97 32.14 35.29 38.32 41.21 43.97 46.60 200 60.19 45.98 37.09 29.66 28.68 30.32 33.05 35.96 38.84 41.63 44.32 46.90 229 230 D2 Properties of Selected Important Pure Substances D2.4. Table 13. (continued) Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 250 69.78 56.19 46.35 34.78 31.80 31.96 34.13 36.75 39.46 42.13 44.74 47.25 300 77.55 64.26 54.17 40.21 35.34 33.86 35.38 37.66 40.16 42.70 45.21 47.65 350 84.33 71.11 60.88 45.49 39.06 35.95 36.76 38.67 40.94 43.33 45.73 48.10 400 90.48 77.22 66.84 50.46 42.80 38.16 38.24 39.76 41.79 44.02 46.30 48.58 450 96.21 82.82 72.26 55.10 46.47 40.45 39.81 40.92 42.70 44.75 46.91 49.10 88.07 77.31 59.47 50.03 42.77 41.43 42.13 43.65 45.53 47.56 49.65 97.81 86.61 67.53 56.78 47.41 44.78 44.68 45.67 47.18 48.94 50.84 95.20 74.95 63.10 51.97 48.18 47.32 47.79 48.93 50.43 52.11 500 101.6 600 111.8 700 121.3 106.9 800 130.4 115.5 103.3 81.93 69.08 56.40 51.57 50.00 49.98 50.76 51.98 53.45 900 139.2 123.8 111.1 88.60 74.79 60.69 54.91 52.70 52.20 52.63 53.58 54.84 1,000 147.8 131.8 118.7 95.04 80.31 64.86 58.20 55.37 54.44 54.53 55.22 56.28 20 30 40 50 D2.4. Table 14. Kinematic viscosity v of carbon dioxide in 107 m2/s Temperature in C Pressure in bar 55 50 40 1 44.57 46.69 51.05 30 20 10 0 10 55.60 60.32 65.21 70.28 75.51 80.92 86.49 92.22 98.12 10.70 11.67 12.67 13.70 14.77 15.87 17.00 18.16 19.36 5 8.401 8.846 9.756 10 2.153 2.010 4.563 5.063 5.573 6.093 6.627 7.175 7.737 8.314 8.905 9.512 20 2.167 2.023 1.780 1.579 1.407 2.780 3.074 3.368 3.666 3.969 4.278 4.592 30 2.181 2.037 1.793 1.592 1.420 1.266 1.864 2.086 2.303 2.519 2.736 2.955 40 2.196 2.051 1.806 1.604 1.432 1.280 1.138 1.424 1.613 1.791 1.965 2.138 50 2.210 2.064 1.818 1.616 1.445 1.293 1.154 1.016 1.182 1.349 1.502 1.650 60 2.225 2.078 1.831 1.628 1.457 1.306 1.169 1.037 0.8907 1.045 1.192 1.327 70 2.239 2.092 1.843 1.640 1.468 1.319 1.183 1.055 0.9218 0.8029 0.9698 1.098 80 2.254 2.105 1.856 1.652 1.480 1.331 1.197 1.071 0.9464 0.7979 0.8023 0.9305 90 2.268 2.119 1.868 1.664 1.492 1.343 1.210 1.087 0.9673 0.8321 0.7194 0.8090 100 2.282 2.132 1.880 1.675 1.503 1.354 1.222 1.101 0.9858 0.8575 0.7610 0.7374 150 2.355 2.200 1.941 1.732 1.558 1.409 1.280 1.164 1.059 0.9443 0.8688 0.8080 200 2.428 2.267 2.000 1.787 1.610 1.460 1.331 1.217 1.116 1.006 0.9355 0.8788 250 2.501 2.335 2.060 1.840 1.660 1.508 1.378 1.265 1.165 1.058 0.9897 0.9342 300 2.575 2.403 2.119 1.894 1.709 1.555 1.423 1.309 1.209 1.105 1.037 0.9820 350 2.651 2.472 2.179 1.947 1.758 1.600 1.466 1.350 1.249 1.147 1.081 1.025 400 2.727 2.542 2.238 1.999 1.805 1.644 1.507 1.390 1.288 1.188 1.121 1.065 450 2.805 2.612 2.298 2.052 1.852 1.687 1.548 1.428 1.325 1.226 1.159 1.103 500 2.885 2.684 2.359 2.104 1.900 1.730 1.588 1.466 1.360 1.262 1.196 1.139 600 3.049 2.832 2.482 2.211 1.993 1.815 1.666 1.538 1.429 1.332 1.266 1.207 700 3.221 2.985 2.608 2.318 2.088 1.899 1.742 1.609 1.494 1.398 1.332 1.272 800 3.401 3.145 2.738 2.428 2.183 1.983 1.818 1.678 1.558 1.462 1.396 1.334 900 3.591 3.312 2.872 2.540 2.279 2.068 1.894 1.747 1.622 1.524 1.457 1.394 1,000 3.793 3.488 3.012 2.656 2.378 2.154 1.970 1.816 1.684 1.585 1.517 1.452 Properties of Carbon Dioxide D2.4 D2.4. Table 14. (continued) Temperature in C Pressure in bar 1 60 80 104.2 116.8 100 129.9 150 165.5 200 204.4 300 291.8 400 500 600 700 800 390.6 499.5 617.7 744.3 878.9 123.6 149.0 176.0 900 1,021 5 20.58 23.12 25.78 32.93 40.77 58.32 78.13 99.97 204.4 10 10.13 11.42 12.76 16.37 20.31 29.13 39.08 50.03 61.89 74.60 88.10 10.09 14.55 19.55 25.06 31.02 37.40 44.17 51.32 13.05 16.74 20.73 25.00 29.53 34.31 102.4 20 4.913 5.574 6.261 8.097 30 3.177 3.631 4.100 5.345 6.695 9.690 40 2.312 2.664 3.025 3.975 5.000 7.267 9.804 12.59 15.59 18.81 22.21 25.81 50 1.796 2.088 2.384 3.158 3.987 5.816 7.858 10.09 12.51 15.09 17.83 20.71 60 1.455 1.708 1.962 2.617 3.316 4.852 6.563 8.436 10.46 12.61 14.90 17.31 70 1.216 1.441 1.664 2.235 2.840 4.166 5.641 7.253 8.992 10.85 12.81 14.88 80 1.041 1.246 1.445 1.952 2.486 3.654 4.951 6.368 7.894 9.523 11.25 13.06 10.03 11.65 90 0.9116 1.099 1.280 1.735 2.213 3.257 4.416 5.680 7.042 8.494 100 0.8187 0.9879 1.152 1.565 1.998 2.942 3.990 5.132 6.361 7.672 9.058 150 0.7631 0.7589 0.8328 1.091 1.379 2.017 2.726 3.499 4.330 5.214 6.149 7.132 200 0.8316 0.7740 0.7721 0.9067 1.107 1.579 2.114 2.698 3.328 3.998 4.705 5.449 250 0.8869 0.8184 0.7871 0.8378 0.9737 1.336 1.761 2.230 2.737 3.277 3.847 4.446 300 0.9343 0.8613 0.8180 0.8169 0.9069 1.189 1.538 1.929 2.352 2.804 3.281 3.784 350 0.9769 0.9009 0.8507 0.8184 0.8744 1.096 1.388 1.721 2.083 2.472 2.883 3.315 400 1.016 0.9377 0.8828 0.8307 0.8605 1.036 1.284 1.571 1.888 2.228 2.589 2.968 450 1.053 0.9724 0.9139 0.8472 0.8578 0.9961 1.208 1.461 1.741 2.043 2.364 2.702 500 1.089 1.006 0.9439 0.8656 0.8618 0.9698 1.153 1.376 1.627 1.898 2.187 2.492 600 1.155 1.068 1.001 0.9049 0.8800 0.9422 1.081 1.259 1.464 1.689 1.929 2.184 700 1.218 1.127 1.056 0.9453 0.9044 0.9342 1.040 1.185 1.357 1.548 1.753 1.971 800 1.278 1.183 1.108 0.9858 0.9318 0.9365 1.017 1.137 1.284 1.448 1.626 1.817 900 1.336 1.238 1.158 1.026 0.9609 0.9447 1.005 1.105 1.231 1.375 1.533 1.701 1,000 1.393 1.291 1.208 1.066 0.9909 0.9566 1.001 1.085 1.194 1.321 1.461 1.612 10 20 30 40 50 105.7 113.5 121.5 129.8 10.52 D2.4. Table 15. Thermal diffusivity a of carbon dioxide in 107 m2/s Temperature in C Pressure in bar 1 55 56.24 50 40 30 20 10 0 59.05 64.85 70.92 77.28 83.94 90.89 98.13 10.10 11.44 12.80 14.19 15.62 17.09 18.62 5 9.419 20.19 21.81 23.47 25.19 10 0.7749 0.7546 4.681 5.504 6.292 7.076 7.870 8.680 9.507 20 0.7797 0.7598 0.7153 0.6642 0.6051 2.756 3.236 3.701 4.163 10.35 4.628 11.22 5.097 12.11 5.572 30 0.7843 0.7650 0.7215 0.6720 0.6154 0.5479 1.623 2.010 2.368 2.713 3.054 3.395 40 0.7889 0.7700 0.7276 0.6795 0.6251 0.5615 0.4818 1.094 1.438 1.741 2.027 2.305 50 0.7934 0.7749 0.7334 0.6868 0.6344 0.5741 0.5008 0.4005 0.8159 1.131 1.399 1.646 60 0.7978 0.7797 0.7392 0.6938 0.6432 0.5858 0.5178 0.4298 0.2847 0.6736 0.9599 1.200 70 0.8022 0.7844 0.7448 0.7006 0.6517 0.5968 0.5332 0.4544 0.3407 0.2192 0.6147 0.8685 80 0.8064 0.7890 0.7503 0.7071 0.6598 0.6073 0.5474 0.4756 0.3802 0.2185 0.3097 0.6049 90 0.8106 0.7935 0.7556 0.7135 0.6676 0.6171 0.5605 0.4944 0.4114 0.2931 0.1126 0.3889 231 232 D2 Properties of Selected Important Pure Substances D2.4. Table 15. (continued) Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 100 0.8148 0.7980 0.7608 0.7197 0.6751 0.6265 0.5727 0.5113 0.4374 0.3413 0.2065 0.2375 150 0.8345 0.8192 0.7853 0.7484 0.7091 0.6677 0.6240 0.5777 0.5279 0.4743 0.4169 0.3613 200 0.8529 0.8388 0.8076 0.7739 0.7385 0.7020 0.6646 0.6264 0.5876 0.5485 0.5096 0.4725 250 0.8701 0.8571 0.8282 0.7970 0.7646 0.7317 0.6986 0.6656 0.6330 0.6014 0.5709 0.5427 300 0.8864 0.8743 0.8473 0.8182 0.7882 0.7580 0.7280 0.6986 0.6701 0.6429 0.6174 0.5941 350 0.9019 0.8905 0.8651 0.8378 0.8098 0.7817 0.7541 0.7273 0.7017 0.6775 0.6552 0.6349 400 0.9167 0.9060 0.8820 0.8562 0.8298 0.8034 0.7777 0.7529 0.7293 0.7074 0.6872 0.6690 450 0.9308 0.9207 0.8980 0.8734 0.8484 0.8235 0.7993 0.7760 0.7541 0.7337 0.7151 0.6984 500 0.9443 0.9348 0.9132 0.8897 0.8658 0.8422 0.8192 0.7973 0.7766 0.7575 0.7400 0.7245 600 0.9700 0.9614 0.9416 0.9200 0.8980 0.8762 0.8552 0.8353 0.8165 0.7992 0.7834 0.7693 700 0.9940 0.9862 0.9678 0.9477 0.9271 0.9068 0.8873 0.8687 0.8513 0.8352 0.8205 0.8074 800 1.017 1.009 0.9922 0.9732 0.9538 0.9347 0.9162 0.8988 0.8824 0.8672 0.8533 0.8408 900 1.038 1.031 1.015 0.9971 0.9786 0.9603 0.9428 0.9261 0.9106 0.8961 0.8828 0.8707 1,000 1.058 1.052 1.037 1.019 1.002 0.9842 0.9673 0.9514 0.9364 0.9225 0.9096 0.8980 700 800 900 Temperature in C Pressure in bar 1 60 80 138.4 156.3 100 175.0 150 225.4 200 280.5 300 402.6 400 500 600 539.4 689.7 853.2 107.8 138.0 170.7 1,030 1,219 1,420 5 26.95 30.59 34.41 44.63 55.74 80.33 206.1 244.0 10 13.02 14.89 16.84 22.03 27.65 40.05 53.86 69.00 85.44 284.3 103.2 122.1 142.4 10.74 13.62 19.91 26.89 34.52 42.79 51.69 61.22 71.36 13.21 17.91 23.03 28.57 34.54 40.91 47.70 20 6.054 7.041 8.060 30 3.737 4.430 5.139 6.986 8.946 40 2.580 3.129 3.683 5.112 6.615 9.861 13.42 17.29 21.47 25.96 30.76 35.87 50 1.885 2.350 2.813 3.993 5.221 7.857 10.73 13.85 17.21 20.82 24.68 28.77 60 1.419 1.834 2.237 3.250 4.295 6.524 8.941 11.56 14.37 17.40 20.62 24.04 70 1.083 1.466 1.829 2.723 3.637 5.574 7.665 9.922 12.35 14.95 17.72 20.67 80 0.8251 1.192 1.526 2.331 3.146 4.865 6.710 8.697 10.83 13.12 15.55 18.14 90 0.6206 0.9807 1.293 2.029 2.767 4.315 5.969 7.746 9.653 11.69 13.86 16.17 100 0.4589 0.8136 1.110 1.791 2.466 3.878 5.378 6.987 8.711 10.55 12.51 14.59 150 0.3255 0.4142 0.6161 1.111 1.590 2.585 3.622 4.723 5.897 7.147 8.474 9.879 200 0.4411 0.4248 0.487 0.8289 1.191 1.965 2.764 3.609 4.505 5.456 6.465 7.531 250 0.5178 0.4878 0.5059 0.7081 0.9861 1.613 2.265 2.952 3.680 4.451 5.268 6.130 300 0.5735 0.5445 0.5420 0.6587 0.8771 1.394 1.945 2.525 3.139 3.789 4.476 5.201 350 0.6172 0.5907 0.5810 0.6546 0.8155 1.252 1.725 2.227 2.759 3.322 3.916 4.543 400 0.6531 0.6290 0.6171 0.6637 0.7831 1.156 1.568 2.011 2.480 2.976 3.501 4.054 450 0.6839 0.6615 0.6490 0.6761 0.7707 1.089 1.453 1.847 2.267 2.711 3.181 3.676 500 0.7109 0.6899 0.6774 0.6914 0.7682 1.042 1.365 1.720 2.100 2.503 2.928 3.377 600 0.7569 0.7377 0.7254 0.7258 0.7746 0.9840 1.246 1.539 1.857 2.196 2.555 2.934 700 0.7958 0.7774 0.7653 0.7595 0.7892 0.9552 1.172 1.420 1.692 1.985 2.295 2.623 800 0.8297 0.8118 0.7996 0.7903 0.8082 0.9410 1.125 1.338 1.574 1.831 2.105 2.394 900 0.8600 0.8423 0.8299 0.8180 0.8287 0.9347 1.094 1.279 1.488 1.715 1.960 2.220 1,000 0.8874 0.8700 0.8572 0.8432 0.8491 0.9337 1.073 1.237 1.422 1.627 1.847 2.082 Properties of Carbon Dioxide D2.4 D2.4. Table 16. Prandtl number Pr of carbon dioxide Temperature in C Pressure in bar 55 50 40 30 20 10 0 10 20 30 40 50 1 0.7925 0.7907 0.7873 0.7839 0.7805 0.7769 0.7732 0.7695 0.7659 0.7623 0.7589 0.7557 5 0.8920 0.8758 0.8525 0.8356 0.8223 0.8112 0.8017 0.7934 0.7861 0.7795 0.7737 0.7684 10 2.778 2.663 0.9747 0.9199 0.8857 0.8612 0.8421 0.8267 0.8138 0.8029 0.7936 0.7855 20 2.779 2.663 2.489 2.378 2.325 1.009 0.9499 0.9100 0.8806 0.8577 0.8393 0.8242 30 2.781 2.663 2.485 2.369 2.307 2.310 1.149 1.038 0.9728 0.9285 0.8958 0.8704 40 2.783 2.663 2.482 2.361 2.291 2.279 2.362 1.302 1.121 1.029 0.9695 0.9277 50 2.786 2.664 2.479 2.353 2.277 2.253 2.304 2.538 1.449 1.193 1.074 1.002 60 2.789 2.665 2.477 2.347 2.265 2.230 2.258 2.412 3.129 1.552 1.242 1.106 70 2.791 2.666 2.475 2.341 2.253 2.209 2.219 2.321 2.706 3.662 1.578 1.264 80 2.795 2.668 2.473 2.336 2.243 2.192 2.186 2.253 2.489 3.652 2.590 1.538 90 2.798 2.670 2.472 2.331 2.234 2.176 2.158 2.198 2.351 2.839 6.388 2.080 100 2.801 2.672 2.471 2.327 2.226 2.162 2.134 2.154 2.254 2.512 3.684 3.105 150 2.822 2.685 2.471 2.314 2.197 2.111 2.051 2.015 2.006 1.991 2.084 2.237 200 2.846 2.703 2.477 2.309 2.180 2.080 2.002 1.943 1.899 1.835 1.836 1.860 250 2.874 2.724 2.487 2.309 2.171 2.061 1.973 1.900 1.840 1.760 1.733 1.721 300 2.905 2.749 2.501 2.315 2.169 2.051 1.955 1.873 1.804 1.718 1.680 1.653 350 2.939 2.776 2.518 2.323 2.170 2.047 1.944 1.857 1.781 1.694 1.649 1.615 400 2.975 2.806 2.538 2.335 2.176 2.046 1.938 1.846 1.766 1.679 1.631 1.592 450 3.014 2.837 2.559 2.349 2.184 2.049 1.937 1.841 1.757 1.670 1.621 1.579 500 3.055 2.871 2.583 2.365 2.194 2.054 1.938 1.838 1.752 1.666 1.616 1.572 600 3.143 2.945 2.636 2.403 2.220 2.071 1.947 1.842 1.750 1.667 1.616 1.569 700 3.240 3.027 2.695 2.446 2.252 2.094 1.963 1.852 1.755 1.674 1.624 1.575 800 3.345 3.115 2.759 2.495 2.288 2.122 1.984 1.867 1.766 1.686 1.636 1.586 900 3.460 3.211 2.829 2.548 2.329 2.154 2.009 1.886 1.781 1.701 1.651 1.601 1,000 3.583 3.315 2.905 2.605 2.374 2.189 2.036 1.908 1.798 1.718 1.668 1.617 Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 1 0.7526 0.7471 0.7425 0.7339 0.7289 0.7248 0.7242 0.7242 0.7239 0.7229 0.7212 0.7189 5 0.7637 0.7557 0.7492 0.7379 0.7314 0.7260 0.7248 0.7246 0.7242 0.7231 0.7213 0.7189 10 0.7785 0.7669 0.7579 0.7429 0.7346 0.7274 0.7256 0.7251 0.7244 0.7232 0.7214 0.7190 20 0.8115 0.7916 0.7769 0.7536 0.7412 0.7305 0.7272 0.7260 0.7250 0.7236 0.7216 0.7191 30 0.8501 0.8195 0.7979 0.7652 0.7483 0.7336 0.7289 0.7270 0.7256 0.7240 0.7218 0.7193 40 0.8962 0.8515 0.8213 0.7776 0.7558 0.7369 0.7306 0.7279 0.7262 0.7243 0.7221 0.7195 50 0.9530 0.8884 0.8474 0.7910 0.7637 0.7402 0.7323 0.7290 0.7268 0.7247 0.7224 0.7196 60 1.026 0.9316 0.8768 0.8053 0.7720 0.7437 0.7341 0.7300 0.7275 0.7252 0.7226 0.7198 70 1.123 0.9830 0.9100 0.8208 0.7809 0.7473 0.7359 0.7311 0.7281 0.7256 0.7229 0.7200 80 1.262 1.045 0.9474 0.8373 0.7902 0.7510 0.7378 0.7322 0.7288 0.7260 0.7232 0.7202 90 1.469 1.121 0.9899 0.8550 0.7999 0.7549 0.7398 0.7333 0.7295 0.7265 0.7235 0.7204 100 1.784 1.214 1.038 0.8737 0.8102 0.7588 0.7418 0.7345 0.7303 0.7270 0.7239 0.7207 150 2.345 1.832 1.352 0.9820 0.8674 0.7802 0.7526 0.7407 0.7342 0.7296 0.7257 0.7220 200 1.885 1.822 1.582 1.094 0.9299 0.8039 0.7645 0.7478 0.7387 0.7327 0.7278 0.7235 233 234 D2 Properties of Selected Important Pure Substances D2.4. Table 16. (continued) Temperature in C Pressure in bar 60 80 100 150 200 300 400 500 600 700 800 900 250 1.713 1.678 1.556 1.183 0.9875 0.8286 0.7775 0.7555 0.7437 0.7361 0.7303 0.7253 300 1.629 1.582 1.509 1.240 1.034 0.8531 0.7910 0.7638 0.7492 0.7400 0.7331 0.7274 350 1.583 1.525 1.464 1.250 1.072 0.8760 0.8048 0.7725 0.7551 0.7441 0.7362 0.7297 400 1.556 1.491 1.431 1.252 1.099 0.8965 0.8186 0.7816 0.7614 0.7486 0.7395 0.7322 450 1.540 1.470 1.408 1.253 1.113 0.9148 0.8319 0.7909 0.7679 0.7534 0.7431 0.7350 500 1.531 1.458 1.393 1.252 1.122 0.9310 0.8445 0.8002 0.7747 0.7584 0.7468 0.7379 600 1.526 1.448 1.380 1.247 1.136 0.9576 0.8672 0.8182 0.7885 0.7689 0.7550 0.7443 700 1.531 1.450 1.379 1.245 1.146 0.9780 0.8867 0.8350 0.8022 0.7799 0.7637 0.7513 800 1.540 1.458 1.386 1.247 1.153 0.9953 0.9036 0.8503 0.8154 0.7909 0.7727 0.7587 900 1.554 1.469 1.396 1.254 1.159 1.011 0.9187 0.8640 0.8278 0.8016 0.7819 0.7664 1,000 1.569 1.484 1.409 1.264 1.167 1.024 0.9326 0.8767 0.8393 0.8120 0.7909 0.7741 6 1. Bibliography Span R, Wagner W (1996) A new equation of state for carbon dioxide covering the fluid region from the triple point temperature to 1100 K at pressures up to 800 MPa. J Phys Chem Ref Data 25:1509/1596 2. Vesovic V, Wakeham WA, Olchowy GA, Sengers JV, Watson JTR, Millat J (1990) The transport properties of carbon dioxide. J Phys Chem Ref Data 19:763/808 Properties of Oxygen D2.5 D2.5 Properties of Oxygen Roland Span1 . Rolf Krauss2 1 2 Ruhr-Universität Bochum, Bochum, Germany Universität Stuttgart, Stuttgart, Germany 1 Characteristic Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 4 Reference States of Enthalpy and Entropy . . . . . . . . . . . . . . 235 2 Critical Point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 5 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 3 Triple Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 The tables with thermodynamic properties of oxygen were calculated using the fundamental equation of state by Schmidt and Wagner [1], see also Wagner and de Reuck [2]. This equation formally is valid for temperatures up to 300 K (26.85 C). However, it allows for reasonable extrapolation to much higher p Pressure in bar b r Density in kg/m3 ws Isentropic speed of sound in m/s Isobaric expansion coefficient in 103/K b = v1·(∂v/∂T)p # Temperature in C l Thermal conductivity in mW/(m K) Z Compression factor Z = p/(rRT ) Dynamic viscosity in 106 Pa·s h Specific enthalpy in kJ/kg n Kinematic viscosity n in 107 m2/s s Specific entropy in kJ/(kg K) a Thermal diffusivity in 107 m2/s cp Specific isobaric heat capacity in kJ/(kg K) Pr Prandtl number Pr = cp/ l cv Specific isochoric heat capacity in kJ/(kg K) v Specific volume in m3/kg temperatures [2], even far beyond the limit of 100 C chosen for the tables in this section. The correlations by Laesecke et al. [3] were used to calculate the thermal conductivity and viscosities. The required densities were calculated using the fundamental equation [1, 2]. 1 Characteristic Quantities ~ = 31.9988 g/mol, specific gas constant Molecular mass M R = 259.832869 J/(kg K). 2 Critical Point [1] pc = 50.460 bar, Tc = 154.599 K (#c = 118.551 C), rc = 417 kg/m3. 3 Triple Point [1] pt = 0.0014633 bar, Tt = 54.361 K (#t = 218.789 C). 4 Reference States of Enthalpy and Entropy h = 0 kJ/kg, s = 0 kJ/(kg K) at T = 298.15 K (# = 25 C), p = 1 bar for the ideal gas. 235 236 D2 Properties of Selected Important Pure Substances D2.5. Table 1. Properties of oxygen at p = 1 bar q C r kg/m3 h kJ/kg s kJ/(kg K) cp kJ/(kg K) cv kJ/(kg K) b 103/K ws m/s l mW/(m K) h 106 Pa·s n 107 m2/s Pr – a 107 m2/s 215 1290.2 458.5 4.207 1.671 1.113 3.36 1132 – – – – – 210 1268.1 450.1 4.069 1.676 1.059 3.53 1113 – – – – – 1042 200 1222.6 433.3 3.822 1.678 1.001 3.78 190 1175.6 416.5 3.607 1.685 0.9566 4.08 962.1 176.6 311.6 2.55 0.861 2.96 162.5 224.8 1.91 0.820 2.33 180 4.2538 188.7 1.072 0.9473 0.6587 11.7 181.1 8.611 6.810 16.0 21.4 0.749 170 3.8130 179.3 0.9768 0.9338 0.6531 10.3 191.5 9.633 7.640 20.0 27.1 0.741 160 3.4584 170.0 0.8906 0.9305 0.6543 9.26 201.1 10.64 8.452 24.4 33.1 0.739 150 3.1660 160.7 0.8119 0.9269 0.6542 8.43 210.2 11.62 9.244 29.2 39.6 0.737 140 2.9205 151.5 0.7397 0.9237 0.6535 7.74 218.9 12.58 34.3 46.6 0.735 10.02 130 2.7111 142.2 0.6729 0.9211 0.6528 7.16 227.2 13.52 10.77 39.7 54.1 0.734 120 2.5302 133.0 0.6108 0.9191 0.6522 6.66 235.2 14.44 11.51 45.5 62.1 0.733 110 2.3723 123.9 0.5527 0.9175 0.6518 6.23 242.9 15.33 12.23 51.5 70.5 0.732 100 2.2332 114.7 0.4982 0.9164 0.6515 5.86 250.4 16.21 12.93 57.9 79.2 0.731 90 2.1097 105.5 0.4467 0.9155 0.6513 5.53 257.6 17.07 13.62 64.6 88.4 0.730 80 1.9992 96.38 0.3981 0.9149 0.6512 5.23 264.6 17.92 14.29 71.5 98.0 0.730 70 1.8999 87.24 0.3519 0.9145 0.6513 4.97 271.5 18.74 14.95 78.7 108 60 1.8100 78.09 0.3080 0.9143 0.6514 4.73 278.1 19.55 15.60 86.2 118 0.729 50 1.7283 68.95 0.2661 0.9142 0.6517 4.51 284.6 20.35 16.23 93.9 129 0.729 0.730 40 1.6536 59.81 0.2260 0.9144 0.6521 4.32 290.9 21.14 16.86 102 140 0.729 30 1.5852 50.66 0.1876 0.9147 0.6527 4.14 297.1 21.91 17.47 110 151 0.729 20 1.5223 41.52 0.1507 0.9152 0.6534 3.97 303.1 22.68 18.07 119 163 0.729 10 1.4642 32.36 0.1152 0.9158 0.6542 3.82 309.0 23.43 18.66 127 175 0.729 0 1.4103 23.20 0.0811 0.9167 0.6552 3.68 314.8 24.18 19.24 136 187 0.729 10 1.3603 14.03 0.0481 0.9177 0.6564 3.54 320.5 24.92 19.81 146 200 0.729 20 1.3138 4.843 0.0162 0.9189 0.6577 3.42 326.0 25.66 20.37 155 213 0.730 25 1.2917 0.2470 0.0007 0.9196 0.6584 3.36 328.7 26.02 20.65 160 219 0.730 30 1.2703 0.0146 0.9203 0.6592 3.31 331.4 26.38 20.92 165 226 0.730 40 1.2296 13.56 0.0445 0.9219 0.6609 3.20 336.7 27.11 21.47 175 239 0.730 50 1.1915 22.79 0.0735 0.9236 0.6627 3.10 341.9 27.83 22.00 815 253 0.730 60 1.1556 32.04 0.1017 0.9255 0.6647 3.01 347.1 28.54 22.53 195 267 0.731 70 1.1219 41.30 0.1291 0.9276 0.6668 2.92 352.1 29.25 23.06 206 281 0.731 80 1.0900 50.59 0.1558 0.9298 0.6690 2.84 357.0 29.96 23.57 216 296 0.732 90 1.0600 59.90 0.1818 0.9321 0.6714 2.76 361.9 30.67 24.08 227 310 0.732 100 1.0315 69.23 0.2071 0.9345 0.6739 2.68 366.6 31.37 24.58 238 325 0.732 110 1.0045 78.59 0.2319 0.9371 0.6765 2.61 371.3 32.07 25.08 250 341 0.733 120 0.97896 87.97 0.2561 0.9398 0.6792 2.55 375.9 32.77 25.57 261 356 0.733 130 0.95465 97.38 0.2797 0.9425 0.6820 2.48 380.5 33.46 26.06 273 372 0.734 140 0.93151 106.8 0.3028 0.9454 0.6849 2.42 384.9 34.16 26.54 285 388 0.734 150 0.90947 116.3 0.3255 0.9483 0.6879 2.37 389.3 34.85 27.01 297 404 0.735 160 0.88846 125.8 0.3477 0.9513 0.6909 2.31 393.7 35.54 27.48 309 421 0.736 170 0.86839 135.3 0.3694 0.9543 0.6940 2.26 398.0 36.23 27.95 322 437 0.736 180 0.84921 144.9 0.3907 0.9574 0.6971 2.21 402.2 36.92 28.41 334 454 0.737 190 0.83086 154.5 0.4117 0.9605 0.7002 2.16 406.4 37.60 28.86 347 471 0.737 200 0.81329 164.1 0.4322 0.9636 0.7034 2.11 410.5 38.28 29.31 360 488 0.738 250 0.73551 212.7 0.5298 0.9795 0.7193 1.91 430.3 41.66 31.50 428 578 0.741 300 0.67133 262.0 0.6199 0.9951 0.7350 1.75 449.1 44.98 33.60 501 673 0.743 350 0.61745 312.2 0.7038 1.010 0.7500 1.61 467.1 48.23 35.63 577 773 0.746 400 0.57158 363.0 0.7823 1.024 0.7640 1.49 484.3 51.41 37.58 657 878 0.748 450 0.53206 414.5 0.8561 1.037 0.7769 1.38 500.9 54.52 39.47 742 988 0.751 500 0.49765 466.7 0.9258 1.049 0.7887 1.29 517.0 57.56 41.30 830 1103 0.752 4.353 D2.5 Properties of Oxygen D2.5. Table 1. (continued) q C r kg/m3 h kJ/kg s kJ/(kg K) cp kJ/(kg K) cv kJ/(kg K) b 103/K ws m/s l mW/(m K) h 106 Pa·s n 107 m2/s a 107 m2/s Pr – 550 0.46742 519.4 0.9919 1.059 0.7994 1.21 532.5 60.52 43.09 922 1222 0.754 600 0.44066 572.6 1.055 1.069 0.8091 1.15 547.6 63.42 44.83 1017 1346 0.756 650 0.41679 626.3 1.114 1.078 0.8180 1.08 562.4 66.25 46.53 1116 1475 0.757 700 0.39538 680.4 1.171 1.086 0.8261 1.03 576.7 69.02 48.20 1219 1607 0.758 D2.5. Table 2. Properties of the saturated liquid q C p bar r0 kg/m3 h0 kJ/kg s0 kJ/(kg K) cp0 kJ/(kg K) cv0 kJ/(kg K) b0 103/K ws0 m/s l0 mW/(m K) h0 106 Pa·s n0 107 m2/s a0 107 m2/s Pr 0 – 218 0.00187 1302.8 463.6 4.295 1.671 1.173 3.18 1128 – – – – – 216 0.00337 1294.4 460.2 4.236 1.671 1.129 3.31 1132 – – – – – 214 0.00582 1285.7 456.9 4.178 1.673 1.099 3.40 1130 – – – – – 212 0.00967 1276.9 453.5 4.122 1.675 1.077 3.47 1123 – – – – – 210 0.01552 1268.0 450.2 4.068 1.676 1.059 3.53 1113 – – – – – 208 0.02411 1259.0 446.8 4.016 1.677 1.045 3.59 1101 – – – – – 206 0.03640 1250.0 443.5 3.965 1.678 1.032 3.63 1087 – – – – – 204 0.05354 1240.8 440.1 3.916 1.678 1.021 3.68 1073 – – – – – 202 0.07690 1231.7 436.7 3.868 1.678 1.011 3.73 1058 179.3 335.8 2.73 0.868 3.14 200 0.10808 1222.5 433.4 3.822 1.678 1.001 3.78 1042 176.5 311.2 2.55 0.860 2.96 198 0.14892 1213.2 430.0 3.777 1.679 0.9914 3.84 1026 173.7 289.6 2.39 0.853 2.80 196 0.20148 1203.9 426.7 3.732 1.680 0.9822 3.89 1010 170.9 270.6 2.25 0.845 2.66 194 0.26807 1194.5 423.3 3.690 1.681 0.9734 3.95 994.3 168.1 253.6 2.12 0.837 2.54 192 0.35123 1185.0 419.9 3.648 1.683 0.9648 4.02 978.1 165.3 238.4 2.01 0.829 2.43 190 0.45372 1175.5 416.6 3.607 1.685 0.9565 4.08 961.9 162.5 224.6 1.91 0.820 2.33 188 0.57851 1165.8 413.2 3.567 1.688 0.9483 4.16 945.6 159.7 212.2 1.82 0.811 2.24 186 0.72876 1156.1 409.8 3.527 1.692 0.9404 4.24 929.3 156.9 200.8 1.74 0.802 2.17 184 0.90782 1146.3 406.4 3.489 1.697 0.9328 4.32 912.9 154.0 190.4 1.66 0.792 2.10 182 1.1192 1136.4 403.0 3.451 1.702 0.9253 4.42 896.4 151.2 180.8 1.59 0.782 2.03 180 1.3666 1126.3 399.6 3.414 1.708 0.9181 4.52 879.8 148.4 172.0 1.53 0.771 1.98 178 1.6538 1116.2 396.1 3.378 1.716 0.9110 4.62 863.1 145.7 163.7 1.47 0.761 1.93 176 1.9848 1105.8 392.7 3.343 1.724 0.9042 4.74 846.3 143.0 156.1 1.41 0.750 1.88 174 2.3636 1095.4 389.2 3.308 1.733 0.8976 4.86 829.4 140.2 149.0 1.36 0.739 1.84 172 2.7943 1084.8 385.7 3.273 1.744 0.8913 5.00 812.4 137.5 142.3 1.31 0.727 1.81 170 3.2812 1074.0 382.2 3.239 1.755 0.8851 5.14 795.1 134.7 136.1 1.27 0.714 1.77 168 3.8286 1063.0 378.6 3.205 1.769 0.8792 5.30 777.8 131.9 130.2 1.22 0.702 1.74 166 4.4408 1051.8 375.1 3.172 1.783 0.8735 5.48 760.2 129.1 124.6 1.18 0.689 1.72 164 5.1223 1040.4 371.4 3.140 1.799 0.8680 5.67 742.4 126.4 119.3 1.15 0.675 1.70 162 5.8776 1028.8 367.8 3.107 1.817 0.8628 5.87 724.4 123.6 114.3 1.11 0.661 1.68 160 6.7111 1016.9 364.1 3.075 1.838 0.8578 6.10 706.1 120.8 109.6 1.08 0.646 1.67 158 7.6276 1004.7 360.4 3.043 1.860 0.8532 6.35 687.6 118.0 105.0 1.05 0.631 1.66 100.7 156 8.6316 992.21 356.6 3.012 1.886 0.8488 6.63 668.8 115.2 1.02 0.616 1.65 154 9.7278 979.40 352.8 2.980 1.914 0.8447 6.94 649.7 112.3 96.57 0.986 0.599 1.65 966.24 348.9 2.949 1.946 0.8409 7.29 630.3 109.5 92.59 0.958 0.582 1.65 152 10.921 150 12.216 952.67 345.0 2.918 1.982 0.8375 7.68 610.5 106.7 88.75 0.932 0.565 1.65 148 13.618 938.65 341.0 2.887 2.024 0.8346 8.13 590.3 103.8 85.05 0.906 0.547 1.66 101.0 146 15.131 924.14 336.9 2.856 2.072 0.8320 8.65 569.7 81.46 0.882 0.527 1.67 144 16.761 909.07 332.7 2.824 2.127 0.8300 9.25 548.6 98.10 77.98 0.858 0.507 1.69 142 18.513 893.36 328.5 2.793 2.192 0.8285 9.95 527.0 95.21 74.59 0.835 0.486 1.72 237 238 D2 Properties of Selected Important Pure Substances D2.5. Table 2. (continued) q C p bar r0 kg/m3 h0 kJ/kg s0 kJ/(kg K) cp0 kJ/(kg K) cv0 kJ/(kg K) b0 103/K ws0 m/s l0 mW/(m K) h0 Pa·s 106 n0 m2/s 107 a0 m2/s Pr 0 – 107 140 20.393 876.93 324.1 2.762 2.269 0.8277 10.8 504.8 92.31 71.27 0.813 0.464 1.75 138 22.406 859.66 319.6 2.730 2.362 0.8277 11.8 481.9 89.38 68.01 0.791 0.440 1.80 136 24.558 841.39 314.9 2.697 2.475 0.8287 13.1 458.3 86.44 64.80 0.770 0.415 1.86 134 26.856 821.93 310.1 2.664 2.618 0.8309 14.7 433.8 83.48 61.60 0.749 0.388 1.93 132 29.305 801.01 305.0 2.630 2.803 0.8348 16.8 408.3 80.52 58.41 0.729 0.359 2.03 130 31.915 778.27 299.7 2.595 3.050 0.8410 19.6 381.4 77.59 55.18 0.709 0.327 2.17 128 34.692 753.15 294.0 2.559 3.399 0.8506 23.7 353.0 74.76 51.88 0.689 0.292 2.36 126 37.646 724.78 287.9 2.519 3.930 0.8657 30.1 322.5 72.23 48.45 0.668 0.254 2.64 124 40.789 691.67 281.1 2.477 4.840 0.8903 41.5 289.2 70.63 44.78 0.647 0.211 3.07 122 44.137 650.56 273.2 2.427 6.805 0.9344 66.9 251.3 72.09 40.68 0.625 0.163 3.84 120 47.710 590.99 262.7 2.362 204.4 86.69 35.45 0.600 0.100 5.99 14.65 1.031 174 D2.5. Table 3. Properties of the saturated vapor q C 218 p bar 0.00187 r00 kg/m3 h00 kJ/kg 0.01305 221.4 s00 kJ/(kg K) cp00 kJ/(kg K) cv00 kJ/(kg K) b00 103/K ws00 m/s 0.0951 0.9286 0.6660 18.2 141.3 l00 mW/(m K) – h00 106 Pa·s – n00 107 m2/s – a00 107 m2/s Pr00 – – – 216 0.00337 0.02272 219.6 0.0259 0.9359 0.6721 17.6 143.7 – – – – – 214 0.00582 0.03792 217.8 0.1368 0.9440 0.6788 17.1 146.1 – – – – – 212 0.00967 0.06095 216.0 0.2387 0.9523 0.6857 16.6 148.3 – – – – – 210 0.01552 0.0947 214.3 0.3326 0.9602 0.6921 16.1 150.6 – – – – – 208 0.02411 0.14271 212.5 0.4191 0.9672 0.6976 15.7 152.8 – – – – – 206 0.03640 0.20920 210.7 0.4990 0.9728 0.7018 15.3 155.0 – – – – – 204 0.05354 0.29909 208.9 0.5729 0.9768 0.7045 14.9 157.2 – – – – 202 0.07690 0.41798 207.2 0.6415 0.9791 0.7056 14.5 159.3 6.111 4.878 117 149 0.782 200 0.10808 0.57218 205.4 0.7052 0.9798 0.7052 14.2 161.4 6.335 5.056 88.4 113 0.782 198 0.14892 0.76864 203.7 0.7646 0.9792 0.7034 13.8 163.5 6.561 5.233 68.1 87.2 0.781 196 0.20148 1.0150 202.0 0.8199 0.9776 0.7005 13.5 165.5 6.878 5.409 53.3 68.4 0.779 194 0.26807 1.3194 200.3 0.8717 0.9753 0.6967 13.2 167.5 7.015 5.586 42.3 54.5 0.777 192 0.35123 1.6906 198.6 0.9203 0.9729 0.6925 13.0 169.5 7.244 5.763 34.1 44.0 0.774 190 0.45372 2.1381 197.0 0.9659 0.9708 0.6882 12.8 171.4 7.475 5.939 27.8 36.0 0.771 188 0.57851 2.6715 195.4 1.009 0.9693 0.6840 12.6 173.2 7.708 6.115 22.9 29.8 0.769 186 0.72876 3.3014 193.8 1.049 0.9688 0.6801 12.4 174.9 7.944 6.292 19.1 24.8 0.767 184 0.90782 4.0386 192.3 1.088 0.9696 0.6769 12.3 176.6 8.184 6.469 16.0 20.9 0.766 182 1.1192 4.8944 190.9 1.124 0.9721 0.6745 12.2 178.2 8.427 6.646 13.6 17.7 0.767 180 1.3666 5.8808 189.5 1.159 0.9763 0.6729 12.1 179.7 8.675 6.823 11.6 15.1 0.768 178 1.6538 7.0102 188.1 1.192 0.9824 0.6724 12.1 181.1 8.928 7.001 9.99 13.0 0.770 176 1.9848 8.2958 186.8 1.224 0.9907 0.6728 12.0 182.4 9.188 7.180 8.65 11.2 0.774 174 2.3636 9.7513 185.6 1.254 1.001 0.6743 12.1 183.6 9.455 7.359 7.55 9.68 0.779 172 2.7943 11.391 184.4 1.283 1.014 0.6767 12.1 184.7 9.730 7.540 6.62 8.42 0.786 170 3.2812 13.231 183.4 1.312 1.029 0.6802 12.2 185.6 10.01 7.722 5.84 7.35 0.794 168 3.8286 15.287 182.3 1.339 1.047 0.6846 12.3 186.5 10.31 7.905 5.17 6.44 0.803 166 4.4408 17.577 181.4 1.365 1.068 0.6899 12.5 187.3 10.62 8.091 4.60 5.66 0.813 164 5.1223 20.119 180.5 1.391 1.091 0.6960 12.7 187.9 10.94 8.278 4.11 4.99 0.825 162 5.8776 22.935 179.8 1.415 1.117 0.7029 12.9 188.4 11.28 8.468 3.69 4.40 0.838 160 6.7111 26.046 179.1 1.440 1.146 0.7105 13.2 188.8 11.64 8.662 3.33 3.90 0.853 158 7.6276 29.479 178.5 1.464 1.179 0.7187 13.5 189.1 12.02 8.858 3.00 3.46 0.869 156 8.6316 33.259 178.0 1.487 1.216 0.7277 13.9 189.3 12.43 9.059 2.72 3.07 0.886 154 9.7278 37.417 177.6 1.510 1.257 0.7372 14.4 189.4 12.87 9.265 2.48 2.73 0.905 152 10.921 41.990 177.4 1.533 1.304 0.7474 14.9 189.4 13.34 9.477 2.26 2.44 0.926 150 12.216 47.016 177.2 1.556 1.356 0.7582 15.6 189.2 13.85 9.696 2.06 2.17 0.949 – D2.5 Properties of Oxygen D2.5. Table 3. (continued) p bar r00 kg/m3 h00 kJ/kg s00 kJ/(kg K) cp00 kJ/(kg K) cv00 kJ/(kg K) b00 103/K ws00 m/s l00 mW/(m K) 148 13.618 52.542 177.2 1.578 1.416 0.7696 16.3 188.9 14.41 1.89 1.94 0.975 146 15.131 58.621 177.3 1.601 1.484 0.7816 17.2 188.5 15.02 10.16 1.73 1.73 1.00 144 16.761 65.318 177.6 1.624 1.563 0.7945 18.2 188.0 15.70 10.41 1.59 1.54 1.04 142 18.513 72.708 178.1 1.647 1.655 0.8081 19.4 187.4 16.46 10.67 1.47 1.37 1.07 140 20.393 80.886 178.7 1.670 1.765 0.8228 20.9 186.6 17.32 10.95 1.35 1.21 1.12 138 22.406 89.968 179.6 1.694 1.897 0.8386 22.7 185.7 18.29 11.25 1.25 1.07 1.17 1.23 q C h00 Pa·s 106 9.923 n00 m2/s 107 a00 m2/s 107 Pr00 – 136 24.558 100.10 180.7 1.719 2.060 0.8558 24.9 184.6 19.41 11.58 1.16 0.941 134 26.856 111.48 182.1 1.745 2.265 0.8747 27.7 183.4 20.70 11.94 1.07 0.820 1.31 132 29.305 124.37 183.8 1.772 2.533 0.8960 31.5 182.0 22.23 12.34 0.992 0.706 1.41 130 31.915 139.13 186.0 1.801 2.896 0.9202 36.5 180.4 24.06 12.80 0.920 0.597 1.54 128 34.692 156.30 188.7 1.833 3.416 0.9484 43.8 178.6 26.30 13.34 0.853 0.493 1.73 126 37.646 176.76 192.0 1.868 4.223 0.9827 55.1 176.6 29.15 13.98 0.791 0.390 2.03 124 40.789 202.04 196.4 1.909 5.640 1.026 74.9 174.1 32.97 14.81 0.733 0.289 2.53 122 44.137 235.45 202.4 1.959 8.750 1.087 118 170.9 38.68 15.96 0.678 0.188 3.61 120 47.710 287.30 212.1 2.031 1.185 285 165.9 50.23 17.89 0.623 0.084 7.39 20.74 D2.5. Table 4. Density r of oxygen in kg/m3 Temperature in C Pressure in bar 1 200 1223 180 4.254 160 3.458 18.66 140 2.920 120 2.530 100 2.233 90 2.110 80 1.999 70 1.900 1.810 9.139 50 40 1.728 1.654 8.714 8.327 5 1223 1127 15.27 13.02 11.38 10.72 10.13 10 1224 1128 1018 32.57 27.06 23.36 21.90 20.62 19.50 18.51 17.61 16.80 20 1226 1131 1022 78.50 59.30 49.38 45.80 42.79 40.21 37.97 35.99 34.22 30 1227 1133 1026 886.7 100.3 72.17 66.76 62.28 58.47 55.17 52.28 40 1229 1135 1030 895.8 161.3 113.2 101.6 92.83 85.85 80.08 75.20 70.98 50 1230 1138 1034 904.2 632.9 154.3 134.9 121.4 111.1 102.9 96.11 90.36 60 1231 1140 1038 911.9 696.9 205.8 173.0 152.7 138.2 127.0 117.9 110.4 70 1233 1142 1041 919.0 729.6 273.3 217.3 187.3 167.2 152.3 140.6 131.1 80 1234 1144 1045 925.7 753.0 360.9 268.6 225.3 198.2 178.9 164.2 152.4 78.90 9.609 60 90 1236 1146 1148 932.0 771.5 453.7 326.5 266.6 231.1 206.8 188.6 174.2 100 1237 1148 1051 938.0 787.0 525.4 387.1 310.4 265.6 235.6 213.6 196.5 120 1240 1152 1058 949.1 812.4 613.3 493.6 399.1 336.9 295.1 265.0 242.0 140 1243 1156 1064 959.3 832.9 666.3 568.0 476.7 405.8 354.4 316.7 287.9 160 1245 1160 1070 968.7 850.3 703.9 620.2 537.9 466.5 410.1 366.6 332.8 180 1248 1164 1075 977.4 865.5 733.0 659.4 585.5 517.6 459.9 413.1 375.6 200 1251 1168 1080 985.6 879.1 757.0 690.6 623.5 559.9 503.3 455.3 415.4 225 1254 1172 1087 995.2 894.3 782.0 722.2 661.8 603.3 549.4 501.7 460.6 250 1257 1176 1093 1004 908.0 803.2 748.3 693.0 638.9 588.0 541.7 500.5 275 1260 1181 1099 1013 920.5 821.8 770.6 719.3 668.9 620.8 576.2 535.8 300 1263 1185 1105 1021 931.9 838.3 790.2 742.0 694.7 649.2 606.4 567.0 325 1266 1189 1110 1028 942.6 853.1 807.6 762.1 717.3 674.0 633.0 594.7 350 1269 1193 1115 1035 952.5 866.7 823.3 780.0 737.4 696.1 656.7 619.6 375 1272 1197 1120 1042 961.9 879.2 837.6 796.2 755.5 715.9 678.0 642.1 400 1275 1200 1125 1049 970.7 890.9 850.8 811.1 772.0 733.9 697.3 662.5 450 1281 1208 1135 1061 987.0 911.9 874.5 837.5 801.1 765.6 731.3 698.5 500 1286 1215 1144 1073 930.6 895.3 860.5 826.3 792.9 760.5 729.4 1002 239 240 D2 Properties of Selected Important Pure Substances D2.5. Table 4. (continued) Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 1 1.585 1.522 1.464 1.410 1.360 1.314 1.270 1.230 1.191 1.156 1.090 1.032 5 7.975 7.651 7.354 7.079 6.824 6.587 6.366 6.160 5.967 5.786 5.455 5.160 10 16.07 15.40 14.79 14.22 13.70 13.22 12.77 12.36 11.96 11.59 10.92 10.33 20 32.64 31.21 29.91 28.72 27.62 26.61 25.68 24.81 24.01 23.25 21.88 20.67 30 49.71 47.42 45.35 43.47 41.75 40.18 38.73 37.38 36.14 34.98 32.88 31.03 40 67.30 64.03 61.10 58.47 56.08 53.90 51.90 50.05 48.34 46.76 43.90 41.39 50 85.39 81.03 77.17 73.71 70.60 67.77 65.18 62.80 60.61 58.59 54.95 51.76 60 104.0 70 123.0 116.1 98.41 110.1 93.52 104.8 89.18 100.1 85.28 81.76 78.56 75.63 72.94 70.45 66.00 62.13 95.88 92.03 88.52 85.31 82.35 77.06 72.48 80 142.5 134.2 127.0 120.7 115.1 110.1 105.6 101.5 97.70 94.25 88.12 82.82 99.17 93.13 90 162.4 152.5 144.1 136.7 130.2 124.4 119.2 114.4 110.1 106.2 100 182.6 171.1 161.3 152.8 145.3 138.7 132.8 127.4 122.5 118.1 110.2 103.4 120 223.7 208.7 196.1 185.2 175.8 167.4 160.0 153.4 147.3 141.8 132.1 123.9 140 265.1 246.5 230.9 217.7 206.2 196.1 187.2 179.2 172.0 165.4 153.9 144.1 160 305.8 283.8 265.4 249.8 236.3 224.5 214.0 204.7 196.3 188.7 175.4 164.1 180 345.2 320.1 299.1 281.3 265.8 252.4 240.5 229.8 220.3 211.7 196.6 183.8 200 382.4 354.9 331.7 311.8 294.6 279.6 266.3 254.5 243.8 234.2 217.4 203.2 225 425.6 395.8 370.3 348.4 329.3 312.5 297.6 284.4 272.4 261.6 242.8 226.9 250 464.6 433.4 406.4 382.8 362.1 343.9 327.7 313.1 300.0 288.2 267.5 250.0 275 499.7 467.8 439.8 415.0 393.1 373.7 356.3 340.7 326.6 313.8 291.3 272.3 300 531.2 499.1 470.5 445.0 422.2 401.8 383.5 366.9 352.0 338.3 314.3 294.0 325 559.6 527.6 498.8 472.8 449.4 428.3 409.2 391.9 376.2 361.8 336.5 314.9 350 585.2 553.6 524.8 498.5 474.7 453.1 433.5 415.6 399.3 384.3 357.8 335.1 375 608.5 577.3 548.7 522.4 498.4 476.5 456.4 438.0 431.2 405.7 378.2 354.5 400 629.7 599.1 570.8 544.6 520.5 498.4 478.0 459.3 442.0 426.1 397.8 373.3 450 667.3 637.9 610.3 584.5 560.5 538.3 517.6 498.4 480.7 464.1 434.4 408.6 500 699.6 671.3 644.6 619.4 595.8 573.6 553.0 533.6 515.6 498.7 468.1 441.2 D2.5. Table 5. Compression factor Z of oxygen Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 50 40 1 0.004 0.971 0.984 0.990 0.993 0.995 0.996 0.997 0.997 0.998 0.998 0.998 5 0.022 0.018 0.911 0.947 0.965 0.976 0.980 0.983 0.986 0.988 0.990 0.991 10 0.043 0.037 0.033 0.887 0.929 0.952 0.960 0.966 0.971 0.976 0.979 0.982 20 0.086 0.073 0.067 0.736 0.848 0.900 0.918 0.931 0.942 0.951 0.959 0.965 30 0.129 0.109 0.099 0.098 0.751 0.845 0.874 0.895 0.913 0.926 0.938 0.947 40 0.171 0.146 0.132 0.129 0.623 0.785 0.827 0.859 0.883 0.902 0.917 0.930 50 0.214 0.182 0.164 0.160 0.199 0.720 0.779 0.821 0.853 0.877 0.897 0.913 60 0.256 0.218 0.197 0.190 0.216 0.648 0.729 0.783 0.823 0.853 0.878 0.897 70 0.299 0.253 0.229 0.220 0.241 0.569 0.677 0.745 0.793 0.830 0.858 0.882 80 0.341 0.289 0.260 0.250 0.267 0.493 0.626 0.708 0.765 0.807 0.840 0.867 90 0.383 0.324 0.292 0.279 0.293 0.441 0.579 0.673 0.738 0.786 0.823 0.853 100 0.425 0.360 0.324 0.308 0.319 0.423 0.543 0.642 0.713 0.766 0.807 0.840 D2.5 Properties of Oxygen D2.5. Table 5. (continued) Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 50 40 120 0.509 0.430 0.386 0.365 0.371 0.435 0.511 0.599 0.675 0.734 0.781 0.818 140 0.583 0.500 0.448 0.422 0.422 0.467 0.518 0.585 0.654 0.713 0.762 0.803 160 0.676 0.570 0.509 0.477 0.473 0.505 0.542 0.593 0.650 0.704 0.753 0.794 180 0.759 0.639 0.570 0.532 0.523 0.546 0.574 0.613 0.659 0.707 0.751 0.791 200 0.841 0.708 0.630 0.587 0.572 0.587 0.609 0.639 0.677 0.717 0.758 0.795 225 0.944 0.793 0.704 0.653 0.632 0.640 0.655 0.677 0.707 0.739 0.774 0.806 250 1.046 0.878 0.778 0.720 0.692 0.692 0.702 0.719 0.741 0.768 0.796 0.824 275 1.148 0.962 0.851 0.785 0.751 0.744 0.750 0.762 0.779 0.800 0.823 0.847 300 1.249 1.046 0.924 0.850 0.809 0.795 0.798 0.806 0.818 0.834 0.853 0.873 325 1.350 1.130 0.996 0.914 0.866 0.847 0.846 0.850 0.858 0.871 0.886 0.902 350 1.451 1.212 1.067 0.977 0.923 0.898 0.893 0.894 0.899 0.908 0.919 0.932 375 1.551 1.295 1.138 1.040 0.980 0.948 0.941 0.938 0.940 0.946 0.954 0.964 400 1.650 1.377 1.209 1.102 1.036 0.998 0.988 0.983 0.982 0.984 0.989 0.997 450 1.849 1.540 1.349 1.225 1.146 1.097 1.081 1.071 1.064 1.061 1.061 1.063 500 2.045 1.701 1.487 1.347 1.254 1.194 1.174 1.158 1.146 1.139 1.134 1.132 Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 1 0.998 0.999 0.999 0.999 0.999 0.999 0.999 1.000 1.000 1.000 1.000 1.000 5 0.992 0.994 0.994 0.995 0.996 0.997 0.997 0.998 0.998 0.998 0.999 0.999 10 0.985 0.987 0.989 0.991 0.992 0.993 0.994 0.995 0.996 0.997 0.998 0.999 20 0.970 0.974 0.978 0.981 0.984 0.987 0.989 0.991 0.992 0.994 0.996 0.998 30 0.955 0.962 0.968 0.972 0.977 0.980 0.983 0.986 0.989 0.991 0.994 0.997 40 0.941 0.950 0.957 0.964 0.969 0.974 0.979 0.982 0.985 0.988 0.993 0.997 50 0.927 0.938 0.948 0.956 0.963 0.969 0.974 0.978 0.982 0.986 0.992 0.996 60 0.913 0.927 0.938 0.948 0.956 0.963 0.970 0.975 0.980 0.984 0.991 0.996 70 0.901 0.916 0.929 0.941 0.950 0.959 0.966 0.972 0.977 0.982 0.990 0.996 80 0.888 0.906 0.921 0.934 0.945 0.954 0.962 0.969 0.975 0.981 0.989 0.996 90 0.877 0.897 0.914 0.928 0.940 0.950 0.959 0.967 0.973 0.979 0.989 0.997 100 0.867 0.888 0.907 0.922 0.935 0.946 0.956 0.965 0.972 0.978 0.989 0.997 120 0.849 0.874 0.895 0.913 0.928 0.941 0.952 0.962 0.970 0.977 0.990 0.999 140 0.836 0.864 0.887 0.906 0.923 0.937 0.950 0.960 0.970 0.978 0.991 1.002 160 0.828 0.857 0.882 0.903 0.920 0.936 0.949 0.961 0.971 0.979 0.994 1.005 180 0.825 0.855 0.880 0.902 0.920 0.936 0.950 0.962 0.973 0.982 0.998 1.010 200 0.828 0.857 0.882 0.904 0.923 0.939 0.953 0.966 0.977 0.987 1.003 1.015 225 0.837 0.864 0.889 0.910 0.929 0.945 0.960 0.972 0.984 0.993 1.010 1.023 250 0.852 0.877 0.900 0.920 0.938 0.954 0.969 0.981 0.992 1.002 1.019 1.032 275 0.871 0.894 0.915 0.934 0.951 0.966 0.980 0.992 1.003 1.013 1.029 1.041 300 0.894 0.914 0.933 0.950 0.966 0.980 0.993 1.005 1.015 1.024 1.040 1.052 325 0.919 0.936 0.953 0.969 0.983 0.996 1.008 1.019 1.029 1.038 1.053 1.064 350 0.947 0.961 0.975 0.989 1.002 1.014 1.025 1.035 1.044 1.052 1.066 1.077 375 0.975 0.987 1.000 1.011 1.023 1.033 1.043 1.052 1.060 1.068 1.081 1.091 1.005 1.015 1.025 1.035 1.045 1.054 1.062 1.070 1.078 1.084 1.096 1.105 1.073 1.078 1.085 1.091 1.098 1.104 1.110 1.115 1.120 1.129 1.136 1.132 1.134 1.137 1.141 1.144 1.148 1.152 1.155 1.158 1.164 1.169 400 450 500 10.67 1.131 241 242 D2 Properties of Selected Important Pure Substances D2.5. Table 6. Specific enthalpy h of oxygen in kJ/kg Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 50 40 1 433.3 188.7 170.0 151.5 133.0 114.7 105.5 96.38 87.24 78.09 68.95 59.81 5 433.1 399.4 176.1 155.8 136.4 117.3 107.9 98.55 89.22 79.91 70.63 61.36 10 432.8 399.1 364.0 161.8 140.7 120.7 111.0 101.3 91.73 82.21 72.74 63.31 20 432.2 398.6 363.7 177.9 150.6 128.0 117.4 107.1 96.92 86.93 77.05 67.27 30 431.6 398.1 363.4 324.5 162.8 136.1 124.3 113.1 91.78 81.46 71.29 102.3 40 431.0 397.5 363.0 324.8 180.0 145.1 131.8 119.5 107.9 50 430.4 397.0 362.6 325.0 268.0 155.4 139.9 126.3 113.8 96.78 101.9 85.95 75.37 90.54 79.50 60 429.8 396.5 362.3 325.1 275.6 167.6 148.9 133.5 119.8 107.2 95.19 83.67 70 429.2 395.9 361.9 325.2 279.1 182.2 158.7 141.1 126.1 112.6 99.91 87.87 80 428.6 395.4 361.5 325.2 281.3 199.1 169.3 149.1 132.6 118.0 104.7 92.07 90 428.0 394.9 361.1 325.1 282.9 214.6 180.4 157.3 139.2 123.5 109.4 96.26 100 427.4 394.3 360.7 325.0 284.1 225.3 191.0 165.5 145.7 129.0 114.2 100.4 120 426.2 393.2 359.8 324.7 285.7 236.7 207.5 180.5 158.4 139.7 123.4 108.5 140 425.0 392.1 358.9 324.3 286.7 242.6 217.4 192.2 169.4 149.5 132.0 116.2 160 423.8 391.0 358.0 323.8 287.3 246.2 223.5 200.3 178.1 157.9 139.7 123.2 180 422.6 389.9 357.0 323.3 287.6 248.5 227.5 206.0 184.8 164.8 146.4 129.4 200 421.4 388.7 356.1 322.6 287.6 250.1 230.2 209.9 189.7 170.3 151.9 134.8 225 419.9 387.3 354.8 321.8 287.5 251.4 232.6 213.4 194.2 175.5 157.5 140.4 250 418.4 385.9 353.6 320.8 287.2 252.1 234.0 215.7 197.4 179.3 161.7 144.8 275 416.8 384.4 352.3 319.8 286.7 252.5 235.0 217.3 199.6 182.1 165.0 148.4 300 415.3 383.0 351.0 318.8 286.1 252.6 235.5 218.4 201.2 184.2 167.4 151.1 325 413.8 381.5 349.7 317.7 285.3 252.4 235.8 219.0 202.3 185.7 169.3 153.2 350 412.2 380.1 348.3 316.6 284.5 252.1 235.8 219.4 203.0 186.7 170.6 154.8 375 410.7 378.6 347.0 315.4 283.7 251.7 235.6 219.5 203.4 187.4 171.6 156.0 400 409.2 377.1 345.6 314.2 282.7 251.1 235.2 219.4 203.6 187.8 172.3 156.9 450 406.1 374.1 342.8 311.7 280.7 249.7 234.2 218.7 203.3 188.0 172.8 157.8 500 403.0 371.2 340.0 309.2 278.5 248.0 232.8 217.6 202.5 187.5 172.7 158.0 Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 1 50.66 41.52 32.36 23.20 14.03 4.843 4.353 13.56 22.79 32.04 50.59 69.23 5 52.10 42.85 33.61 24.36 15.12 5.863 3.397 12.67 21.95 31.24 49.89 68.63 11.55 10 53.91 44.53 35.17 25.82 16.48 7.137 2.203 20 57.56 47.91 38.31 28.74 19.20 9.680 0.1772 9.316 20.90 30.25 49.01 67.83 18.80 28.29 47.27 66.29 30 61.25 51.31 41.46 31.66 21.92 12.21 2.545 7.101 16.73 24.34 45.56 64.77 40 64.98 54.74 44.61 34.58 24.63 14.74 4.896 4.904 14.67 24.42 42.86 63.28 50 68.73 58.17 47.76 37.49 27.32 17.24 7.228 2.729 12.64 22.52 42.19 61.80 60 72.50 61.60 50.91 40.39 30.00 19.72 9.536 0.5786 10.63 20.64 40.54 60.35 70 76.28 65.03 54.04 43.27 32.66 22.18 18.79 38.92 58.93 11.82 1.544 8.654 80 80.05 68.44 57.15 46.11 35.28 24.61 14.07 3.636 6.705 16.97 37.33 57.53 90 83.79 71.82 60.23 48.93 37.87 27.00 16.28 5.693 4.789 15.18 35.77 56.16 54.82 100 87.50 75.16 63.26 51.70 40.42 29.35 18.46 2.909 13.43 34.24 120 94.72 81.66 69.16 57.09 45.36 33.91 22.68 11.63 0.7338 10.04 31.28 52.23 87.35 74.78 62.23 50.08 38.26 26.71 15.37 4.207 28.46 49.76 140 101.6 7.713 7.497 6.801 160 107.9 93.62 80.05 67.07 54.53 42.37 30.51 18.90 180 113.7 98.91 84.93 71.56 58.69 46.22 34.09 22.22 10.59 200 118.8 103.7 89.36 75.68 62.52 49.79 37.41 25.32 13.48 225 124.2 108.9 94.28 80.30 66.85 53.84 41.20 28.87 16.80 4.959 18.18 40.75 250 128.7 113.3 98.50 84.33 70.67 57.44 44.59 32.06 19.80 7.772 15.70 35.58 3.736 25.79 47.42 0.8499 23.27 45.21 20.91 43.15 1.850 275 132.3 116.9 102.1 87.79 73.99 60.60 47.59 34.89 22.47 12.53 13.47 34.85 300 135.2 119.9 105.1 90.73 76.84 63.35 50.21 37.39 24.84 12.53 11.48 34.85 D2.5 Properties of Oxygen D2.5. Table 6. (continued) Temperature in C Pressure in bar 325 30 20 10 0 10 20 137.5 122.3 107.5 93.19 79.26 65.70 30 52.48 40 39.56 50 26.91 60 14.50 80 100 9.718 33.29 350 139.4 124.3 109.5 95.23 81.29 67.69 54.42 41.44 28.71 16.22 8.173 31.91 375 140.7 125.8 111.2 96.90 82.97 69.37 56.06 43.03 30.25 17.69 6.835 30.72 400 141.8 127.0 112.4 98.24 84.35 70.75 57.43 44.37 31.55 18.95 5.690 29.69 450 143.0 128.5 114.2 100.1 86.30 72.76 59.45 46.38 33.52 20.86 3.931 28.12 500 143.5 129.1 115.0 101.1 87.40 73.93 60.67 47.62 34.75 22.07 2.798 27.10 100 90 80 D2.5. Table 7. Specific entropy s of oxygen in kJ/(kg K) Pressure in bar 1 200 180 160 140 120 70 60 50 40 3.822 1.072 0.8906 0.7397 0.6108 0.4982 0.4467 0.3981 0.3519 0.3080 0.2661 0.2260 5 3.823 3.416 1.345 1.180 1.043 0.9266 0.8738 0.8240 0.7769 0.7322 0.6896 0.6490 10 3.825 3.418 3.077 1.391 1.243 1.120 1.065 1.014 0.9657 0.9199 0.8765 0.8351 20 3.828 3.422 3.083 1.660 1.468 1.330 1.270 1.215 1.164 1.116 1.071 1.028 30 3.831 3.426 3.088 2.773 1.633 1.468 1.402 1.343 1.288 1.238 1.190 1.146 40 3.834 3.430 3.094 2.784 1.797 1.581 1.507 1.442 1.383 1.329 1.280 1.233 50 3.837 3.433 3.099 2.793 2.399 1.685 1.598 1.525 1.462 1.405 1.353 1.305 60 3.840 3.437 3.105 2.803 2.458 1.787 1.682 1.601 1.532 1.471 1.416 1.365 70 3.843 3.441 3.110 2.811 2.490 1.896 1.764 1.671 1.595 1.530 1.472 1.419 1.467 80 3.846 3.444 3.115 2.819 2.514 2.012 1.845 1.737 1.654 1.584 1.522 90 3.849 3.448 3.119 2.827 2.533 2.116 1.924 1.801 1.709 1.634 1.569 1.512 100 3.851 3.451 3.124 2.834 2.549 2.190 1.997 1.861 1.761 1.681 1.613 1.553 120 3.857 3.458 3.133 2.848 2.576 2.276 2.112 1.968 1.856 1.767 1.692 1.627 140 3.863 3.465 3.142 2.861 2.598 2.328 2.187 2.052 1.937 1.842 1.761 1.692 160 3.868 3.471 3.150 2.873 2.617 2.366 2.238 2.115 2.003 1.906 1.822 1.750 180 3.873 3.478 3.159 2.884 2.634 2.395 2.277 2.162 2.056 1.960 1.875 1.801 200 3.879 3.484 3.166 2.895 2.650 2.420 2.308 2.200 2.098 2.005 1.921 1.845 225 3.885 3.492 3.176 2.907 2.667 2.446 2.340 2.238 2.141 2.051 1.969 1.894 250 3.892 3.499 3.185 2.919 2.683 2.468 2.367 2.269 2.177 2.090 2.009 1.935 275 3.898 3.507 3.194 2.930 2.698 2.488 2.390 2.296 2.207 2.123 2.044 1.971 300 3.904 3.514 3.202 2.940 2.711 2.506 2.410 2.319 2.233 2.151 2.074 2.002 325 3.910 3.521 3.211 2.951 2.724 2.522 2.429 2.340 2.255 2.175 2.100 2.030 350 3.916 3.527 3.219 2.960 2.736 2.537 2.445 2.358 2.276 2.197 2.124 2.054 375 3.922 3.534 3.226 2.970 2.748 2.551 2.461 2.375 2.294 2.217 2.145 2.077 400 3.928 3.541 3.234 2.979 2.758 2.564 2.475 2.391 2.311 2.235 2.164 2.097 450 3.940 3.553 3.248 2.995 2.778 2.588 2.501 2.419 2.341 2.268 2.198 2.132 500 3.951 3.566 3.262 3.011 2.797 2.609 2.524 2.443 2.367 2.295 2.227 2.163 Temperature in C Pressure in bar 30 20 10 0 10 20 1 0.1876 0.1507 0.1152 0.0811 0.0481 0.0162 30 0.0146 40 0.0445 50 0.0735 60 0.1017 80 0.1558 100 0.2071 5 0.6101 0.5728 0.5370 0.5025 0.4693 0.4372 0.4061 0.3760 0.3468 0.3185 0.2642 0.2126 10 0.7957 0.7579 0.7216 0.6857 0.6531 0.6207 0.5894 0.5591 0.5297 0.5011 0.4465 0.3946 20 0.9869 0.9480 0.9108 0.8751 0.8408 0.8077 0.7759 0.7450 0.7152 0.6863 0.6310 0.5786 243 244 D2 Properties of Selected Important Pure Substances D2.5. Table 7. (continued) Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 30 0.104 1.063 1.025 0.9887 0.9537 0.9200 0.8876 0.8563 0.8260 0.7967 0.7407 0.6878 40 1.190 1.148 1.109 1.072 1.036 1.002 0.9687 0.9369 0.9061 0.8764 0.8198 0.7663 50 1.259 1.217 1.176 1.138 1.102 1.067 1.033 1.001 0.9695 0.9394 0.8820 0.8280 60 1.318 1.274 1.233 1.194 1.156 1.121 1.087 1.054 1.022 0.9917 0.9337 0.8791 70 1.370 1.325 1.282 1.242 1.204 1.168 1.133 1.100 1.067 1.037 0.9779 0.9228 80 1.417 1.370 1.326 1.285 1.246 1.209 1.174 1.140 1.107 1.076 1.017 0.9611 90 1.459 1.411 1.366 1.324 1.284 1.246 1.210 1.176 1.143 1.111 1.051 0.9953 100 1.498 1.449 1.402 1.359 1.319 1.280 1.244 1.209 1.176 1.144 1.083 1.026 120 1.569 1.516 1.468 1.423 1.380 1.341 1.303 1.267 1.233 1.200 1.138 1.080 140 1.631 1.575 1.525 1.478 1.434 1.393 1.354 1.318 1.282 1.249 1.186 1.127 160 1.686 1.628 1.575 1.527 1.482 1.440 1.400 1.362 1.326 1.292 1.228 1.168 180 1.734 1.675 1.621 1.571 1.525 1.481 1.441 1.402 1.366 1.331 1.265 1.205 200 1.778 1.717 1.662 1.611 1.563 1.519 1.478 1.438 1.401 1.366 1.299 1.238 225 1.826 1.764 1.708 1.655 1.607 1.562 1.519 1.479 1.441 1.405 1.338 1.276 250 1.867 1.805 1.748 1.695 1.646 1.600 1.557 1.516 1.478 1.441 1.373 1.310 275 1.904 1.842 1.784 1.731 1.681 1.635 1.591 1.550 1.511 1.474 1.404 1.341 300 1.936 1.874 1.816 1.763 1.713 1.666 1.622 1.580 1.541 1.503 1.433 1.369 325 1.964 1.903 1.845 1.792 1.742 1.695 1.650 1.608 1.569 1.531 1.460 1.395 350 1.989 1.928 1.871 1.818 1.768 1.721 1.676 1.634 1.594 1.556 1.485 1.420 375 2.012 1.952 1.895 1.842 1.792 1.745 1.700 1.658 1.618 1.579 1.508 1.442 400 2.033 1.973 1.917 1.864 1.814 1.767 1.722 1.680 1.640 1.601 1.529 1.463 450 2.070 2.011 1.956 1.903 1.854 1.807 1.762 1.720 1.679 1.641 1.568 1.502 500 2.102 2.044 1.989 1.937 1.888 1.841 1.797 1.755 1.714 1.676 1.603 1.536 D2.5. Table 8. Specific isobaric heat capacity cp of oxygen in kJ/(kg K) Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 50 40 1 1.678 0.9473 0.9305 0.9237 0.9191 0.9164 0.9155 0.9149 0.9145 0.9143 0.9142 0.9144 5 1.677 1.706 1.047 0.9885 0.9599 0.9440 0.9348 0.9317 0.9293 0.9275 0.9262 0.9253 10 1.676 1.703 1.832 1.100 1.021 0.9829 0.9709 0.9618 0.9547 0.9492 0.9449 0.9415 20 1.674 1.698 1.815 1.706 1.198 1.079 1.047 1.023 1.006 0.9928 0.9824 0.9742 30 1.672 1.692 1.799 2.182 1.535 1.210 1.143 1.098 1.066 1.042 1.024 1.010 40 1.669 1.687 1.785 2.110 2.531 1.400 1.268 1.188 1.135 1.097 1.069 1.048 50 1.667 1.682 1.771 2.052 6.755 1.690 1.434 1.299 1.216 1.159 1.119 1.089 60 1.665 1.677 1.759 2.004 3.640 2.167 1.657 1.435 1.309 1.229 1.173 1.133 70 1.663 1.673 1.748 1.963 2.974 2.964 1.956 1.599 1.416 1.305 1.232 1.179 80 1.661 1.669 1.737 1.928 2.648 3.974 2.329 1.790 1.535 1.388 1.293 1.228 90 1.660 1.664 1.727 1.897 2.447 4.194 2.718 1.998 1.663 1.476 1.358 1.278 100 1.658 1.660 1.717 1.870 2.308 3.658 2.984 2.199 1.793 1.565 1.423 1.328 120 1.654 1.653 1.700 1.823 2.124 2.838 2.904 2.448 2.015 1.732 1.550 1.427 D2.5 Properties of Oxygen D2.5. Table 8. (continued) Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 50 40 140 1.651 1.646 1.684 1.785 2.005 2.434 2.571 2.430 2.127 1.855 1.657 1.515 160 1.648 1.639 1.670 1.754 1.920 2.204 2.317 2.293 2.128 1.916 1.730 1.585 180 1.645 1.633 1.658 1.726 1.856 2.056 2.141 2.153 2.068 1.921 1.766 1.631 200 1.642 1.627 1.646 1.703 1.806 1.952 2.016 2.036 1.992 1.894 1.774 1.656 225 1.639 1.621 1.633 1.678 1.756 1.859 1.903 1.922 1.902 1.842 1.757 1.663 250 1.636 1.614 1.621 1.656 1.715 1.790 1.822 1.837 1.826 1.787 1.726 1.653 275 1.633 1.609 1.611 1.637 1.683 1.737 1.759 1.770 1.763 1.736 1.691 1.634 300 1.630 1.603 1.601 1.621 1.655 1.695 1.710 1.717 1.712 1.691 1.657 1.611 325 1.628 1.599 1.593 1.606 1.631 1.660 1.671 1.675 1.669 1.653 1.625 1.588 350 1.626 1.594 1.585 1.593 1.611 1.631 1.638 1.639 1.634 1.619 1.596 1.565 375 1.623 1.590 1.577 1.581 1.593 1.607 1.610 1.610 1.604 1.591 1.570 1.544 400 1.621 1.586 1.570 1.570 1.578 1.585 1.587 1.584 1.578 1.565 1.548 1.525 450 1.618 1.579 1.558 1.552 1.551 1.551 1.548 1.544 1.536 1.524 1.509 1.490 500 1.614 1.572 1.548 1.536 1.530 1.523 1.518 1.512 1.503 1.492 1.478 1.462 Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 1 0.9147 0.9152 0.9158 0.9167 0.9177 0.9189 0.9203 0.9219 0.9236 0.9255 0.9298 0.9345 5 0.9253 0.9247 0.9245 0.9246 0.9249 0.9255 0.9264 0.9275 0.9288 0.9304 0.9340 0.9382 10 0.9389 0.9370 0.9355 0.9346 0.9341 0.9339 0.9341 0.9346 0.9354 0.9364 0.9392 0.9428 20 0.9677 0.9626 0.9585 0.9553 0.9528 0.9510 0.9497 0.9490 0.9487 0.9487 0.9498 0.9521 30 0.9985 0.9896 0.9824 0.9767 0.9721 0.9685 0.9657 0.9636 0.9621 0.9611 0.9605 0.9613 40 1.031 1.018 1.007 0.9989 0.9920 0.9864 0.9819 0.9784 0.9756 0.9735 0.9711 0.9706 50 1.066 1.048 1.033 1.022 1.012 1.005 0.9983 0.9933 0.9892 0.9860 0.9818 0.9798 60 1.102 1.079 1.060 1.045 1.033 1.023 1.015 1.008 1.003 0.9985 0.9924 0.9889 70 1.140 1.111 1.087 1.069 1.054 1.042 1.032 1.023 1.017 1.011 1.003 0.9980 80 1.180 1.143 1.115 1.093 1.075 1.060 1.048 1.038 1.030 1.023 1.013 1.007 90 1.220 1.177 1.143 1.117 1.096 1.079 1.065 1.053 1.044 1.036 1.024 1.016 100 1.260 1.210 1.171 1.141 1.117 1.097 1.081 1.068 1.057 1.048 1.034 1.024 120 1.340 1.276 1.227 1.188 1.158 1.134 1.113 1.097 1.083 1.072 1.054 1.041 140 1.413 1.337 1.279 1.233 1.197 1.168 1.144 1.124 1.108 1.094 1.073 1.058 160 1.474 1.390 1.325 1.274 1.233 1.200 1.173 1.150 1.131 1.116 1.091 1.073 180 1.521 1.434 1.365 1.310 1.266 1.229 1.199 1.174 1.153 1.135 1.108 1.088 200 1.553 1.467 1.397 1.340 1.293 1.255 1.223 1.196 1.173 1.154 1.124 1.101 225 1.574 1.494 1.427 1.370 1.322 1.282 1.248 1.219 1.195 1.174 1.141 1.117 250 1.578 1.508 1.445 1.390 1.343 1.303 1.268 1.239 1.214 1.192 1.157 1.131 275 1.572 1.512 1.455 1.404 1.358 1.319 1.285 1.255 1.229 1.207 1.171 1.144 300 1.561 1.508 1.458 1.411 1.368 1.330 1.297 1.268 1.242 1.220 1.183 1.155 325 1.546 1.501 1.456 1.413 1.374 1.338 1.306 1.278 1.253 1.230 1.193 1.165 350 1.529 1.490 1.451 1.413 1.376 1.343 1.312 1.285 1.260 1.239 1.202 1.173 375 1.513 1.479 1.444 1.409 1.376 1.345 1.316 1.290 1.266 1.245 1.209 1.180 400 1.497 1.467 1.436 1.405 1.374 1.345 1.318 1.294 1.271 1.250 1.215 1.186 450 1.469 1.444 1.419 1.393 1.367 1.342 1.319 1.296 1.276 1.257 1.223 1.196 500 1.444 1.423 1.402 1.380 1.358 1.336 1.315 1.296 1.277 1.259 1.229 1.203 245 246 D2 Properties of Selected Important Pure Substances D2.5. Table 9. Specific isochoric heat capacity cv of oxygen in kJ/(kg K) Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 50 40 1 1.001 0.6587 0.6543 0.6535 0.6522 0.6515 0.6513 0.6512 0.6513 0.6514 0.6517 0.6521 5 1.002 0.9188 0.6798 0.6690 0.6617 0.6574 0.6560 0.6551 0.6545 0.6542 0.6540 0.6541 10 1.003 0.9198 0.8584 0.6922 0.6748 0.6652 0.6622 0.6601 0.6586 0.6576 0.6570 0.6567 20 1.005 0.9218 0.8601 0.8111 0.7064 0.6825 0.6756 0.6707 0.6672 0.6647 0.6630 0.6618 30 1.006 0.9238 0.8619 0.8264 0.7513 0.7023 0.6904 0.6821 0.6762 0.6720 0.6691 0.6670 40 1.008 0.9258 0.8637 0.8258 0.8400 0.7255 0.7067 0.6942 0.6856 0.6796 0.6753 0.6722 50 1.010 0.9277 0.8655 0.8257 0.9324 0.7527 0.7247 0.7072 0.6954 0.6873 0.6815 0.6774 60 1.012 0.9297 0.8673 0.8260 0.8515 0.7846 0.7441 0.7207 0.7055 0.6951 0.6878 0.6826 70 1.013 0.9316 0.8691 0.8266 0.8301 0.8193 0.7644 0.7345 0.7156 0.7029 0.6940 0.6877 80 1.015 0.9334 0.8709 0.8275 0.8196 0.8449 0.7835 0.7480 0.7255 0.7105 0.7001 0.6927 90 1.017 0.9353 0.8727 0.8285 0.8136 0.8436 0.7981 0.7601 0.7349 0.7178 0.7060 0.6976 100 1.018 0.9371 0.8745 0.8296 0.8099 0.8286 0.8052 0.7699 0.7432 0.7246 0.7115 0.7022 120 1.022 0.9407 0.8780 0.8322 0.8063 0.8066 0.8009 0.7796 0.7555 0.7359 0.7213 0.7105 140 1.025 0.9442 0.8815 0.8350 0.8054 0.7954 0.7912 0.7793 0.7612 0.7434 0.7288 0.7175 160 1.028 0.9477 0.8849 0.8379 0.8060 0.7897 0.7841 0.7755 0.7624 0.7475 0.7340 0.7229 180 1.031 0.9510 0.8883 0.8409 0.8074 0.7871 0.7799 0.7720 0.7616 0.7494 0.7374 0.7269 200 1.034 0.9543 0.8916 0.8440 0.8093 0.7864 0.7779 0.7697 0.7606 0.7502 0.7396 0.7299 225 1.038 0.9582 0.8956 0.8478 0.8121 0.7870 0.7773 0.7685 0.7598 0.7507 0.7415 0.7327 250 1.041 0.9621 0.8995 0.8515 0.8151 0.7885 0.7780 0.7687 0.7599 0.7514 0.7429 0.7349 275 1.045 0.9658 0.9032 0.8552 0.8183 0.7907 0.7796 0.7698 0.7608 0.7524 0.7444 0.7369 300 1.048 0.9694 0.9069 0.8588 0.8216 0.7932 0.7816 0.7714 0.7623 0.7538 0.7460 0.7388 325 1.052 0.9730 0.9104 0.8622 0.8248 0.7959 0.7840 0.7735 0.7641 0.7556 0.7478 0.7407 350 1.055 0.9764 0.9138 0.8657 0.8280 0.7986 0.7865 0.7757 0.7661 0.7575 0.7497 0.7426 375 1.058 0.9797 0.9172 0.8690 0.8312 0.8015 0.7891 0.7781 0.7683 0.7596 0.7517 0.7446 400 1.061 0.9829 0.9204 0.8722 0.8342 0.8043 0.7917 0.7806 0.7706 0.7617 0.7538 0.7467 450 1.067 0.9891 0.9266 0.8783 0.8402 0.8098 0.7970 0.7855 0.7753 0.7662 0.7580 0.7508 500 1.072 0.9950 0.9325 0.8841 0.8458 0.8151 0.8020 0.7904 0.7800 0.7706 0.7623 0.7548 Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 1 0.6527 0.6534 0.6542 0.6552 0.6564 0.6577 0.6592 0.6609 0.6627 0.6647 0.6690 0.6739 5 0.6544 0.6549 0.6556 0.6565 0.6575 0.6587 0.6602 0.6617 0.6635 0.6654 0.6697 0.6745 10 0.6566 0.6569 0.6573 0.6580 0.6589 0.6600 0.6613 0.6628 0.6645 0.6663 0.6705 0.6752 20 0.6611 0.6608 0.6608 0.6611 0.6617 0.6626 0.6637 0.6650 0.6665 0.6682 0.6721 0.6766 30 0.6655 0.6647 0.6642 0.6642 0.6645 0.6651 0.6660 0.6671 0.6684 0.6700 0.6737 0.6780 40 0.6700 0.6685 0.6677 0.6672 0.6672 0.6676 0.6682 0.6692 0.6703 0.6718 0.6752 0.6793 50 0.6744 0.6724 0.6710 0.6702 0.6699 0.6700 0.6704 0.6712 0.6722 0.6735 0.6767 0.6807 60 0.6788 0.6762 0.6744 0.6732 0.6726 0.6724 0.6726 0.6732 0.6741 0.6752 0.6782 0.6820 70 0.6832 0.6799 0.6776 0.6761 0.6751 0.6747 0.6748 0.6751 0.6759 0.6769 0.6796 0.6833 80 0.6874 0.6835 0.6808 0.6789 0.6777 0.6770 0.6768 0.6771 0.6776 0.6785 0.6811 0.6845 90 0.6915 0.6870 0.6839 0.6816 0.6801 0.6792 0.6789 0.6789 0.6793 0.6801 0.6824 0.6857 100 0.6854 0.6904 0.6868 0.6843 0.6825 0.6814 0.6808 0.6807 0.6810 0.6816 0.6838 0.6869 120 0.7026 0.6968 0.6924 0.6893 0.6870 0.6855 0.6846 0.6842 0.6842 0.6846 0.6864 0.6892 140 0.7089 0.7024 0.6975 0.6938 0.6912 0.6893 0.6881 0.6874 0.6872 0.6874 0.6889 0.6914 160 0.7141 0.7072 0.7020 0.6980 0.6950 0.6928 0.6914 0.6905 0.6901 0.6901 0.6912 0.6935 180 0.7183 0.7113 0.7059 0.7017 0.6984 0.6960 0.6944 0.6933 0.6927 0.6926 0.6934 0.6954 D2.5 Properties of Oxygen D2.5. Table 9. (continued) Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 200 0.7217 0.7148 0.7093 0.7049 0.7016 0.6992 0.6972 0.6959 0.6952 0.6949 0.6955 0.6973 225 0.7250 0.7184 0.7129 0.7085 0.7050 0.7023 0.7003 0.6989 0.6980 0.6986 0.6979 0.6995 250 0.7277 0.7214 0.7161 0.7117 0.7081 0.7053 0.7032 0.7017 0.7007 0.7001 0.7002 0.7016 275 0.7300 0.7240 0.7188 0.7144 0.7109 0.7080 0.7058 0.7042 0.7031 0.7025 0.7023 0.7035 300 0.7322 0.7263 0.7212 0.7169 0.7134 0.7105 0.7082 0.7065 0.7054 0.7046 0.7043 0.7053 325 0.7342 0.7285 0.7235 0.7193 0.7157 0.7128 0.7105 0.7087 0.7075 0.7066 0.7062 0.7070 350 0.7363 0.7306 0.7257 0.7214 0.7179 0.7149 0.7126 0.7107 0.7094 0.7085 0.7079 0.7086 375 0.7383 0.7327 0.7277 0.7235 0.7199 0.7169 0.7145 0.7127 0.7113 0.7103 0.7096 0.7102 400 0.7403 0.7347 0.7297 0.7255 0.7219 0.7189 0.7164 0.7145 0.7130 0.7120 0.7111 0.7116 450 0.7443 0.7386 0.7336 0.7293 0.7256 0.7225 0.7199 0.7179 0.7163 0.7152 0.7141 0.7143 500 0.7482 0.7424 0.7373 0.7328 0.7290 0.7258 0.7231 0.7210 0.7193 0.7181 0.7167 0.7168 D2.5. Table 10. Isobaric expansion coefficient b of oxygen in 103/K Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 50 40 1 3.78 11.7 9.26 7.74 6.66 5.86 5.53 5.23 4.97 4.73 4.51 4.32 8.81 7.25 6.21 5.81 5.46 5.16 4.89 4.65 4.43 8.14 6.71 6.20 5.78 5.41 5.09 4.82 4.57 5 3.77 4.49 10 3.75 4.46 11.6 6.04 10.7 20 3.72 4.40 5.87 20.0 10.7 7.95 7.12 6.48 5.97 5.54 5.18 4.87 30 3.70 4.35 5.72 9.90 15.6 7.64 8.29 7.33 6.61 6.04 5.58 5.20 40 3.67 4.29 5.58 9.17 30.0 12.1 9.78 8.35 7.34 6.60 6.01 5.54 50 3.64 4.24 5.45 8.58 66.8 15.7 11.7 9.57 8.18 7.20 6.47 5.90 60 3.61 4.19 5.33 8.10 27.3 21.6 14.3 11.0 9.13 7.87 6.96 6.27 70 3.59 4.14 5.21 7.68 19.4 31.0 17.6 12.7 10.2 8.57 7.47 6.65 80 3.56 4.09 5.10 7.33 15.6 41.5 21.5 14.6 11.3 7.98 7.04 90 3.54 4.04 5.00 7.02 13.4 40.4 25.1 16.6 12.4 10.0 8.50 7.41 100 3.51 4.00 4.91 6.74 11.9 31.2 26.7 18.2 13.5 10.7 8.99 7.77 120 3.47 3.92 4.73 6.28 9.85 19.6 22.7 19.2 14.9 11.8 140 3.42 3.84 4.57 5.90 8.57 14.4 17.3 17.2 14.8 12.3 10.3 8.83 160 3.38 3.76 4.43 5.58 7.68 11.5 13.7 14.5 13.7 12.0 10.4 9.02 180 3.34 3.69 4.30 5.30 7.00 9.79 11.3 12.3 12.2 11.3 10.1 8.96 200 3.30 3.62 4.18 5.07 6.48 8.59 9.75 10.6 10.8 10.4 225 3.25 3.54 4.04 4.81 5.95 7.53 8.37 9.05 9.37 250 3.20 3.47 3.92 4.59 5.53 6.76 7.40 7.94 8.26 275 3.16 3.40 3.81 4.39 5.19 6.17 6.67 7.10 300 3.11 3.33 3.70 4.22 4.90 5.70 6.11 325 3.07 3.27 3.61 4.07 4.65 5.32 5.65 350 3.03 3.21 3.52 3.93 4.44 5.00 375 2.99 3.16 3.43 3.80 4.25 400 2.96 3.11 3.36 3.69 4.08 450 2.89 3.01 3.21 3.49 500 2.82 2.92 3.09 3.31 9.31 9.82 8.40 9.61 8.71 9.28 8.85 8.24 8.30 8.08 7.69 7.39 7.49 7.39 7.14 6.46 6.71 6.82 6.79 6.63 5.94 6.16 6.27 6.27 6.18 5.28 5.52 5.70 5.81 5.83 5.77 4.73 4.96 5.17 5.32 5.42 5.45 5.42 4.50 4.70 4.87 5.00 5.09 5.13 5.11 3.80 4.11 4.26 4.39 4.49 4.56 4.59 4.59 3.56 3.81 3.92 4.02 4.10 4.15 4.18 4.18 247 248 D2 Properties of Selected Important Pure Substances D2.5. Table 10. (continued) Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 1 4.14 3.97 3.82 3.68 3.54 3.42 3.31 3.20 3.10 3.01 2.84 2.68 5 4.23 4.05 3.89 3.74 3.60 3.47 3.35 3.24 3.13 3.04 2.86 2.70 10 4.35 4.15 3.98 3.81 3.66 3.53 3.40 3.28 3.17 3.07 2.89 2.72 20 4.61 4.37 4.16 3.97 3.80 3.64 3.50 3.37 3.25 3.14 2.94 2.76 30 4.87 4.59 4.34 4.13 3.93 3.76 3.60 3.46 3.33 3.20 2.99 2.81 40 5.15 4.82 4.53 4.29 4.07 3.87 3.70 3.54 3.40 3.27 3.04 2.84 50 5.43 5.05 4.72 4.45 4.20 3.99 3.80 3.63 3.47 3.33 3.09 2.88 60 5.73 5.28 4.92 4.60 4.33 4.10 3.89 3.71 3.54 3.40 3.14 2.92 70 6.02 5.52 5.11 4.76 4.47 4.21 3.99 3.79 3.61 3.46 3.18 2.95 80 6.32 5.75 5.29 4.91 4.59 4.32 4.08 3.87 3.68 3.51 3.23 2.99 90 6.60 5.98 5.47 5.06 4.71 4.42 4.16 3.94 3.74 3.57 3.27 3.02 100 6.88 6.19 5.64 5.20 4.83 4.51 4.24 4.01 3.80 3.62 3.30 3.05 120 7.36 6.57 5.95 5.45 5.03 4.69 4.39 4.13 3.91 3.71 3.37 3.10 140 7.72 6.87 6.19 5.65 5.20 4.83 4.51 4.23 3.99 3.78 3.43 3.14 160 7.92 7.06 6.36 5.80 5.33 4.94 4.60 4.31 4.06 3.84 3.48 3.18 180 7.96 7.13 6.45 5.88 5.41 5.01 4.67 4.37 4.11 3.89 3.51 3.21 200 7.86 7.10 6.46 5.91 5.44 5.04 4.70 4.41 4.15 3.92 3.53 3.22 225 7.57 6.94 6.37 5.87 5.43 5.04 4.71 4.42 4.16 3.93 3.55 3.24 250 7.20 6.69 6.20 5.76 5.35 5.00 4.68 4.40 4.15 3.92 3.54 3.23 275 6.79 6.39 5.99 5.60 5.24 4.91 4.62 4.35 4.11 3.90 3.53 3.22 300 6.38 6.07 5.74 5.41 5.10 4.80 4.53 4.29 4.06 3.86 3.50 3.20 325 5.99 5.76 5.49 5.21 4.94 4.68 4.43 4.20 3.99 3.80 3.46 3.18 350 5.64 5.46 5.24 5.01 4.77 4.54 4.32 4.11 3.92 3.74 3.41 3.14 375 5.32 5.18 5.00 4.81 4.60 4.40 4.20 4.01 3.83 3.67 3.36 3.10 400 5.03 4.92 4.78 4.61 4.44 4.26 4.08 3.91 3.75 3.59 3.31 3.06 450 4.55 4.47 4.37 4.25 4.12 3.98 3.84 3.70 3.56 3.43 3.18 2.96 500 4.15 4.10 4.03 3.94 3.84 3.73 3.62 3.50 3.39 3.27 3.06 2.86 D2.5. Table 11. Isentropic speed of sound ws in oxygen in m/s Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 50 40 1 1042 181.1 201.1 218.9 235.2 250.4 257.6 264.6 271.5 278.1 284.6 290.9 5 1044 881.7 193.1 213.8 231.8 248.1 255.7 263.1 270.2 277.1 283.8 290.3 10 1045 884.3 709.2 206.7 227.4 245.2 253.4 261.2 268.7 275.8 282.8 289.5 20 1048 889.4 718.2 187.7 217.8 239.3 248.7 257.4 265.7 273.5 281.0 288.1 30 1052 894.5 726.8 523.8 206.7 233.4 244.1 253.9 263.0 271.4 279.4 287.0 40 1055 899.4 735.1 541.5 192.4 227.5 239.8 250.7 260.6 269.7 278.1 286.1 50 1058 904.2 743.1 557.6 248.5 222.0 236.0 248.0 258.6 268.3 277.3 285.6 60 1061 909.0 750.8 572.4 323.5 217.5 233.1 246.0 257.3 267.5 276.8 285.5 70 1064 913.6 758.2 586.0 365.3 216.0 231.6 245.0 256.7 267.3 276.9 285.8 80 1067 918.2 765.4 598.8 396.9 222.1 232.7 245.4 257.2 267.8 277.6 286.6 90 1070 922.8 772.5 610.8 423.0 242.5 237.9 247.9 258.8 269.2 278.9 288.0 D2.5 Properties of Oxygen D2.5. Table 11. (continued) Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 50 40 100 1073 927.2 779.3 622.2 445.5 271.9 248.6 252.9 262.0 271.7 281.1 290.0 120 1079 936.0 792.4 643.2 483.4 328.3 284.3 271.7 273.6 280.1 287.8 295.8 140 1085 944.5 804.9 662.4 514.9 374.8 325.5 300.0 292.3 293.4 298.2 304.4 160 1091 952.7 816.8 680.1 542.2 413.6 364.0 331.9 316.0 311.1 311.9 315.6 180 1097 960.8 828.2 696.5 566.4 446.8 398.5 363.4 342.1 331.7 328.4 329.2 200 1102 968.8 839.2 712.0 588.3 475.8 429.3 393.1 368.4 353.9 346.8 344.5 225 1110 978.4 852.4 730.1 613.0 507.7 463.3 427.1 400.2 382.0 371.1 365.4 250 1116 987.8 865.1 747.1 635.6 536.0 493.6 457.9 429.9 409.4 395.7 387.2 275 1123 997.1 877.3 763.2 656.3 561.4 520.7 485.9 457.5 435.7 419.9 409.2 300 1130 1006 889.1 778.4 675.6 584.7 545.5 511.5 483.1 460.4 443.3 430.9 325 1137 1015 900.5 793.0 693.7 606.2 568.3 535.1 506.9 483.8 465.7 452.0 350 1144 1024 911.6 806.9 710.8 626.3 589.5 557.1 529.2 505.9 487.1 472.5 375 1150 1032 922.4 820.2 727.0 645.1 609.4 577.7 550.1 526.8 507.6 492.2 400 1157 1040 932.8 833.1 742.4 662.9 628.1 597.0 569.8 546.5 527.1 511.1 450 1170 1057 953.0 857.6 771.3 695.8 662.7 632.8 606.3 583.3 563.5 546.9 500 1183 1073 972.3 880.6 798.1 726.0 694.2 665.4 639.6 616.9 597.1 580.2 Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 1 297.1 303.1 309.0 314.8 320.5 326.0 331.4 336.7 341.9 347.1 357.0 366.6 5 296.6 302.8 308.8 314.7 320.4 326.0 331.5 336.9 342.2 347.3 357.4 367.0 10 296.0 302.4 308.5 314.5 320.4 326.1 331.6 337.1 342.4 347.7 357.8 367.6 20 295.0 301.7 308.1 314.3 320.4 326.3 332.0 337.6 343.1 348.4 358.8 368.7 30 294.2 301.2 307.9 314.4 320.6 326.7 332.6 338.3 343.9 349.3 359.8 369.9 40 293.7 301.0 307.9 314.6 321.0 327.3 333.3 339.1 344.8 350.4 361.0 371.2 50 293.5 301.0 308.2 315.1 321.7 328.0 334.2 340.1 345.9 351.5 362.3 372.6 60 293.7 304.4 308.7 315.8 322.5 329.0 335.2 341.3 347.1 352.8 363.7 374.1 70 294.2 302.1 309.6 316.7 323.6 330.1 336.5 342.6 348.5 354.2 365.3 375.7 80 395.1 303.1 310.7 317.9 324.9 331.5 337.9 344.1 350.0 355.8 366.9 377.4 90 296.5 304.6 312.2 319.5 326.4 333.1 339.5 345.7 351.7 357.5 368.7 379.2 100 298.4 306.4 314.0 321.3 328.2 334.9 341.4 347.6 353.6 359.4 370.6 381.1 120 303.7 311.3 318.7 325.8 332.6 339.3 345.6 351.8 357.8 363.6 374.7 385.3 140 311.1 318.0 324.8 331.6 338.1 344.5 350.7 356.8 362.7 368.4 379.3 389.8 160 320.7 326.4 332.5 338.6 344.7 350.7 356.7 362.5 368.2 373.7 384.4 394.7 180 332.2 336.5 341.4 346.7 352.2 357.8 363.3 368.8 374.3 379.6 390.0 400.0 200 345.3 347.9 351.6 356.0 360.7 365.7 370.7 375.9 381.0 386.0 396.0 405.7 225 363.4 363.8 365.8 368.8 372.5 376.6 380.9 385.4 390.1 374.7 404.0 413.2 250 382.7 380.9 381.2 382.7 385.2 388.4 392.0 395.8 399.9 404.1 412.6 421.2 275 402.5 398.8 397.4 397.5 398.8 401.0 403.7 406.9 410.3 414.0 421.7 429.7 300 422.4 417.0 414.1 412.9 413.0 414.2 416.1 418.5 421.3 424.4 431.2 438.5 325 442.1 435.3 431.0 428.5 427.6 427.8 428.8 430.5 432.7 435.2 441.1 447.7 350 461.4 453.4 447.9 444.3 442.4 441.6 441.8 442.8 444.3 446.3 451.3 457.1 375 480.2 471.2 464.7 460.1 457.2 455.6 455.1 455.3 456.2 457.7 461.7 466.7 400 498.5 488.6 481.2 475.8 472.1 469.7 468.4 468.0 468.3 469.2 472.3 476.5 450 533.2 522.2 513.4 506.5 501.4 497.6 495.0 493.4 492.6 492.5 493.8 496.5 500 565.8 553.9 544.1 536.2 529.9 525.0 521.4 518.7 517.0 515.9 515.5 516.9 249 250 D2 Properties of Selected Important Pure Substances D2.5. Table 12. Thermal conductivity l of oxygen in mW/(m K) Temperature in C Pressure in bar 200 180 1 176.6 5 176.8 148.7 8.611 10 177.0 149.1 20 177.5 149.8 30 178.0 40 50 160 140 120 100 90 80 70 60 50 40 10.64 12.58 14.44 16.21 17.07 17.92 18.74 19.55 20.35 21.14 11.25 13.00 14.76 16.48 17.32 18.15 18.96 19.76 20.55 21.32 121.1 13.77 15.28 16.88 17.68 18.48 19.27 20.05 20.81 21.58 122.2 17.09 16.90 17.96 18.62 19.30 20.01 20.72 21.44 22.15 150.5 123.2 94.09 19.81 19.52 19.88 20.37 20.94 21.55 22.18 22.83 178.5 151.1 124.2 95.82 26.00 21.76 21.57 21.74 22.08 22.53 23.05 23.62 179.0 151.8 125.1 97.43 70.65 24.96 23.80 23.44 23.46 23.70 24.06 24.50 60 179.5 152.5 126.1 98.95 68.91 29.58 26.69 25.53 25.09 25.04 25.20 25.50 70 180.0 153.1 127.0 100.4 71.67 36.10 30.33 28.03 26.99 26.56 26.48 26.60 80 180.4 153.8 127.9 101.8 74.29 44.05 34.69 30.93 29.14 28.27 27.88 27.80 90 180.9 154.4 128.7 103.1 76.66 50.60 39.44 34.14 31.51 30.12 29.41 29.09 100 181.4 155.1 129.6 104.3 78.80 54.46 43.96 37.49 34.02 32.10 31.03 30.45 120 182.3 156.3 131.3 106.7 82.59 60.02 50.88 43.84 39.17 36.26 34.47 33.36 140 183.3 157.5 132.9 109.0 85.91 64.73 56.00 49.09 43.96 40.39 37.99 36.40 160 184.2 158.7 134.5 111.1 88.88 68.79 60.36 53.49 48.20 44.26 41.43 39.42 180 185.1 159.9 136.0 113.1 91.60 72.36 64.20 57.38 51.97 47.81 44.68 42.36 200 185.9 161.0 137.4 115.0 94.11 75.55 67.63 60.88 55.40 51.07 47.72 45.16 225 187.0 162.4 139.2 117.3 97.03 79.15 71.47 64.83 59.30 54.82 51.27 48.47 250 188.1 163.8 140.9 119.5 99.75 82.42 74.94 68.40 62.85 58.27 54.56 51.58 275 189.2 165.2 142.6 121.6 102.3 85.42 78.11 71.67 66.13 61.48 57.64 54.51 300 190.2 166.5 144.2 123.6 104.7 88.22 81.06 74.70 69.17 64.47 60.54 57.28 325 191.2 167.8 145.7 125.5 107.0 90.84 83.80 77.52 72.02 67.29 63.28 59.92 350 192.2 169.0 147.2 127.3 109.2 93.33 86.39 80.18 74.70 69.95 65.88 62.43 375 193.2 170.3 148.8 129.1 111.3 95.68 88.84 82.69 77.24 72.47 68.35 64.83 400 194.2 171.5 150.2 130.9 113.3 91.18 85.09 79.66 74.88 70.72 67.14 450 196.1 173.8 153.1 134.2 117.1 102.2 95.55 89.56 84.17 79.39 75.17 71.49 500 198.0 176.1 155.8 137.3 120.7 106.1 99.60 93.69 88.35 83.56 79.31 75.56 97.93 Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 1 21.91 22.68 23.43 24.18 24.92 25.66 26.38 27.11 27.83 28.54 29.96 31.37 5 22.09 22.85 23.59 24.34 25.07 25.80 26.52 27.24 27.95 28.66 30.08 31.48 10 22.33 23.07 23.81 24.54 25.27 25.99 26.70 27.41 28.12 28.83 30.23 31.62 20 22.87 23.58 24.29 25.00 25.70 26.40 27.10 27.79 28.48 29.18 30.55 31.93 30 23.49 24.16 24.83 25.50 26.18 26.85 27.53 28.20 28.87 29.55 30.90 32.25 40 24.21 24.81 25.44 26.07 26.71 27.35 27.99 28.63 29.29 29.95 31.28 32.60 50 25.00 25.54 26.10 26.68 27.28 27.88 28.49 29.10 29.74 30.38 31.67 32.96 60 25.89 26.34 26.83 27.35 27.89 28.45 29.03 29.60 30.21 30.83 32.08 33.34 70 26.85 27.20 27.61 28.06 28.55 29.06 29.59 30.12 30.71 31.30 32.51 33.74 80 27.90 28.13 28.44 28.82 29.24 29.70 30.18 30.66 31.22 31.79 32.96 34.15 90 29.02 29.11 29.32 29.62 29.97 30.37 30.80 31.23 31.76 32.30 33.42 34.58 100 30.20 30.15 30.25 30.45 30.73 31.07 31.44 31.81 32.31 32.83 33.90 35.01 120 32.71 32.36 32.21 32.22 32.34 32.53 32.78 33.04 33.46 33.92 34.89 35.92 140 35.35 34.68 34.29 34.09 34.03 34.08 34.19 34.31 34.67 35.06 35.92 36.86 160 38.02 37.06 36.42 36.01 35.78 35.67 35.64 35.63 35.91 36.23 36.98 37.83 180 40.66 39.44 38.57 37.96 37.55 37.30 37.13 36.98 37.18 37.44 38.06 38.82 200 43.23 41.78 40.70 39.91 39.34 38.94 38.64 38.35 38.47 38.65 39.16 39.82 D2.5 Properties of Oxygen D2.5. Table 12. (continued) Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 225 46.30 44.61 43.31 42.32 41.56 40.99 40.52 40.07 40.09 40.19 40.55 41.09 250 49.21 47.33 45.84 44.67 43.75 43.02 42.40 41.79 41.72 41.73 41.95 42.36 275 51.97 49.93 48.28 46.95 45.88 45.01 44.26 43.51 43.34 43.27 43.34 43.64 300 54.61 52.42 50.63 49.16 47.96 46.97 46.09 45.21 44.95 44.79 44.72 44.91 325 57.12 54.81 52.89 51.31 49.99 48.88 47.89 46.89 46.54 46.30 46.10 46.17 350 59.53 57.11 55.08 53.38 51.96 50.74 49.66 48.55 48.11 47.80 47.46 47.42 375 61.85 59.32 57.19 55.40 53.88 52.57 51.39 50.18 49.67 49.28 48.81 48.66 400 64.07 61.46 59.24 57.36 55.74 54.35 53.08 51.79 51.20 50.74 50.15 49.89 450 68.30 65.54 63.17 61.12 59.35 57.80 56.38 54.94 54.20 53.61 52.77 52.31 500 72.27 69.39 66.88 64.70 62.79 61.10 59.56 58.00 57.12 56.40 55.34 54.69 D2.5. Table 13. Dynamic viscosity of oxygen in 106 Pa·s Temperature in C Pressure in bar 200 180 6.810 160 140 120 100 90 80 70 60 50 40 8.452 10.02 11.51 12.93 13.62 14.29 14.95 15.60 16.23 16.86 8.587 10.12 11.60 13.01 13.69 14.36 15.02 15.66 16.29 16.91 1 311.6 5 313.1 172.7 10 315.1 173.7 110.1 10.30 11.74 13.12 13.80 14.46 15.11 15.75 16.37 16.99 20 319.0 175.8 111.8 10.91 12.13 13.42 14.07 14.70 15.33 15.95 16.57 17.17 30 323.0 177.9 113.5 73.31 12.77 13.84 14.43 15.02 15.62 16.21 16.80 17.39 40 327.1 180.0 115.2 75.29 14.04 14.43 14.91 15.43 15.98 16.53 17.09 17.65 50 331.2 182.1 116.8 77.16 39.15 15.30 15.56 15.96 16.42 16.92 17.43 17.95 60 335.4 184.2 118.4 78.95 45.66 16.64 16.45 16.63 16.97 17.38 17.83 18.31 70 339.6 186.3 120.1 80.67 49.48 18.81 17.66 17.49 17.64 17.93 18.30 18.72 80 343.9 188.4 121.7 82.33 52.45 22.39 19.33 18.58 18.45 18.58 18.85 19.19 90 348.3 190.6 123.3 83.93 54.96 27.24 21.56 19.93 19.42 19.34 19.47 19.72 100 352.7 192.7 124.9 85.50 57.18 31.86 24.33 21.58 20.56 20.21 20.17 20.30 120 361.7 197.1 128.1 88.53 61.08 38.80 30.36 25.61 23.35 22.29 21.82 21.67 140 371.1 201.5 131.2 91.44 64.50 43.83 35.71 29.99 26.61 24.77 23.78 23.27 160 380.7 205.9 134.4 94.26 67.60 47.87 40.10 34.11 30.03 27.49 25.96 25.07 180 390.7 210.4 137.5 97.02 70.49 51.32 43.82 37.79 33.34 30.28 28.28 27.01 200 401.0 215.0 140.6 99.71 73.22 54.40 47.07 41.07 36.42 33.02 30.64 29.03 225 414.3 220.8 144.6 103.0 76.45 57.88 50.69 44.73 39.95 36.27 33.54 31.58 250 428.3 226.8 148.5 106.3 79.54 61.06 53.95 48.01 43.16 39.31 36.33 34.09 275 442.9 232.8 152.5 109.5 82.51 64.04 56.95 51.02 46.11 42.14 38.98 36.53 300 458.2 239.0 156.5 112.7 85.40 66.86 59.77 53.81 48.86 44.79 41.49 38.87 325 474.2 245.4 160.5 115.9 88.22 69.55 62.43 56.45 51.44 47.29 43.88 41.12 350 491.1 251.9 164.6 119.0 90.98 72.15 64.98 58.95 53.89 49.66 46.16 43.28 375 508.8 258.5 168.7 122.1 93.70 74.67 67.44 61.35 56.23 51.93 48.34 45.36 400 527.5 265.3 172.8 125.3 96.38 77.12 69.81 63.66 58.48 54.11 50.44 47.37 450 568.0 279.5 181.3 131.6 101.7 81.88 74.39 68.08 62.76 58.24 54.42 51.19 500 613.4 294.5 190.0 137.9 106.9 86.49 78.79 72.30 66.81 62.15 58.18 54.80 251 252 D2 Properties of Selected Important Pure Substances D2.5. Table 13. (continued) Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 1 17.47 18.07 18.66 19.24 19.81 20.37 20.92 21.47 22.00 22.53 23.57 24.58 5 17.52 18.12 18.71 19.28 19.85 20.41 20.96 21.51 22.04 22.57 23.61 24.62 10 17.59 18.19 18.77 19.35 19.91 20.47 21.02 21.56 22.10 22.62 23.66 24.66 20 17.76 18.35 18.92 19.49 20.05 20.60 21.15 21.68 22.21 22.73 23.76 24.76 30 17.97 18.54 19.10 19.66 20.21 20.75 21.29 21.82 22.34 22.86 23.87 24.87 40 18.21 18.76 19.31 19.85 20.39 20.92 21.45 21.97 22.49 23.00 24.00 24.99 50 18.48 19.01 19.54 20.07 20.60 21.12 21.63 22.14 22.65 23.15 24.14 25.11 60 18.80 19.30 19.81 20.32 20.82 21.33 21.83 22.33 22.83 23.32 24.30 25.25 70 19.17 19.63 20.11 20.59 21.08 21.56 22.05 22.54 23.02 23.51 24.46 25.40 80 19.58 20.00 20.44 20.89 21.35 21.82 22.29 22.76 23.23 23.70 24.64 25.56 90 20.04 20.40 20.80 21.22 21.66 22.10 22.55 23.00 23.46 23.91 24.83 25.73 100 20.54 20.85 21.20 21.58 21.98 22.40 22.83 23.26 23.70 24.14 25.03 25.92 120 21.71 21.86 22.09 22.38 22.71 23.06 23.44 23.83 24.23 24.63 25.46 26.31 140 23.06 23.03 23.12 23.29 23.53 23.81 24.12 24.46 24.81 25.18 25.94 26.74 160 24.57 24.33 24.26 24.31 24.44 24.63 24.87 25.15 25.45 25.77 26.47 27.20 180 26.22 25.75 25.50 25.41 25.43 25.53 25.69 25.90 26.14 26.42 27.03 27.70 200 27.95 27.26 26.83 26.58 26.48 26.48 26.56 26.70 26.88 27.10 27.63 28.23 225 30.19 29.22 28.56 28.13 27.87 27.74 27.71 27.75 27.86 28.01 28.42 28.93 250 32.43 31.22 30.35 29.74 29.33 29.07 28.92 28.87 28.89 28.96 29.25 29.66 275 34.65 33.23 32.17 31.39 30.83 30.44 30.18 30.03 29.96 29.96 30.12 30.44 300 36.81 35.21 33.98 33.05 32.34 31.83 31.46 31.22 31.06 30.99 31.02 31.24 325 38.91 37.16 35.78 34.70 33.87 33.24 32.77 32.43 32.19 32.04 31.95 32.06 350 40.94 39.05 37.54 36.34 35.39 34.65 34.08 33.65 33.33 33.11 32.90 32.90 375 42.91 40.91 39.28 37.96 36.90 36.06 35.40 34.88 34.49 34.20 33.86 33.76 400 44.82 42.71 40.97 39.55 38.40 37.46 36.71 36.11 35.65 35.29 34.83 34.63 450 48.46 46.18 44.26 42.66 41.32 40.22 39.31 38.57 37.96 37.47 36.79 36.40 500 51.92 49.48 47.40 45.65 44.16 42.91 41.86 40.99 40.25 39.65 38.75 38.18 D2.5. Table 14. Kinematic viscosity v of oxygen in 107 m2/s Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 50 1 2.55 16.0 24.4 34.3 45.5 5 2.56 1.53 4.60 6.63 8.91 10 2.57 1.54 1.08 3.16 4.34 5.62 6.30 7.01 7.75 8.51 9.30 20 2.60 1.55 1.09 1.39 2.04 2.72 3.07 3.44 3.81 4.20 4.60 5.02 30 2.63 1.57 1.11 0.827 1.27 1.75 2.00 2.25 2.51 2.77 3.05 3.33 40 2.66 1.59 1.12 0.840 0.971 1.28 1.47 1.66 1.86 2.06 2.27 2.49 50 2.69 1.60 1.13 0.853 0.619 0.992 1.15 1.31 1.48 1.64 1.81 1.99 60 2.72 1.62 1.14 0.866 0.655 0.808 0.950 1.09 1.23 1.37 1.51 1.66 70 2.75 1.63 1.15 0.878 0.678 0.688 0.813 0.934 1.05 1.18 1.30 1.43 80 2.79 1.65 1.16 0.889 0.697 0.620 0.720 0.825 0.931 1.04 1.15 1.26 90 2.82 1.66 1.18 0.901 0.712 0.600 0.661 0.748 0.840 0.935 1.03 1.13 57.9 64.6 71.5 78.7 86.2 93.9 11.4 12.8 14.2 15.6 17.1 18.7 40 102 20.3 10.1 D2.5 Properties of Oxygen D2.5. Table 14. (continued) Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 50 40 100 2.85 1.68 1.19 0.911 0.727 0.606 0.629 0.695 0.774 0.858 0.944 1.03 120 2.92 1.71 1.21 0.933 0.752 0.633 0.616 0.642 0.693 0.755 0.823 0.895 140 2.99 1.74 1.23 0.953 0.774 0.658 0.629 0.629 0.656 0.699 0.751 0.808 160 3.06 1.77 1.26 0.973 0.795 0.680 0.647 0.634 0.644 0.670 0.708 0.753 180 3.13 1.81 1.28 0.993 0.814 0.700 0.664 0.645 0.644 0.658 0.685 0.719 200 3.21 1.84 1.30 1.01 0.833 0.719 0.682 0.659 0.650 0.656 0.673 0.699 225 3.30 1.88 1.33 1.04 0.855 0.740 0.702 0.676 0.662 0.660 0.669 0.686 250 3.41 1.93 1.36 1.06 0.876 0.760 0.721 0.693 0.675 0.668 0.671 0.681 275 3.51 1.97 1.39 1.08 0.896 0.779 0.739 0.709 0.689 0.679 0.676 0.682 300 3.63 2.02 1.42 1.10 0.916 0.798 0.756 0.725 0.703 0.690 0.684 0.686 325 3.74 2.06 1.45 1.13 0.936 0.815 0.773 0.741 0.717 0.702 0.693 0.691 350 3.87 2.11 1.48 1.15 0.955 0.832 0.789 0.756 0.731 0.713 0.703 0.699 375 4.00 2.16 1.51 1.17 0.974 0.849 0.805 0.771 0.744 0.725 0.713 0.707 400 4.14 2.21 1.54 1.19 0.993 0.866 0.821 0.785 0.757 0.737 0.723 0.715 450 4.43 2.31 1.60 1.24 1.03 0.898 0.851 0.813 0.783 0.761 0.744 0.733 500 4.77 2.42 1.66 1.29 1.07 0.929 0.880 0.840 0.809 0.784 0.765 0.751 30 40 50 60 80 100 Temperature in C Pressure in bar 1 30 110 20 119 10 127 0 136 10 146 20 155 165 175 185 195 216 238 5 22.0 23.7 25.4 27.2 29.1 31.0 32.9 34.9 36.9 39.0 43.3 47.7 10 10.9 11.8 12.7 13.6 14.5 15.5 16.5 17.5 18.5 19.5 21.7 23.9 10.9 12.0 20 5.44 5.88 6.33 6.79 7.26 7.74 8.23 8.74 9.25 9.78 30 3.61 3.91 4.21 4.52 4.84 5.17 5.50 5.84 6.18 6.54 7.26 8.01 40 2.71 2.93 3.16 3.40 3.64 3.88 4.13 4.39 4.65 4.92 5.47 6.04 50 2.16 2.35 2.53 2.72 2.92 3.12 3.32 3.53 3.74 3.95 4.39 4.85 60 1.81 1.96 2.12 2.28 2.44 2.61 2.78 2.95 3.13 3.31 3.68 4.06 70 1.56 1.69 1.83 1.96 2.11 2.25 2.40 2.55 2.70 2.85 3.17 3.50 80 1.37 1.49 1.61 1.73 1.86 1.98 2.11 2.24 2.38 2.51 2.80 3.09 90 1.23 1.34 1.44 1.55 1.66 1.78 1.89 2.01 2.13 2.25 2.50 2.76 100 1.12 1.22 1.31 1.41 1.51 1.61 1.72 1.83 1.93 2.04 2.27 2.51 120 0.970 1.05 1.13 1.21 1.29 1.38 1.46 1.55 1.64 1.74 1.93 2.12 140 0.870 0.934 1.00 1.07 1.14 1.21 1.29 1.36 1.44 1.52 1.69 1.85 160 0.804 0.857 0.914 0.973 1.03 1.10 1.16 1.23 1.30 1.37 1.51 1.66 180 0.760 0.804 0.853 0.903 0.956 1.01 1.07 1.13 1.19 1.25 1.37 1.51 200 0.731 0.768 0.809 0.853 0.899 0.947 0.997 1.05 1.10 1.16 1.27 1.39 225 0.709 0.738 0.771 0.808 0.847 0.888 0.931 0.976 1.02 1.07 1.17 1.27 250 0.698 0.720 0.747 0.777 0.810 0.845 0.883 0.922 0.963 1.01 1.09 1.19 275 0.693 0.710 0.731 0.756 0.784 0.814 0.847 0.881 0.917 0.955 1.03 1.12 300 0.693 0.705 0.722 0.743 0.766 0.792 0.820 0.851 0.883 0.916 0.987 1.06 325 0.695 0.704 0.717 0.734 0.754 0.776 0.801 0.827 0.856 0.886 0.950 1.02 350 0.700 0.705 0.715 0.729 0.746 0.765 0.786 0.810 0.835 0.862 0.919 0.982 375 0.705 0.709 0.716 0.727 0.740 0.757 0.776 0.796 0.819 0.843 0.895 0.952 400 0.712 0.713 0.718 0.726 0.738 0.752 0.768 0.786 0.806 0.828 0.876 0.928 450 0.726 0.724 0.725 0.730 0.737 0.747 0.759 0.774 0.790 0.807 0.847 0.891 500 0.742 0.737 0.735 0.737 0.741 0.748 0.757 0.768 0.781 0.795 0.828 0.865 253 254 D2 Properties of Selected Important Pure Substances D2.5. Table 15. Thermal diffusivity a of oxygen in 107 m2/s Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 1 0.861 21.4 33.1 46.6 62.1 79.2 88.4 98.0 5 0.862 0.773 5.76 8.61 11.8 15.3 17.2 19.2 10 0.863 0.776 0.649 3.84 5.53 7.36 8.32 9.32 20 0.865 0.780 0.658 1.28 2.38 3.37 3.88 4.41 4.95 5.50 6.06 6.64 30 0.868 0.785 0.667 0.486 1.29 2.04 2.41 2.78 3.15 3.54 3.93 4.33 40 0.870 0.789 0.675 0.507 0.637 1.37 1.67 1.97 2.27 2.56 2.87 3.17 50 0.873 0.793 0.683 0.525 0.165 0.957 1.23 1.49 1.74 1.99 2.24 2.49 60 0.875 0.798 0.691 0.541 0.272 0.663 0.930 1.16 1.39 1.60 1.82 2.04 70 0.878 0.802 0.698 0.556 0.330 0.446 0.714 0.936 1.14 1.34 1.53 1.72 80 0.880 0.806 0.705 0.570 0.373 0.307 0.554 0.767 0.958 1.14 1.31 1.49 108 118 50 129 40 140 21.2 23.3 25.4 27.6 10.3 11.4 12.5 13.6 90 0.882 0.810 0.711 0.583 0.406 0.266 0.444 0.641 0.820 0.987 1.15 1.31 100 0.884 0.813 0.718 0.595 0.434 0.283 0.381 0.549 0.715 0.871 1.02 1.17 120 0.889 0.821 0.730 0.617 0.479 0.345 0.355 0.449 0.577 0.709 0.839 0.966 140 0.893 0.828 0.742 0.636 0.514 0.399 0.383 0.424 0.509 0.614 0.724 0.834 160 0.897 0.835 0.753 0.654 0.544 0.443 0.420 0.434 0.486 0.563 0.653 0.748 180 0.901 0.841 0.763 0.670 0.570 0.480 0.455 0.455 0.486 0.541 0.612 0.691 200 0.905 0.848 0.773 0.685 0.593 0.511 0.486 0.480 0.497 0.536 0.591 0.657 225 0.910 0.855 0.784 0.703 0.618 0.544 0.520 0.510 0.517 0.542 0.582 0.633 250 0.915 0.863 0.795 0.718 0.640 0.573 0.550 0.537 0.539 0.555 0.584 0.623 275 0.919 0.870 0.806 0.733 0.661 0.598 0.576 0.563 0.561 0.570 0.592 0.623 300 0.923 0.876 0.815 0.747 0.679 0.621 0.600 0.586 0.582 0.587 0.603 0.627 325 0.927 0.883 0.824 0.760 0.696 0.641 0.621 0.607 0.601 0.604 0.615 0.634 350 0.932 0.889 0.833 0.772 0.711 0.660 0.641 0.627 0.620 0.621 0.629 0.644 375 0.935 0.895 0.842 0.784 0.726 0.677 0.659 0.645 0.648 0.636 0.642 0.654 400 0.939 0.901 0.850 0.794 0.740 0.693 0.675 0.662 0.654 0.652 0.655 0.665 450 0.947 0.912 0.866 0.815 0.765 0.722 0.706 0.693 0.684 0.680 0.681 0.687 500 0.953 0.922 0.880 0.833 0.787 0.748 0.733 0.720 0.711 0.706 0.705 0.709 80 100 Temperature in C Pressure in bar 1 30 151 20 163 10 175 0 187 10 200 20 213 30 226 40 239 50 253 60 267 296 325 5 29.9 32.3 34.7 37.2 39.7 42.3 45.0 47.7 50.4 53.3 59.0 65.0 10 14.8 16.0 17.2 18.5 19.7 21.1 22.4 23.8 25.1 26.6 29.5 32.5 10.4 11.1 11.8 12.5 13.2 14.7 16.2 20 7.24 7.85 8.47 9.11 9.76 30 4.73 5.15 5.57 6.01 6.45 6.90 7.36 7.83 8.30 8.79 9.79 40 3.49 3.81 4.13 4.46 4.80 5.14 5.49 5.85 6.21 6.58 7.34 8.11 50 2.75 3.01 3.27 3.54 3.82 4.10 4.38 4.67 4.96 5.26 5.87 6.50 60 2.26 2.48 2.71 2.93 3.17 3.40 3.64 3.88 4.13 4.38 4.90 5.43 70 1.91 2.11 2.31 2.50 2.71 2.91 3.12 3.32 3.54 3.76 4.21 4.66 80 1.66 1.83 2.01 2.18 2.36 2.54 2.73 2.91 3.10 3.30 3.69 4.10 90 1.46 1.62 1.78 1.94 2.10 2.26 2.43 2.59 2.76 2.94 3.29 3.65 100 1.31 1.46 1.60 1.75 1.89 2.04 2.19 2.34 2.49 2.65 2.98 3.30 120 1.09 1.22 1.34 1.46 1.59 1.71 1.84 1.96 2.10 2.23 2.51 2.78 140 0.944 1.05 1.16 1.27 1.38 1.49 1.60 1.70 1.82 1.94 2.18 2.42 160 0.843 0.939 1.04 1.13 1.23 1.32 1.42 1.51 1.62 1.72 1.93 2.15 180 0.774 0.859 0.944 1.03 1.12 1.20 1.29 1.37 1.46 1.56 1.75 1.94 10.8 D2.5 Properties of Oxygen D2.5. Table 15. (continued) Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 200 0.728 0.802 0.878 0.955 1.03 1.11 1.19 1.26 1.35 1.43 1.60 1.78 225 0.691 0.754 0.820 0.887 0.955 1.02 1.09 1.16 1.23 1.31 1.46 1.62 250 0.671 0.724 0.781 0.839 0.899 0.960 1.02 1.08 1.15 1.21 1.36 1.50 275 0.661 0.706 0.755 0.806 0.859 0.913 0.967 1.02 1.08 1.14 1.27 1.40 300 0.659 0.696 0.738 0.783 0.830 0.879 0.927 0.972 1.03 1.09 1.20 1.32 325 0.660 0.692 0.728 0.768 0.810 0.853 0.896 0.936 0.988 1.04 1.15 1.26 350 0.665 0.692 0.723 0.758 0.795 0.834 0.873 0.909 0.956 1.00 1.10 1.21 375 0.672 0.695 0.722 0.752 0.785 0.820 0.855 0.888 0.931 0.976 1.07 1.16 400 0.679 0.699 0.723 0.750 0.779 0.811 0.842 0.872 0.911 0.952 1.04 1.13 450 0.697 0.711 0.729 0.751 0.774 0.800 0.826 0.850 0.884 0.919 0.993 1.07 500 0.716 0.726 0.740 0.757 0.776 0.797 0.819 0.839 0.868 0.898 0.962 1.03 D2.5. Table 16. Prandtl number Pr of oxygen Temperature in C Pressure in bar 200 180 160 140 120 100 90 80 70 60 50 40 1 2.96 0.749 0.739 0.735 0.733 0.731 0.730 0.730 0.730 0.729 0.729 0.729 5 2.97 1.98 0.800 0.770 0.754 0.745 0.742 0.740 0.738 0.737 0.735 0.735 10 2.98 1.99 1.67 0.823 0.784 0.764 0.758 0.753 0.749 0.746 0.743 0.741 20 3.01 1.99 1.66 1.09 0.860 0.806 0.791 0.780 0.771 0.764 0.759 0.755 30 3.03 2.00 1.66 1.70 0.989 0.858 0.829 0.809 0.795 0.784 0.776 0.769 40 3.06 2.01 1.66 1.66 1.37 0.929 0.876 0.844 0.821 0.805 0.793 0.783 50 3.08 2.02 1.65 1.63 3.74 1.04 0.938 0.885 0.851 0.828 0.811 0.798 60 3.11 2.03 1.65 1.60 2.41 1.22 1.02 0.935 0.885 0.853 0.830 0.813 70 3.14 2.04 1.65 1.58 2.05 1.54 1.14 0.998 0.925 0.881 0.851 0.830 80 3.17 2.04 1.65 1.56 1.87 2.02 1.30 1.08 0.972 0.912 0.874 0.847 90 3.19 2.05 1.65 1.54 1.75 2.26 1.49 1.17 1.02 0.947 0.899 0.866 100 3.22 2.06 1.65 1.53 1.67 2.14 1.65 1.27 1.08 0.985 0.925 0.886 120 3.28 2.08 1.66 1.51 1.57 1.83 1.73 1.43 1.20 1.06 0.981 0.927 140 3.34 2.10 1.66 1.50 1.51 1.65 1.64 1.49 1.29 1.14 1.04 0.969 160 3.41 2.13 1.67 1.49 1.46 1.53 1.54 1.46 1.33 1.19 1.08 1.01 180 3.47 2.15 1.68 1.48 1.43 1.46 1.46 1.42 1.33 1.22 1.12 1.04 200 3.54 2.17 1.68 1.48 1.40 1.41 1.40 1.37 1.31 1.22 1.14 1.06 225 3.63 2.20 1.70 1.47 1.38 1.36 1.35 1.33 1.28 1.22 1.15 1.08 250 3.72 2.23 1.71 1.47 1.37 1.33 1.31 1.29 1.25 1.21 1.15 1.09 275 3.82 2.27 1.72 1.47 1.36 1.30 1.28 1.26 1.23 1.19 1.14 1.10 300 3.93 2.30 1.74 1.48 1.35 1.28 1.26 1.24 1.21 1.17 1.14 1.09 325 4.04 2.34 1.75 1.48 1.35 1.27 1.24 1.22 1.19 1.16 1.13 1.09 350 4.15 2.38 1.77 1.49 1.34 1.26 1.23 1.21 1.18 1.15 1.12 1.09 375 4.27 2.41 1.79 1.50 1.34 1.25 1.22 1.19 1.17 1.14 1.11 1.08 400 4.40 2.45 1.81 1.50 1.34 1.25 1.21 1.19 1.16 1.13 1.10 1.08 450 4.68 2.54 1.85 1.52 1.35 1.24 1.21 1.17 1.14 1.12 1.09 1.07 500 5.00 2.63 1.89 1.54 1.36 1.24 1.20 1.17 1.14 1.11 1.08 1.06 255 256 D2 Properties of Selected Important Pure Substances D2.5. Table 16. (continued) Temperature in C Pressure in bar 30 20 10 0 10 20 30 40 50 60 80 100 1 0.729 0.729 0.729 0.729 0.729 0.730 0.730 0.730 0.730 0.731 0.732 0.732 5 0.734 0.733 0.733 0.733 0.732 0.732 0.732 0.732 0.732 0.733 0.733 0.734 10 0.740 0.739 0.738 0.737 0.736 0.736 0.735 0.735 0.735 0.735 0.735 0.735 20 0.752 0.749 0.747 0.745 0.743 0.742 0.741 0.740 0.740 0.739 0.739 0.738 30 0.764 0.759 0.756 0.753 0.750 0.748 0.747 0.746 0.744 0.743 0.742 0.741 40 0.776 0.770 0.765 0.761 0.757 0.755 0.752 0.751 0.749 0.748 0.745 0.744 50 0.788 0.780 0.774 0.769 0.764 0.761 0.758 0.756 0.753 0.751 0.749 0.746 60 0.801 0.791 0.783 0.776 0.771 0.767 0.763 0.761 0.758 0.755 0.752 0.749 70 0.814 0.802 0.792 0.784 0.778 0.773 0.769 0.766 0.762 0.759 0.755 0.751 80 0.828 0.813 0.801 0.792 0.785 0.779 0.774 0.771 0.767 0.763 0.758 0.754 90 0.842 0.825 0.811 0.800 0.792 0.785 0.780 0.776 0.771 0.767 0.760 0.756 100 0.857 0.837 0.821 0.809 0.799 0.791 0.785 0.781 0.775 0.771 0.763 0.758 120 0.889 0.862 0.841 0.826 0.813 0.804 0.796 0.791 0.784 0.778 0.769 0.763 140 0.922 0.888 0.862 0.843 0.828 0.816 0.807 0.801 0.793 0.786 0.775 0.767 160 0.953 0.913 0.883 0.860 0.842 0.829 0.818 0.812 0.802 0.794 0.781 0.772 180 0.981 0.937 0.903 0.877 0.857 0.841 0.830 0.822 0.811 0.801 0.787 0.776 200 1.00 0.957 0.921 0.893 0.871 0.853 0.840 0.832 0.820 0.809 0.793 0.781 225 1.03 0.979 0.941 0.911 0.886 0.867 0.853 0.845 0.830 0.818 0.800 0.786 250 1.04 0.995 0.957 0.926 0.901 0.880 0.865 0.856 0.840 0.827 0.807 0.792 275 1.05 1.01 0.969 0.938 0.913 0.892 0.876 0.866 0.850 0.836 0.814 0.798 300 1.05 1.01 0.978 0.948 0.923 0.902 0.885 0.875 0.859 0.844 0.821 0.803 325 1.05 1.02 0.985 0.956 0.931 0.910 0.894 0.884 0.866 0.851 0.827 0.809 350 1.05 1.02 0.989 0.962 0.937 0.917 0.901 0.891 0.873 0.858 0.833 0.814 375 1.05 1.02 0.992 0.966 0.943 0.923 0.907 0.897 0.879 0.864 0.839 0.819 400 1.05 1.02 0.993 0.969 0.947 0.927 0.912 0.902 0.885 0.869 0.844 0.824 450 1.04 1.02 0.994 0.972 0.952 0.934 0.919 0.910 0.893 0.878 0.853 0.832 500 1.04 1.01 0.994 0.974 0.955 0.938 0.925 0.916 0.900 0.885 0.860 0.840 5 1. Bibliography Schmidt R, Wagner W (1985) A new form of equation of state for pure substances and its application to oxygen. Fluid Phase Equilibria 19:175–200 2. 3. Wagner W, de Reuck M (1987) International thermodynamic tables of the fluid state – 9, oxygen. Blackwell Science Publications, Oxford Laesecke A, Krauss R, Stephan K, Wagner W (1990) Transport properties of fluid oxygen. J Phys Chem Ref Data 19:1089–1122 Properties of Ammonia D2.6 D2.6 Properties of Ammonia Roland Span1 . Rolf Krauss2 1 2 Ruhr-Universität Bochum, Bochum, Germany Universität Stuttgart, Stuttgart, Germany 1 Characteristic Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 4 Reference States of Enthalpy and Entropy . . . . . . . . . . . . . 257 2 Critical Point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 5 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 3 Triple Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Tables with thermodynamic properties of ammonia were calculated using the reference equation of state established by TillnerRoth et al. [1, 2]. Tabulated thermal conductivities were calculated using the equation by Tufeu et al. [3]. Viscosities were calculated using the equation by Fenghour et al. [4]. The densities required as input to these correlations were calculated using the reference equation of state. p Pressure in bar 3 n Specific volume in m3/kg b Isobaric expansion coefficient in 103/K b = n1·(∂v/∂T )p r Density in kg/m # Temperature in C ws Isentropic speed of sound in m/s Z Compression factor Z = p/(rRT ) l Thermal conductivity in mW/(m K) h Specific enthalpy in kJ/kg Dynamic viscosity in 106 Pa·s s Specific entropy in kJ/(kg K) n Kinematic viscosity n in 107 m2/s cp Specific isobaric heat capacity in kJ/(kg K) a Thermal diffusivity in 107 m2/s cv Specific isochoric heat capacity in kJ/(kg K) Pr Prandtl number Pr = cp / l 1 Characteristic Quantities e = 17.0305 g/mol, specific gas constant Molecular mass M R = 488.2175 J/(kg K). 2 Critical Point [2] pc = 113.39 bar, Tc = 405.4 K (#c = 132.25 C), rc = 225 kg/m3. 3 Triple Point [2] Tt = 195.5 K (#t = 77.65 C). 4 Reference States of Enthalpy and Entropy h 0 = 200 kJ/kg and s 0 = 1 kJ/(kg K) for saturated liquid at # = 0 C. 257 258 D2 Properties of Selected Important Pure Substances D2.6. Table 1. Properties of ammonia at p = 1 bar q ˚C r kg/m3 h kJ/kg s kJ/(kg K) cp kJ/(kg K) cv kJ/(kg K) b 103/K ws m/s l mW/(m K) h 106 Pa·s n a 107 m2/s 107 m2/s Pr – 75 730.13 131.9 0.4150 4.216 2.930 1.46 2098 809.7 527.9 7.23 2.63 2.75 70 724.75 110.7 0.3096 4.245 2.921 1.50 2051 792.2 475.1 6.56 2.57 2.55 65 719.25 89.43 0.2060 4.274 2.911 1.54 774.6 430.1 5.98 2.52 2.37 60 713.65 67.99 0.1042 4.303 2.902 1.59 1967 757.1 391.4 5.48 2.47 2.22 2.10 2.008 55 707.93 46.40 0.0041 4.332 2.893 1.63 1928 739.7 358.0 5.06 2.41 50 702.11 24.67 0.0944 4.360 2.884 1.67 1890 722.4 328.9 4.68 2.36 1.99 45 696.19 2.808 0.1913 4.387 2.875 1.72 1853 705.2 303.5 4.36 2.31 1.89 40 690.16 19.19 0.2867 4.414 2.866 1.76 1816 688.1 281.3 4.08 2.26 1.80 35 684.04 41.33 0.3806 4.439 2.858 1.80 1780 671.3 261.5 3.82 2.21 1.73 30 0.86 1426 6.161 2.273 1.690 4.61 389.3 21.12 8.165 94.5 108 0.879 25 0.84 1437 6.207 2.247 1.676 4.46 393.7 21.37 8.332 98.6 113 0.876 20 0.83 1449 6.251 2.226 1.664 4.33 398.0 21.64 8.501 103 118 0.875 15 0.81 1460 6.295 2.210 1.655 4.21 402.2 21.93 8.671 107 123 0.874 10 0.79 1471 6.337 2.196 1.649 4.10 406.4 22.24 8.844 112 128 0.873 5 0.78 1482 6.378 2.186 1.644 3.99 410.4 22.57 9.018 116 133 0.873 0 0.76 1492 6.418 2.178 1.641 3.90 414.3 22.91 9.194 121 138 0.874 5 0.75 1503 6.458 2.172 1.640 3.81 418.2 23.28 9.371 125 144 0.874 10 0.73 1514 6.497 2.168 1.639 3.72 422.0 23.67 9.549 130 149 0.875 15 0.72 1525 6.534 2.165 1.640 3.64 425.8 24.07 9.729 135 155 0.875 20 0.71 1536 6.572 2.164 1.642 3.57 429.4 24.49 9.911 140 160 0.875 25 0.69 1547 6.608 2.164 1.644 3.50 433.1 24.93 10.09 145 166 0.876 30 0.68 1558 6.644 2.164 1.647 3.43 436.6 25.39 10.28 151 172 0.876 35 0.67 1568 6.680 2.166 1.651 3.36 440.2 25.86 10.46 156 178 0.876 40 0.66 1579 6.715 2.169 1.656 3.30 443.6 26.36 10.65 161 184 0.876 45 0.65 1590 6.749 2.172 1.661 3.24 447.1 26.86 10.83 167 191 0.876 50 0.64 1601 6.783 2.176 1.666 3.19 450.4 27.39 11.02 173 197 0.875 55 0.63 1612 6.816 2.180 1.672 3.13 453.8 27.93 11.21 178 204 0.875 60 0.62 1623 6.849 2.185 1.678 3.08 457.1 28.48 11.40 184 211 0.874 65 0.61 1634 6.882 2.191 1.685 3.03 460.3 29.05 11.59 190 218 0.874 70 0.60 1645 6.914 2.196 1.692 2.98 463.6 29.64 11.78 196 225 0.873 75 0.59 1656 6.946 2.203 1.699 2.93 466.7 30.24 11.97 202 232 0.872 80 0.58 1667 6.977 2.209 1.706 2.89 469.9 30.85 12.16 209 239 0.871 85 0.57 1678 7.008 2.216 1.714 2.85 473.0 31.48 12.35 215 247 0.869 90 0.57 1689 7.039 2.223 1.722 2.80 476.1 32.12 12.54 221 255 0.868 95 0.56 1700 7.070 2.231 1.730 2.76 479.1 32.78 12.74 228 263 0.867 100 0.55 1711 7.100 2.238 1.738 2.72 482.2 33.44 12.93 235 271 0.865 110 0.54 1734 7.159 2.254 1.756 2.65 488.1 34.81 13.32 248 288 0.862 120 0.52 1756 7.218 2.271 1.774 2.58 494.0 36.22 13.70 262 305 0.859 130 0.51 1779 7.275 2.289 1.792 2.51 499.7 37.68 14.09 276 323 0.856 140 0.50 1802 7.331 2.307 1.811 2.45 505.4 39.17 14.48 291 341 0.853 150 0.49 1825 7.386 2.326 1.830 2.39 510.9 40.69 14.87 306 360 0.850 160 0.47 1848 7.441 2.345 1.850 2.33 516.4 42.25 15.26 322 380 0.847 170 0.46 1872 7.495 2.365 1.870 2.28 521.8 43.83 15.65 338 400 0.844 180 0.45 1896 7.548 2.385 1.891 2.22 527.1 45.44 16.04 354 421 0.842 190 0.44 1920 7.600 2.405 1.912 2.18 532.3 47.06 16.43 371 442 0.840 200 0.43 1944 7.652 2.426 1.933 2.13 537.5 48.69 16.82 388 463 0.838 210 0.42 1968 7.703 2.447 1.954 2.08 542.5 50.34 17.21 405 484 0.836 220 0.42 1993 7.753 2.468 1.975 2.04 547.6 51.99 17.60 423 506 0.835 230 0.41 2018 7.803 2.489 1.997 2.00 552.5 53.64 17.98 441 529 0.835 240 0.40 2043 7.852 2.511 2.019 1.96 557.4 55.28 18.37 460 551 0.834 250 0.39 2068 7.901 2.533 2.041 1.92 562.2 56.92 18.76 478 573 0.835 260 0.38 2093 7.949 2.555 2.064 1.88 567.0 58.54 19.14 498 596 0.835 D2.6 Properties of Ammonia D2.6. Table 1. (continued) q ˚C r kg/m3 h kJ/kg s kJ/(kg K) cp kJ/(kg K) cv kJ/(kg K) b 103/K ws m/s l mW/(m K) h 106 Pa·s n a 107 m2/s 107 m2/s Pr – 270 0.38 2119 7.996 2.577 2.086 1.85 571.8 60.14 19.52 517 618 0.837 280 0.37 2145 8.044 2.600 2.109 1.82 576.4 61.72 19.91 537 640 0.838 290 0.36 2171 8.090 2.622 2.131 1.78 581.1 63.28 20.29 557 663 0.841 300 0.36 2197 8.137 2.645 2.154 1.75 585.6 64.77 20.67 578 685 0.844 D2.6. Table 2. Properties of the saturated liquid q ˚C p bar r’ kg/m3 h’ kJ/kg s’ kJ/(kg K) cp’ kJ/(kg K) cv’ kJ/(kg K) b’ 103/K ws’ m/s l’ mW/(m K) h’ 106 Pa·s n’ 107 m2/s a’ 107 m2/s Pr’ – 75 0.07507 730.10 132.0 0.4148 4.217 2.930 1.46 2098 809.6 527.8 7.23 2.63 2.75 70 0.10941 724.72 110.8 0.3094 4.245 2.921 1.50 2051 792.1 475.0 6.55 2.57 2.55 65 0.15624 719.22 89.51 0.2058 4.274 2.911 1.54 2008 774.5 429.9 5.98 2.52 2.37 60 0.21893 713.62 68.06 0.1040 4.303 2.902 1.59 1967 757.0 391.2 5.48 2.47 2.22 55 0.30145 707.90 46.47 0.004 4.332 2.893 1.63 1928 739.6 357.8 5.06 2.41 2.10 50 0.40836 702.09 24.73 0.095 4.360 2.884 1.67 1890 722.3 328.8 4.68 2.36 1.99 45 0.54489 696.17 2.847 0.1914 4.387 2.875 1.72 1853 705.1 303.5 4.36 2.31 1.89 40 0.71692 690.15 19.17 0.2867 4.414 2.866 1.76 1816 688.1 281.2 4.07 2.26 1.80 35 0.93098 684.04 41.32 0.3806 4.439 2.858 1.80 1780 671.3 261.5 3.82 2.21 1.73 30 1.1943 677.83 63.60 0.4730 4.465 2.849 1.85 1744 654.6 244.1 3.60 2.16 1.66 25 1.5147 671.53 86.01 0.5641 4.489 2.841 1.90 1709 638.2 228.4 3.40 2.12 1.61 20 1.9008 665.14 108.6 0.6538 4.514 2.833 1.94 1673 622.0 214.4 3.22 2.07 1.56 15 2.3617 658.65 131.2 0.7421 4.538 2.824 1.99 1638 605.9 201.7 3.06 2.03 1.51 10 2.9071 652.06 154.0 0.8293 4.564 2.816 2.05 1602 590.1 190.2 2.92 1.98 1.47 5 3.5476 645.37 176.9 0.9152 4.589 2.808 2.10 1566 574.6 179.7 2.78 1.94 1.44 0 4.2938 638.57 200.0 1.000 4.617 2.800 2.16 1531 559.2 170.1 2.66 1.90 1.40 5 5.1575 631.66 223.2 1.084 4.645 2.793 2.23 1494 544.1 161.2 2.55 1.85 1.38 10 6.1505 624.64 246.6 1.166 4.676 2.785 2.30 1458 529.1 153.0 2.45 1.81 1.35 15 7.2852 617.49 270.1 1.248 4.709 2.778 2.37 1421 514.4 145.4 2.35 1.77 1.33 20 8.5748 610.20 293.8 1.329 4.745 2.771 2.45 1384 499.9 138.3 2.27 1.73 1.31 25 10.032 602.76 317.7 1.409 4.784 2.765 2.54 1347 485.5 131.7 2.18 1.68 1.30 30 11.672 595.17 341.8 1.488 4.828 2.759 2.64 1309 471.4 125.4 2.11 1.64 1.29 35 13.508 587.40 366.1 1.567 4.877 2.753 2.75 1271 457.4 119.6 2.04 1.60 1.28 40 15.554 579.44 390.6 1.645 4.932 2.748 2.87 1232 443.5 114.0 1.97 1.55 1.27 45 17.827 571.27 415.5 1.722 4.994 2.744 3.01 1193 429.9 108.8 1.90 1.51 1.26 50 20.340 562.86 440.6 1.799 5.064 2.741 3.16 1153 416.3 103.8 1.84 1.46 1.26 55 23.111 554.20 466.1 1.876 5.143 2.739 3.34 1112 402.9 99.03 1.79 1.41 1.26 60 26.156 545.24 492.0 1.952 5.235 2.738 3.54 1070 389.6 94.48 1.73 1.36 1.27 65 29.491 535.96 518.3 2.029 5.341 2.738 3.77 1028 376.4 90.12 1.68 1.31 1.28 70 33.135 526.31 545.0 2.105 5.465 2.740 4.04 984.4 363.2 85.93 1.63 1.26 1.29 75 37.105 516.23 572.4 2.182 5.610 2.744 4.36 940.0 350.2 81.89 1.59 1.21 1.31 80 41.420 505.67 600.3 2.260 5.784 2.750 4.75 894.7 337.1 77.98 1.54 1.15 1.34 85 46.100 494.54 629.0 2.338 5.993 2.759 5.22 848.1 324.1 74.18 1.50 1.09 1.37 90 51.167 482.75 658.6 2.417 6.250 2.772 5.81 800.4 311.0 70.47 1.46 1.03 1.42 95 56.643 470.17 689.2 2.497 6.573 2.789 6.55 751.3 297.9 66.83 1.42 0.964 1.47 100 62.553 456.63 721.0 2.580 6.991 2.811 7.53 700.7 284.8 63.23 1.38 0.892 1.55 105 68.923 441.90 754.4 2.665 7.555 2.840 8.88 648.5 271.5 59.64 1.35 0.813 1.66 110 75.783 425.61 789.7 2.753 8.362 2.879 10.8 594.4 258.1 56.03 1.32 0.725 1.82 115 83.170 407.18 827.7 2.847 9.628 2.931 14.0 537.7 244.6 52.30 1.28 0.624 2.06 120 91.125 385.49 869.9 2.950 11.940 3.004 19.9 477.4 231.2 48.34 1.25 0.502 2.50 125 99.702 357.80 919.7 3.070 17.658 3.116 35.0 411.4 219.1 43.80 1.22 0.347 3.53 312.29 992.0 3.244 54.210 3.345 333.6 221.9 37.29 1.19 0.131 9.11 130 108.98 136 259 260 D2 Properties of Selected Important Pure Substances D2.6. Table 3. Properties of the saturated vapour q ˚C p bar r’’ kg/m3 h” kJ/kg s" kJ/(kg K) cp" kJ/(kg K) cv" kJ/(kg K) b” 103/K ws” m/s l" mW/(m K) h" 106 Pa·s n" 107 m2/s a" 107 m2/s Pr” – 75 0.07507 0.08 1346 7.045 2.070 1.561 5.18 356.4 19.66 6.905 886 1218 0.727 70 0.10941 0.11 1356 6.909 2.086 1.572 5.08 360.5 19.73 7.032 633 852 0.743 65 0.15624 0.15 1365 6.781 2.104 1.584 5.00 364.5 19.82 7.162 462 608 0.760 60 0.21893 0.21 1374 6.660 2.125 1.597 4.93 368.4 19.93 7.296 343 441 0.778 55 0.30145 0.29 1383 6.547 2.150 1.613 4.87 372.1 20.07 7.433 259 326 0.796 50 0.40836 0.38 1391 6.440 2.178 1.631 4.82 375.6 20.24 7.573 199 244 0.815 45 0.54489 0.50 1400 6.338 2.209 1.651 4.78 379.0 20.43 7.715 155 186 0.834 40 0.71692 0.64 1408 6.243 2.244 1.672 4.75 382.2 20.64 7.859 122 143 0.854 35 0.93098 0.82 1416 6.152 2.283 1.696 4.73 385.2 20.88 8.004 97.4 111 0.875 30 1.1943 1.04 1423 6.065 2.326 1.722 4.72 388.1 21.15 8.152 78.6 87.7 0.896 25 1.5147 1.30 1431 5.983 2.373 1.750 4.72 390.7 21.44 8.300 64.0 69.7 0.918 20 1.9008 1.60 1438 5.904 2.425 1.779 4.74 393.2 21.77 8.449 52.7 56.0 0.941 15 2.3617 1.97 1444 5.829 2.481 1.811 4.77 395.4 22.12 8.600 43.7 45.4 0.964 10 2.9071 2.39 1451 5.757 2.542 1.845 4.81 397.5 22.50 8.751 36.6 37.0 0.988 5 3.5476 2.88 1457 5.688 2.608 1.880 4.86 399.3 22.92 8.903 30.9 30.5 1.01 0 4.2938 3.46 1462 5.621 2.680 1.918 4.93 400.8 23.37 9.056 26.2 25.2 1.04 5 5.1575 4.11 1467 5.557 2.758 1.957 5.01 402.2 23.85 9.209 22.4 21.0 1.06 10 6.1505 4.87 1472 5.495 2.841 1.998 5.10 403.2 24.37 9.364 19.2 17.6 1.09 15 7.2852 5.73 1476 5.434 2.932 2.041 5.22 404.1 24.92 9.519 16.6 14.8 1.12 20 8.5748 6.70 1480 5.376 3.030 2.085 5.35 404.6 25.52 9.676 14.4 12.6 1.15 10.7 1.18 25 10.032 7.81 1483 5.319 3.135 2.131 5.50 404.9 26.16 9.835 12.6 30 11.672 9.05 1486 5.263 3.250 2.178 5.67 404.9 26.85 9.995 11.0 35 13.508 10.46 1488 5.209 3.375 2.227 5.87 404.6 27.58 10.16 40 15.554 12.03 1490 5.155 3.510 2.278 6.10 404.0 28.38 45 17.827 13.80 1491 5.102 3.659 2.329 6.36 403.1 50 20.340 15.79 1491 5.050 3.823 2.383 6.65 55 23.111 18.01 1491 4.998 4.005 2.438 60 26.156 20.49 1489 4.946 4.208 2.494 65 29.491 23.28 1487 4.894 4.438 70 33.135 26.41 1484 4.842 75 37.105 29.92 1480 80 41.420 33.89 85 46.100 90 9.12 1.21 9.71 7.82 1.24 10.33 8.58 6.72 1.28 29.23 10.50 7.60 5.79 1.31 401.9 30.16 10.67 6.76 5.00 1.35 7.00 400.3 31.16 10.86 6.03 4.32 1.40 7.40 398.3 32.26 11.05 5.39 3.74 1.44 2.552 7.86 396.0 33.47 11.25 4.83 3.24 1.49 4.699 2.613 8.41 393.3 34.80 11.47 4.34 2.80 1.55 4.788 5.001 2.675 9.06 390.1 36.30 11.70 3.91 2.43 1.61 1474 4.734 5.355 2.739 9.84 386.5 38.00 11.95 3.53 2.09 1.68 38.38 1468 4.679 5.777 2.807 10.8 382.5 39.95 12.23 3.19 1.80 1.77 51.167 43.48 1459 4.621 6.291 2.877 12.0 377.9 42.24 12.55 2.89 1.54 1.87 95 56.643 49.34 1449 4.561 6.933 2.951 13.5 372.7 44.99 12.91 2.62 1.32 1.99 100 62.533 56.12 1437 4.497 7.762 3.030 15.5 367.0 48.36 13.32 2.37 1.11 2.14 105 68.923 64.06 1422 4.429 8.877 3.114 18.3 360.5 52.65 13.82 2.16 0.926 2.33 110 75.783 73.55 1403 4.354 10.463 3.205 22.3 353.3 58.33 14.42 1.96 0.758 2.59 115 83.170 85.18 1380 4.270 12.909 3.305 28.5 345.0 66.28 15.19 1.78 0.603 2.96 120 91.125 100.07 1350 4.172 17.212 3.416 39.6 335.4 78.40 16.21 1.62 0.455 3.56 125 99.702 120.73 1309 4.048 26.996 3.545 65.5 323.6 100.01 17.73 1.47 0.307 4.79 156.77 1239 3.857 76.490 3.701 306.6 160.39 20.63 1.32 0.134 9.84 20 30 130 108.98 199 D2.6. Table 4. Density r of ammonia in kg/m3 Pressure in bar Temperature in C 50 40 30 0.8641 20 0.8263 10 0.7923 0 0.7612 10 1 702.1 690.2 5 702.3 690.4 678.0 665.3 652.2 638.6 10 702.5 690.6 678.3 665.6 652.5 639.0 624.9 610.3 15 702.7 690.8 678.5 665.9 652.8 639.3 625.3 610.8 40 50 60 0.7328 0.7066 0.6823 0.6597 0.6387 0.6190 3.883 3.711 3.559 3.422 3.298 3.184 7.574 7.212 6.898 6.621 595.5 11.52 10.90 10.38 Properties of Ammonia D2.6 D2.6. Table 4. (continued) Pressure in bar Temperature in C 50 40 0 10 20 30 40 20 702.9 691.0 678.8 666.2 25 703.1 691.3 679.0 666.4 653.1 639.7 625.7 611.2 596.0 580.0 653.4 640.0 626.1 611.7 596.5 580.5 563.5 30 703.3 691.5 679.3 666.7 653.8 640.4 626.5 612.1 597.0 581.1 564.2 545.9 35 703.5 691.7 40 703.7 692.0 679.6 667.0 654.1 640.7 626.9 612.5 597.5 581.7 564.9 546.7 679.8 667.3 654.4 641.0 627.3 613.0 598.0 582.3 565.5 50 704.2 547.5 692.4 680.3 667.8 655.0 641.7 628.0 613.8 599.0 583.4 566.9 60 549.1 704.6 692.9 680.8 668.4 655.6 642.4 628.8 614.7 599.9 584.5 568.1 550.6 70 705.0 693.3 681.3 668.9 656.2 643.1 629.5 615.5 600.9 585.6 569.4 552.1 80 705.4 693.8 681.8 669.5 656.8 643.7 630.3 616.3 601.8 586.7 570.7 553.6 90 705.8 694.2 682.3 670.0 657.4 644.4 631.0 617.1 602.7 587.7 571.9 555.1 100 706.2 694.7 682.8 670.5 658.0 645.0 631.7 617.9 603.7 588.7 573.1 556.5 110 706.6 695.1 683.3 671.1 658.6 645.7 632.4 618.7 604.6 589.8 574.2 557.8 120 707.0 695.6 683.8 671.6 659.1 646.3 633.1 619.5 605.4 590.8 575.4 559.2 130 707.4 696.0 684.2 672.1 659.7 647.0 633.8 620.3 606.3 591.8 576.5 560.5 140 707.8 696.4 684.7 672.7 660.3 647.6 634.5 621.1 607.2 592.8 577.7 561.8 150 708.2 696.9 685.2 673.2 660.9 648.2 635.2 621.9 608.1 593.7 578.8 563.1 160 708.6 697.3 685.7 673.7 661.4 648.9 635.9 622.6 608.9 594.7 579.9 564.3 180 709.4 698.2 686.6 674.7 662.6 650.1 637.3 624.1 610.6 596.6 582.0 566.7 200 710.2 699.0 687.5 675.7 663.7 651.3 638.6 625.6 612.2 598.4 584.0 569.1 250 712.1 701.1 689.8 678.2 666.4 654.3 641.9 629.2 616.2 602.8 589.0 574.6 300 714.0 703.2 692.1 680.7 669.0 657.1 645.0 642.6 619.9 606.9 593.6 579.8 400 717.7 707.2 696.4 685.4 674.1 662.6 651.0 639.1 627.0 614.7 602.1 589.2 500 721.3 711.1 700.5 689.8 678.9 667.8 656.6 645.2 633.6 621.8 609.9 597.7 Pressure in bar 1 30 20 10 50 60 15.45 14.54 19.29 Temperature in C 70 0.6005 80 0.5832 90 0.5668 100 110 120 140 160 180 200 250 300 0.5513 0.5367 0.5229 0.4973 0.4741 0.4530 0.4337 0.3920 0.3577 5 3.079 2.982 2.892 2.807 2.728 2.654 2.517 2.395 2.285 2.185 1.970 1.795 10 6.372 6.147 5.941 5.751 5.575 5.412 5.116 4.855 4.622 4.412 3.966 3.606 7.803 7.383 7.013 6.682 5.988 5.434 9.985 9.461 8.998 8.038 7.279 15 9.924 9.527 9.171 8.849 8.555 8.285 20 13.80 13.17 12.61 12.12 11.68 11.29 10.59 25 18.09 17.13 16.31 15.61 14.98 14.43 13.47 12.66 11.97 11.36 10.11 30 22.96 21.49 20.32 19.33 18.48 17.73 16.47 15.43 14.54 13.78 12.22 11.02 9.140 35 526.7 26.40 24.71 23.34 22.20 21.22 19.60 18.28 17.18 16.24 14.36 12.92 40 527.7 32.08 29.60 27.71 26.19 24.92 22.86 21.24 19.90 18.76 16.52 14.83 50 529.7 507.9 41.74 37.93 35.21 33.08 29.87 27.47 25.56 23.98 20.94 18.71 60 531.6 510.3 485.8 51.59 46.26 42.63 37.65 34.20 31.56 29.45 25.50 22.67 70 533.4 512.7 489.0 460.2 61.13 54.31 46.43 41.52 37.96 35.19 30.18 26.71 80 535.2 514.9 492.0 464.7 428.9 69.83 56.58 49.56 44.81 41.24 35.02 30.82 90 536.9 517.1 494.8 468.7 435.8 95.43 68.66 58.49 52.17 47.63 40.00 35.01 100 538.6 519.2 497.5 472.5 441.8 398.1 83.79 68.55 60.14 54.39 45.13 39.28 110 540.3 521.2 500.1 475.9 447.0 408.5 104.4 80.06 68.80 61.56 50.43 43.63 120 541.9 523.1 502.5 479.2 451.7 416.8 138.9 93.51 78.28 69.20 55.90 48.07 130 543.4 525.0 504.9 482.3 456.0 423.7 242.3 109.7 88.74 77.34 61.55 52.58 140 544.9 526.8 507.1 485.2 460.0 429.7 317.0 129.8 100.3 86.04 67.37 57.18 150 546.4 528.6 509.3 487.9 463.7 435.1 344.2 155.9 113.3 95.35 73.38 61.87 160 547.9 530.3 511.4 490.6 467.1 440.0 360.8 189.7 127.9 105.3 79.59 66.64 180 550.7 533.7 515.4 495.5 473.5 448.5 382.9 262.1 162.8 127.5 92.56 76.42 200 553.4 536.8 519.1 500.1 479.2 456.0 398.3 308.9 204.0 152.8 106.3 250 559.7 544.1 527.7 510.2 491.5 471.3 424.8 365.9 291.7 223.4 143.7 113.0 300 565.6 550.7 535.3 519.0 501.9 483.7 443.3 396.2 341.0 282.4 183.6 140.8 400 576.0 562.4 548.4 533.9 518.9 503.3 470.0 433.7 394.3 352.5 256.7 196.5 500 585.3 572.7 559.7 546.4 532.8 518.9 489.7 458.9 426.4 392.8 310.5 246.4 86.52 261 262 D2 Properties of Selected Important Pure Substances D2.6. Table 5. Compression factor Z of ammonia Pressure in bar Temperature in C 50 40 30 20 10 0 10 20 30 40 50 60 1 0.001 0.001 0.975 0.979 0.982 0.985 0.987 0.989 0.990 0.991 0.992 0.993 5 0.007 0.006 0.006 0.006 0.006 0.006 0.932 0.941 0.949 0.956 0.961 0.965 10 0.013 0.013 0.012 0.012 0.012 0.012 0.012 0.011 0.892 0.907 0.919 0.929 15 0.020 0.019 0.019 0.018 0.018 0.018 0.017 0.017 0.017 0.852 0.873 0.889 20 0.026 0.025 0.025 0.024 0.024 0.023 0.023 0.023 0.023 0.023 0.821 0.845 25 0.033 0.032 0.031 0.030 0.030 0.029 0.029 0.029 0.028 0.028 0.028 0.797 30 0.039 0.038 0.037 0.026 0.036 0.035 0.035 0.034 0.034 0.034 0.034 0.034 35 0.046 0.044 0.043 0.042 0.042 0.041 0.040 0.040 0.040 0.039 0.039 0.039 40 0.052 0.051 0.050 0.049 0.048 0.047 0.046 0.046 0.045 0.045 0.045 0.045 50 0.065 0.063 0.062 0.061 0.059 0.058 0.058 0.057 0.056 0.056 0.056 0.056 60 0.078 0.076 0.074 0.073 0.071 0.070 0.069 0.068 0.068 0.067 0.067 0.067 70 0.091 0.089 0.087 0.085 0.083 0.082 0.080 0.079 0.079 0.078 0.078 0.078 80 0.104 0.101 0.099 0.097 0.095 0.093 0.092 0.091 0.090 0.089 0.089 0.089 90 0.117 0.114 0.111 0.109 0.107 0.105 0.103 0.102 0.101 0.100 0.100 0.100 100 0.130 0.126 0.123 0.121 0.118 0.116 0.115 0.113 0.112 0.111 0.111 0.110 110 0.143 0.139 0.136 0.133 0.130 0.128 0.126 0.124 0.123 0.122 0.121 0.121 120 0.156 0.152 0.148 0.145 0.142 0.139 0.137 0.135 0.134 0.133 0.132 0.132 130 0.169 0.164 0.160 0.156 0.153 0.151 0.148 0.146 0.145 0.144 0.143 0.143 140 0.182 0.177 0.172 0.168 0.165 0.162 0.160 0.157 0.156 0.154 0.154 0.153 150 0.194 0.189 0.184 0.180 0.177 0.174 0.171 0.169 0.167 0.165 0.164 0.164 160 0.207 0.202 0.197 0.192 0.188 0.185 0.182 0.180 0.178 0.176 0.175 0.174 180 0.233 0.226 0.221 0.216 0.211 0.208 0.204 0.202 0.199 0.197 0.196 0.195 200 0.258 0.251 0.245 0.239 0.235 0.230 0.227 0.223 0.221 0.219 0.217 0.216 250 0.322 0.313 0.305 0.298 0.292 0.287 0.282 0.278 0.274 0.271 0.269 0.267 300 0.386 0.375 0.365 0.357 0.349 0.342 0.336 0.331 0.327 0.323 0.320 0.318 400 0.512 0.497 0.484 0.472 0.462 0.453 0.444 0.437 0.431 0.426 0.421 0.417 500 0.636 0.618 0.601 0.586 0.573 0.561 0.551 0.541 0.533 0.526 0.520 0.514 Pressure in bar Temperature in C 70 80 90 100 110 120 140 160 180 200 250 300 1 0.994 0.995 0.995 0.996 0.996 0.996 0.997 0.997 0.998 0.998 0.999 0.999 5 0.969 0.972 0.975 0.978 0.980 0.982 0.985 0.987 0.989 0.991 0.994 0.995 10 0.937 0.944 0.949 0.954 0.959 0.963 0.969 0.974 0.978 0.981 0.987 0.991 15 0.902 0.913 0.923 0.930 0.937 0.943 0.953 0.961 0.967 0.972 0.981 0.986 20 0.865 0.881 0.894 0.905 0.915 0.923 0.937 0.947 0.956 0.962 0.974 0.982 25 0.825 0.847 0.865 0.879 0.892 0.903 0.920 0.933 0.944 0.953 0.968 0.977 30 0.780 0.810 0.833 0.852 0.868 0.881 0.903 0.919 0.932 0.943 0.961 0.973 35 0.040 0.769 0.799 0.823 0.843 0.859 0.885 0.905 0.921 0.933 0.955 0.968 40 0.045 0.723 0.762 0.792 0.816 0.836 0.867 0.891 0.909 0.923 0.948 0.964 50 0.056 0.057 0.676 0.724 0.759 0.787 0.830 0.861 0.884 0.903 0.935 0.955 60 0.067 0.068 0.070 0.638 0.693 0.733 0.790 0.830 0.859 0.882 0.921 0.946 70 0.078 0.079 0.081 0.083 0.612 0.671 0.747 0.797 0.833 0.861 0.908 0.937 80 0.089 0.090 0.092 0.095 0.100 0.597 0.701 0.763 0.807 0.840 0.895 0.928 90 0.100 0.101 0.103 0.105 0.110 0.491 0.650 0.728 0.780 0.818 0.881 0.919 100 0.111 0.112 0.113 0.116 0.121 0.131 0.592 0.690 0.752 0.796 0.867 0.910 110 0.122 0.122 0.124 0.127 0.132 0.140 0.522 0.650 0.723 0.773 0.854 0.901 120 0.132 0.133 0.135 0.137 0.142 0.150 0.428 0.607 0.693 0.751 0.840 0.892 130 0.143 0.144 0.145 0.148 0.152 0.160 0.266 0.560 0.662 0.728 0.827 0.884 140 0.153 0.154 0.156 0.158 0.163 0.170 0.219 0.510 0.631 0.704 0.814 0.875 D2.6 Properties of Ammonia D2.6. Table 5. (continued) Pressure in bar Temperature in C 70 80 90 100 110 120 140 160 180 200 250 300 150 0.164 0.165 0.166 0.169 0.173 0.180 0.216 0.455 0.598 0.681 0.800 0.866 160 0.174 0.175 0.176 0.179 0.183 0.189 0.220 0.399 0.565 0.658 0.787 0.858 180 0.195 0.196 0.197 0.199 0.203 0.209 0.233 0.325 0.500 0.611 0.761 0.842 200 0.216 0.216 0.217 0.220 0.223 0.229 0.249 0.306 0.443 0.566 0.737 0.826 250 0.267 0.266 0.267 0.269 0.272 0.276 0.292 0.323 0.387 0.484 0.681 0.791 300 0.317 0.316 0.316 0.317 0.320 0.323 0.335 0.358 0.398 0.460 0.640 0.762 400 0.414 0.412 0.411 0.411 0.412 0.414 0.422 0.436 0.459 0.491 0.610 0.727 500 0.510 0.506 0.504 0.502 0.502 0.502 0.506 0.515 0.530 0.551 0.630 0.725 20 30 40 50 60 D2.6. Table 6. Specific enthalpy h of ammonia in kJ/kg Pressure in bar Temperature in C 50 40 30 1 24.67 19.19 5 24.32 19.54 63.91 108.8 154.2 200.0 10 23.87 19.96 64.32 109.2 154.5 200.4 246.8 293.8 15 23.42 20.39 64.73 109.6 154.9 200.7 247.1 294.1 341.9 20 22.98 20.82 65.13 109.9 155.2 201.0 247.3 294.3 342.0 390.7 25 22.53 21.25 65.54 110.3 155.6 201.3 247.6 294.6 342.2 390.8 440.6 30 22.08 21.68 65.95 110.7 155.9 201.7 247.9 294.8 342.4 390.9 440.6 491.8 35 21.63 22.11 66.36 111.1 156.3 202.0 248.2 295.0 342.6 391.0 440.6 491.7 40 21.18 22.54 66.77 111.5 156.7 202.3 248.5 295.3 342.8 391.1 440.6 491.6 50 20.28 23.40 67.59 112.3 157.4 203.0 249.1 295.8 343.1 391.4 440.6 491.3 60 19.38 24.27 68.42 113.0 158.1 203.7 249.7 296.3 343.5 391.6 440.7 491.1 70 18.48 25.14 69.25 113.8 158.8 204.3 250.3 296.8 343.9 391.9 440.8 490.9 80 17.57 26.01 70.08 114.6 159.6 205.0 250.9 297.3 344.4 392.1 440.9 490.8 90 16.67 26.88 70.91 115.4 160.3 205.7 251.5 297.8 344.8 392.4 441.0 490.7 100 15.76 27.75 71.74 116.2 161.1 206.4 252.1 298.4 345.2 392.8 441.2 490.7 110 14.85 28.62 72.58 117.0 161.8 207.1 252.8 298.9 345.7 393.1 441.3 490.6 120 13.94 29.50 73.42 117.8 162.6 207.8 253.4 299.5 346.1 393.4 441.5 490.6 130 13.03 30.38 74.26 118.6 163.3 208.5 254.0 300.0 346.6 393.8 441.7 490.6 140 12.12 31.26 75.10 119.4 164.1 209.2 254.7 300.6 347.1 394.1 442.0 490.7 150 11.20 32.14 75.95 120.2 164.8 209.9 255.3 301.2 347.6 394.5 442.2 490.7 160 10.29 33.02 76.79 121.0 165.6 210.6 256.0 301.8 348.1 394.9 442.5 490.8 1426 20 10 1449 1471 0 1492 10 1514 1536 1558 1579 1601 1623 1482 1508 1533 1558 1582 1605 1499 1528 1556 1582 1494 1527 1557 1494 1529 1497 180 8.452 34.79 78.49 122.6 167.1 212.0 257.3 303.0 349.1 395.7 443.0 491.1 200 6.611 36.57 80.20 124.2 168.7 213.5 258.6 304.2 350.1 396.6 443.6 491.4 250 1.988 41.03 84.50 128.4 172.6 217.2 262.1 307.3 352.9 398.9 445.4 492.5 300 2.666 45.54 88.85 132.5 176.6 220.9 265.6 310.5 355.8 401.5 447.5 494.1 97.65 141.0 184.7 228.7 272.9 317.4 362.1 407.1 452.4 498.0 149.7 193.1 236.7 280.6 324.6 368.9 413.3 458.0 502.9 400 12.05 54.64 500 21.54 63.87 Pressure in bar 106.6 Temperature in C 70 80 90 100 110 120 140 160 180 200 250 300 1 1645 1667 1689 1711 1734 1756 1802 1848 1896 1944 2068 2197 5 1629 1652 1676 1699 1722 1746 1793 1841 1889 1938 2063 2193 10 1608 1634 1659 1683 1708 1733 1781 1830 1880 1930 2057 2188 15 1586 1614 1641 1667 1693 1719 1770 1820 1871 1921 2050 2183 20 1562 1593 1622 1650 1678 1705 1757 1810 1861 1913 2044 2178 263 264 D2 Properties of Selected Important Pure Substances D2.6. Table 6. (continued) Pressure in bar Temperature in C 70 80 90 100 110 120 140 160 180 200 250 300 25 1535 1570 1602 1632 1661 1690 1745 1799 1852 1905 2038 2173 30 1505 1544 1580 1613 1644 1674 1732 1788 1842 1897 2031 2168 35 544.9 1516 1557 1593 1627 1658 1719 1777 1833 1888 2025 2163 40 544.6 1484 1531 1571 1608 1642 1705 1765 1823 1879 2018 2158 50 543.9 599.2 1468 1521 1566 1606 1677 1741 1803 1862 2005 2148 60 543.3 598.1 656.7 1457 1516 1565 1646 1716 1781 1843 1992 2137 70 542.8 597.0 654.7 718.2 1453 1516 1612 1690 1759 1825 1978 2127 80 542.3 596.1 652.9 714.9 786.7 1456 1574 1661 1736 1805 1964 2116 1366 90 541.9 595.2 651.3 712.0 780.7 1532 1631 1713 1785 1951 2106 100 541.6 594.4 649.9 709.4 775.7 857.3 1481 1598 1687 1765 1936 2095 110 541.3 593.7 648.6 707.1 771.4 847.2 1418 1562 1661 1744 1922 2084 120 541.0 593.0 647.4 705.0 767.6 839.5 1326 1523 1633 1722 1907 2073 130 540.7 592.4 646.3 703.1 764.4 833.2 1127 1478 1604 1699 1893 2063 140 540.5 591.9 645.3 701.4 761.4 827.9 1028 1427 1572 1675 1878 2052 150 540.4 591.4 644.4 699.8 758.8 823.3 996.3 1367 1539 1651 1863 2041 160 540.3 591.0 643.5 698.4 756.4 819.3 977.7 1299 1504 1626 1847 2030 180 540.1 590.3 642.1 695.9 752.3 812.6 954.3 1181 1428 1574 1817 2008 200 540.1 589.8 640.9 693.7 748.9 807.2 939.0 1118 1350 1520 1785 1986 250 540.4 589.0 638.8 689.8 742.5 797.2 915.2 1052 1218 1392 1708 1931 300 541.2 589.0 637.7 687.3 738.2 790.5 900.9 1022 1157 1306 1635 1879 400 544.0 590.5 637.6 685.3 733.7 783.0 884.6 991.2 1104 1222 1523 1786 500 548.1 593.6 639.5 685.8 732.6 780.0 876.6 976.1 1079 1185 1457 1717 D2.6. Table 7. Specific entropy s of ammonia in kJ/(kg K) Pressure in bar Temperature in C 50 40 30 20 10 0 10 20 30 40 50 60 1 0.0944 0.2867 6.1607 6.2513 6.3369 6.4184 6.4965 6.5717 6.6443 6.7146 6.7829 6.8493 5 0.0934 0.2856 0.4720 0.6529 0.8286 0.9998 5.6241 5.7143 5.7983 5.8776 5.9530 6.0252 10 0.0922 0.2844 0.4706 0.6514 0.8271 0.9981 1.1650 1.3283 5.3721 5.4667 5.5536 5.6348 15 0.0910 0.2831 0.4693 0.6499 0.8255 0.9964 1.1631 1.3263 1.4866 5.1832 5.2862 5.3789 20 0.0898 0.2818 0.4679 0.6485 0.8239 0.9947 1.1613 1.3243 1.4844 1.6424 5.0641 5.1729 25 0.0887 0.2806 0.4666 0.6471 0.8224 0.9930 1.1595 1.3223 1.4822 1.6399 1.7964 4.9876 30 0.0875 0.2793 0.4652 0.6456 0.8209 0.9914 1.1577 1.3204 1.4800 1.6375 1.7936 1.9498 35 0.0863 0.2781 0.4639 0.6442 0.8193 0.9897 1.1559 1.3184 1.4779 1.6351 1.7909 1.9466 40 0.0851 0.2768 0.4626 0.6428 0.8178 0.9881 1.1541 1.3165 1.4757 1.6327 1.7882 1.9435 50 0.0828 0.2743 0.4599 0.6399 0.8147 0.9848 1.1506 1.3126 1.4715 1.6279 1.7828 1.9373 60 0.0805 0.2718 0.4572 0.6371 0.8117 0.9815 1.1470 1.3088 1.4673 1.6232 1.7775 1.9312 70 0.0782 0.2694 0.4546 0.6343 0.8087 0.9783 1.1436 1.3050 1.4631 1.6186 1.7724 1.9253 80 0.0759 0.2669 0.4520 0.6315 0.8057 0.9751 1.1401 1.3012 1.4590 1.6141 1.7673 1.9194 90 0.0736 0.2645 0.4494 0.6287 0.8027 0.9719 1.1367 1.2975 1.4549 1.6096 1.7622 1.9137 100 0.0713 0.2620 0.4468 0.6259 0.7998 0.9687 1.1333 1.2938 1.4509 1.6052 1.7573 1.9081 110 0.0690 0.2596 0.4442 0.6232 0.7968 0.9656 1.1299 1.2901 1.4469 1.6008 1.7524 1.9026 120 0.0668 0.2572 0.4416 0.6204 0.7939 0.9625 1.1265 1.2865 1.4430 1.5965 1.7476 1.8972 130 0.0645 0.2548 0.4391 0.6177 0.7910 0.9594 1.1232 1.2829 1.4391 1.5922 1.7429 1.8919 140 0.0623 0.2524 0.4365 0.6150 0.7881 0.9563 1.1199 1.2794 1.4352 1.5880 1.7382 1.8867 D2.6 Properties of Ammonia D2.6. Table 7. (continued) Temperature in C Pressure in bar 50 150 160 40 30 20 10 0 10 20 30 40 50 60 0.0600 0.2500 0.4340 0.6123 0.7853 0.9532 1.1166 1.2758 1.4314 1.5838 1.7336 1.8816 0.0578 0.2477 0.4315 0.6096 0.7824 0.9502 1.1134 1.2723 1.4276 1.5797 1.7291 1.8765 180 0.0534 0.2430 0.4265 0.6043 0.7768 0.9442 1.1069 1.2654 1.4202 1.5716 1.7202 1.8667 200 0.0490 0.2383 0.4215 0.5991 0.7712 0.9382 1.1006 1.2586 1.4128 1.5636 1.7115 1.8571 250 0.0382 0.2268 0.4094 0.5862 0.7575 0.9237 1.0851 1.2421 1.3951 1.5444 1.6907 1.8342 300 0.0277 0.2156 0.3975 0.5736 0.7442 0.9096 1.0701 1.2262 1.3780 1.5262 1.6709 1.8128 400 0.0071 0.1938 0.3745 0.5493 0.7186 0.8826 1.0416 1.1959 1.3459 1.4919 1.6342 1.7733 500 0.0126 0.1729 0.3524 0.5261 0.6941 0.8569 1.0146 1.1675 1.3159 1.4601 1.6005 1.7374 Pressure in bar Temperature in C 70 80 90 100 110 120 140 160 180 200 250 300 1 6.9141 6.9774 7.0392 7.0998 7.1592 7.2175 7.3311 7.4410 7.5478 7.6516 7.9006 8.1368 5 6.0948 6.1619 6.2271 6.2905 6.3523 6.4126 6.5295 6.6420 6.7507 6.8561 7.1079 7.3459 10 5.7113 5.7842 5.8540 5.9213 5.9863 6.0494 6.1707 6.2865 6.3979 6.5054 6.7607 7.0010 15 5.4642 5.5439 5.6192 5.6908 5.7595 5.8257 5.9518 6.0712 6.1852 6.2949 6.5539 6.7965 20 5.2695 5.3576 5.4393 5.5160 5.5888 5.6584 5.7897 5.9129 6.0298 6.1417 6.4046 6.6495 25 5.0996 5.1983 5.2879 5.3706 5.4480 5.5214 5.6583 5.7856 5.9056 6.0198 6.2866 6.5340 30 4.9405 5.0534 5.1526 5.2424 5.3253 5.4029 5.5462 5.6778 5.8010 5.9176 6.1885 6.4384 35 2.1040 4.9146 5.0265 5.1250 5.2142 5.2967 5.4469 5.5832 5.7098 5.8290 6.1041 6.3564 40 2.1002 4.7752 4.9044 5.0139 5.1107 5.1988 5.3567 5.4982 5.6283 5.7502 6.0296 6.2845 50 2.0928 2.2517 4.6531 4.7974 4.9156 5.0181 5.1947 5.3477 5.4857 5.6133 5.9019 6.1620 60 2.0856 2.2428 2.4065 4.5651 4.7216 4.8461 5.0475 5.2144 5.3615 5.4954 5.7937 6.0593 70 2.0786 2.2343 2.3954 2.5678 4.5072 4.6709 4.9076 5.0918 5.2492 5.3901 5.6989 5.9702 80 2.0718 2.2261 2.3849 2.5532 2.7430 4.4759 4.7694 4.9755 5.1451 5.2939 5.6138 5.8911 90 2.0652 2.2181 2.3749 2.5396 2.7212 4.2137 4.6272 4.8625 5.0465 5.2040 5.5360 5.8195 100 2.0587 2.2104 2.3654 2.5270 2.7021 2.9123 4.4735 4.7503 4.9516 5.1190 5.4639 5.7538 110 2.0524 2.2030 2.3562 2.5151 2.6851 2.8804 4.2946 4.6363 4.8590 5.0376 5.3964 5.6929 120 2.0462 2.1957 2.3474 2.5039 2.6696 2.8546 4.0508 4.5180 4.7674 4.9588 5.3326 5.6359 130 2.0401 2.1886 2.3389 2.4932 2.6553 2.8326 3.5567 4.3921 4.6759 4.8820 5.2718 5.5823 140 2.0342 2.1818 2.3308 2.4831 2.6419 2.8131 3.3083 4.2544 4.5835 4.8065 5.2136 5.5314 150 2.0284 2.1751 2.3228 2.4734 2.6294 2.7956 3.2238 4.1000 4.4896 4.7319 5.1576 5.4830 160 2.0227 2.1685 2.3151 2.4641 2.6176 2.7796 3.1719 3.9295 4.3935 4.6579 5.1035 5.4367 180 2.0116 2.1559 2.3004 2.4465 2.5958 2.7511 3.1023 3.6370 4.1950 4.5111 5.0001 5.3494 200 2.0009 2.1438 2.2865 2.4300 2.5759 2.7260 3.0529 3.4758 3.9996 4.3660 4.9020 5.2681 250 1.9757 2.1155 2.2544 2.3930 2.5323 2.6732 2.9659 3.2889 3.6630 4.0387 4.6764 5.0849 300 1.9522 2.0895 2.2254 2.3603 2.4948 2.6296 2.9033 3.1890 3.4951 3.8147 4.4783 4.9244 400 1.9094 2.0430 2.1743 2.3039 2.4319 2.5589 2.8110 3.0628 3.3167 3.5727 4.1779 4.6588 500 1.8710 2.0018 2.1299 2.2557 2.3795 2.5015 2.7411 2.9763 3.2082 3.4370 3.9842 4.4582 D2.6. Table 8. Specific isobaric heat capacity cp of ammonia in kJ/(kg K) Pressure in bar 1 Temperature in C 50 40 30 20 10 0 10 20 30 40 50 60 4.360 4.414 2.273 2.226 2.196 2.178 2.168 2.164 2.164 2.169 2.176 2.185 5 4.358 4.412 4.463 4.512 4.562 4.616 2.656 2.546 2.470 2.418 2.382 2.358 10 4.356 4.410 4.461 4.510 4.559 4.612 4.672 4.743 3.009 2.830 2.707 2.621 15 4.355 4.408 4.458 4.507 4.556 4.609 4.668 4.738 4.823 3.427 3.143 2.954 20 4.353 4.406 4.456 4.504 4.553 4.605 4.663 4.732 4.816 4.923 3.770 3.397 265 266 D2 Properties of Selected Important Pure Substances D2.6. Table 8. (continued) Pressure in bar Temperature in C 50 40 30 20 10 0 10 20 30 40 50 60 25 4.351 4.404 4.454 4.502 4.550 4.602 4.659 4.727 4.809 4.914 5.051 4.023 30 4.349 4.402 4.452 4.499 4.547 4.598 4.655 4.721 4.802 4.905 5.039 5.221 35 4.348 4.400 4.450 4.497 4.544 4.595 4.650 4.716 4.795 4.896 5.027 5.203 40 4.346 4.398 4.447 4.495 4.542 4.591 4.646 4.711 4.789 4.887 5.015 5.186 50 4.342 4.394 4.443 4.490 4.536 4.584 4.638 4.700 4.776 4.870 4.991 5.153 60 4.339 4.391 4.439 4.485 4.530 4.578 4.630 4.690 4.763 4.854 4.969 5.122 70 4.335 4.387 4.435 4.480 4.525 4.571 4.622 4.681 4.751 4.838 4.948 5.093 80 4.332 4.383 4.431 4.475 4.519 4.565 4.614 4.671 4.739 4.822 4.928 5.065 90 4.329 4.379 4.427 4.471 4.514 4.559 4.607 4.662 4.728 4.808 4.909 5.039 100 4.325 4.376 4.423 4.466 4.509 4.553 4.600 4.653 4.716 4.794 4.890 5.014 110 4.322 4.372 4.419 4.462 4.504 4.546 4.592 4.644 4.706 4.780 4.872 4.990 120 4.319 4.369 4.415 4.457 4.499 4.541 4.585 4.636 4.695 4.767 4.855 4.968 130 4.315 4.365 4.411 4.453 4.494 4.535 4.579 4.628 4.685 4.754 4.839 4.946 140 4.312 4.362 4.407 4.449 4.489 4.529 4.572 4.619 4.675 4.741 4.823 4.925 150 4.309 4.358 4.403 4.445 4.484 4.524 4.565 4.612 4.665 4.729 4.808 4.905 160 4.306 4.355 4.399 4.440 4.479 4.518 4.559 4.604 4.656 4.717 4.793 4.886 180 4.299 4.348 4.392 4.432 4.470 4.507 4.546 4.589 4.638 4.695 4.765 4.850 200 4.293 4.341 4.385 4.424 4.461 4.497 4.534 4.574 4.620 4.674 4.739 4.817 250 4.278 4.325 4.368 4.405 4.440 4.473 4.506 4.541 4.581 4.626 4.680 4.744 300 4.263 4.310 4.351 4.387 4.420 4.450 4.480 4.511 4.545 4.584 4.629 4.682 400 4.235 4.281 4.321 4.354 4.384 4.410 4.434 4.459 4.485 4.513 4.545 4.582 500 4.209 4.254 4.293 4.325 4.352 4.375 4.395 4.415 4.434 4.455 4.478 4.505 Pressure in bar Temperature in C 70 80 90 100 110 120 140 160 180 200 250 300 1 2.196 2.209 2.223 2.238 2.254 2.271 2.307 2.345 2.385 2.426 2.533 2.645 5 2.344 2.336 2.333 2.334 2.339 2.346 2.366 2.393 2.425 2.459 2.556 2.661 10 2.560 2.517 2.486 2.466 2.453 2.446 2.445 2.457 2.477 2.503 2.585 2.682 15 2.823 2.730 2.663 2.615 2.581 2.556 2.530 2.524 2.531 2.548 2.615 2.704 20 3.154 2.988 2.870 2.785 2.723 2.677 2.621 2.595 2.588 2.595 2.646 2.725 25 3.586 3.306 3.115 2.981 2.883 2.811 2.719 2.670 2.648 2.644 2.678 2.747 30 4.183 3.713 3.414 3.210 3.066 2.961 2.826 2.750 2.711 2.694 2.710 2.770 35 5.455 4.261 3.787 3.484 3.277 3.130 2.941 2.836 2.777 2.747 2.743 2.792 40 5.428 5.055 4.274 3.819 3.525 3.322 3.068 2.927 2.846 2.802 2.777 2.816 50 5.378 5.713 5.966 4.801 4.183 3.802 3.363 3.130 2.997 2.918 2.847 2.863 60 5.332 5.638 6.126 6.805 5.246 4.485 3.731 3.367 3.165 3.045 2.921 2.912 70 5.290 5.570 6.004 6.786 7.409 5.567 4.206 3.647 3.354 3.184 2.998 2.962 80 5.250 5.509 5.898 6.560 8.061 7.662 4.850 3.985 3.570 3.337 3.080 3.014 90 5.212 5.452 5.804 6.376 7.525 14.83 5.785 4.400 3.816 3.504 3.165 3.067 100 5.177 5.400 5.720 6.221 7.143 9.794 7.292 4.923 4.100 3.689 3.255 3.121 110 5.144 5.352 5.645 6.088 6.852 8.633 10.22 5.602 4.432 3.894 3.349 3.178 120 5.113 5.307 5.577 5.973 6.621 7.938 19.01 6.518 4.820 4.121 3.447 3.235 130 5.084 5.266 5.514 5.871 6.430 7.462 49.44 7.807 5.280 4.373 3.550 3.294 140 5.056 5.227 5.457 5.781 6.270 7.110 18.48 9.704 5.829 4.653 3.657 3.354 150 5.029 5.190 5.404 5.700 6.133 6.835 12.50 12.49 6.483 4.963 3.769 3.416 160 5.004 5.156 5.355 5.627 6.014 6.613 10.26 15.63 7.256 5.304 3.885 3.478 180 4.957 5.093 5.268 5.499 5.815 6.271 8.304 14.68 200 4.915 5.036 5.191 5.391 5.655 6.018 7.375 11.05 9.084 10.44 6.082 4.129 3.606 6.933 4.386 3.738 D2.6 Properties of Ammonia D2.6. Table 8. (continued) Pressure in bar Temperature in C 70 80 90 100 110 120 140 160 180 200 250 300 250 4.822 4.917 5.034 5.179 5.360 5.590 6.277 7.517 8.893 8.129 5.039 4.069 300 4.745 4.821 4.913 5.023 5.155 5.316 5.747 6.384 7.179 7.464 5.556 4.380 400 4.625 4.676 4.735 4.804 4.883 4.975 5.196 5.471 5.784 6.052 5.740 4.814 500 4.535 4.569 4.609 4.655 4.707 4.765 4.899 5.055 5.220 5.373 5.411 4.927 D2.6. Table 9. Specific isochoric heat capacity cv of ammonia in kJ/(kg K) Pressure in bar Temperature in C 50 40 30 20 10 0 10 20 30 40 50 60 1 2.884 2.866 1.690 1.664 1.649 1.641 1.639 1.642 1.647 1.656 1.666 1.678 5 2.885 2.867 2.850 2.833 2.816 2.800 1.904 1.848 1.811 1.787 1.773 1.767 10 2.886 2.868 2.851 2.834 2.817 2.801 2.786 2.771 2.071 1.987 1.930 1.893 15 2.887 2.869 2.852 2.835 2.818 2.802 2.786 2.772 2.759 2.244 2.122 2.041 20 2.888 2.870 2.852 2.835 2.819 2.802 2.787 2.772 2.759 2.748 2.364 2.217 25 2.889 2.871 2.853 2.836 2.819 2.803 2.787 2.773 2.759 2.748 2.741 2.436 30 2.890 2.872 2.854 2.837 2.820 2.804 2.788 2.773 2.760 2.748 2.741 2.737 35 2.891 2.873 2.855 2.838 2.821 2.804 2.788 2.773 2.760 2.749 2.740 2.736 40 2.892 2.874 2.856 2.838 2.821 2.805 2.789 2.774 2.760 2.749 2.740 2.736 50 2.894 2.875 2.858 2.840 2.823 2.806 2.790 2.775 2.761 2.749 2.740 2.734 60 2.896 2.877 2.859 2.842 2.824 2.807 2.791 2.776 2.762 2.749 2.739 2.733 70 2.898 2.879 2.861 2.843 2.826 2.809 2.792 2.777 2.762 2.750 2.739 2.732 80 2.900 2.881 2.863 2.845 2.827 2.810 2.794 2.778 2.763 2.750 2.739 2.732 90 2.902 2.883 2.864 2.846 2.829 2.811 2.795 2.779 2.764 2.751 2.739 2.731 100 2.904 2.884 2.866 2.848 2.830 2.813 2.796 2.780 2.765 2.751 2.740 2.731 110 2.906 2.886 2.867 2.849 2.831 2.814 2.797 2.781 2.766 2.752 2.740 2.731 120 2.908 2.888 2.869 2.851 2.833 2.815 2.798 2.782 2.767 2.753 2.740 2.730 130 2.910 2.890 2.871 2.852 2.834 2.817 2.800 2.783 2.768 2.753 2.741 2.730 140 2.912 2.891 2.872 2.854 2.836 2.818 2.801 2.784 2.769 2.754 2.741 2.730 150 2.913 2.893 2.874 2.855 2.837 2.819 2.802 2.785 2.770 2.755 2.742 2.731 160 2.915 2.895 2.875 2.857 2.838 2.821 2.803 2.787 2.771 2.756 2.742 2.731 180 2.919 2.898 2.878 2.860 2.841 2.823 2.806 2.789 2.773 2.757 2.744 2.732 200 2.922 2.901 2.881 2.862 2.844 2.826 2.808 2.791 2.775 2.759 2.745 2.733 250 2.931 2.909 2.889 2.869 2.851 2.833 2.815 2.797 2.780 2.764 2.749 2.736 300 2.939 2.916 2.896 2.876 2.857 2.839 2.821 2.803 2.786 2.770 2.754 2.740 400 2.953 2.930 2.909 2.889 2.870 2.852 2.833 2.816 2.798 2.781 2.765 2.750 500 2.966 2.942 2.921 2.901 2.882 2.864 2.845 2.828 2.810 2.793 2.777 2.762 Pressure in bar Temperature in C 70 80 90 100 110 120 140 160 180 200 250 300 1 1.692 1.706 1.722 1.738 1.756 1.774 1.811 1.850 1.891 1.933 2.041 2.154 5 1.766 1.769 1.775 1.784 1.795 1.808 1.837 1.871 1.908 1.946 2.050 2.160 10 1.868 1.854 1.846 1.844 1.847 1.852 1.871 1.898 1.929 1.964 2.061 2.168 15 1.985 1.948 1.924 1.909 1.901 1.899 1.906 1.925 1.951 1.981 2.073 2.175 20 2.120 2.054 2.009 1.979 1.959 1.948 1.943 1.953 1.972 1.999 2.084 2.183 25 2.278 2.174 2.103 2.054 2.021 2.000 1.980 1.981 1.995 2.017 2.095 2.191 30 2.469 2.312 2.208 2.136 2.087 2.054 2.019 2.010 2.017 2.035 2.106 2.198 35 2.740 2.475 2.326 2.227 2.159 2.112 2.059 2.040 2.040 2.053 2.117 2.206 267 268 D2 Properties of Selected Important Pure Substances D2.6. Table 9. (continued) Pressure in bar Temperature in C 70 80 90 100 110 120 140 160 180 200 250 300 40 2.738 2.674 2.463 2.327 2.236 2.173 2.101 2.070 2.063 2.071 2.129 2.214 50 2.735 2.745 2.823 2.571 2.414 2.310 2.190 2.133 2.111 2.108 2.151 2.229 60 2.732 2.740 2.763 2.913 2.638 2.472 2.287 2.199 2.159 2.146 2.174 2.244 70 2.730 2.736 2.754 2.796 2.946 2.670 2.395 2.270 2.210 2.184 2.196 2.259 80 2.728 2.732 2.746 2.780 2.862 2.931 2.518 2.345 2.262 2.223 2.219 2.274 90 2.727 2.729 2.740 2.767 2.829 3.345 2.658 2.425 2.315 2.263 2.242 2.289 100 2.726 2.726 2.734 2.756 2.805 2.927 2.825 2.510 2.371 2.303 2.264 2.304 110 2.725 2.723 2.729 2.747 2.786 2.873 3.031 2.603 2.428 2.343 2.286 2.319 120 2.724 2.721 2.725 2.739 2.770 2.836 3.305 2.702 2.487 2.384 2.308 2.333 130 2.723 2.720 2.722 2.733 2.758 2.808 3.456 2.809 2.547 2.425 2.330 2.348 140 2.722 2.718 2.710 2.727 2.747 2.787 3.111 2.919 2.607 2.465 2.352 2.362 150 2.722 2.717 2.716 2.723 2.738 2.770 2.975 3.023 2.668 2.506 2.373 2.376 160 2.722 2.716 2.714 2.718 2.731 2.757 2.902 3.092 2.726 2.545 2.394 2.389 180 2.722 2.714 2.711 2.712 2.719 2.736 2.820 3.024 2.824 2.619 2.434 2.416 200 2.722 2.714 2.708 2.707 2.711 2.721 2.774 2.898 2.870 2.681 2.471 2.442 250 2.724 2.714 2.706 2.700 2.698 2.700 2.717 2.756 2.794 2.745 2.550 2.499 300 2.727 2.716 2.706 2.698 2.693 2.690 2.693 2.707 2.724 2.720 2.604 2.548 400 2.736 2.723 2.712 2.702 2.693 2.687 2.678 2.675 2.675 2.675 2.647 2.615 500 2.747 2.734 2.721 2.710 2.700 2.692 2.679 2.670 2.666 2.664 2.658 2.652 60 D2.6. Table 10. Isobaric expansion coefficient b of ammonia in 103/K Pressure in bar Temperature in C 50 40 30 20 10 0 10 20 30 40 50 1 1.67 1.76 4.61 4.33 4.10 3.90 3.72 3.57 3.43 3.30 3.19 3.08 5 1.67 1.76 1.85 1.94 2.04 2.16 4.72 4.34 4.05 3.80 3.60 3.43 10 1.67 1.75 1.84 1.94 2.04 2.15 2.29 2.45 5.16 4.65 4.26 3.96 15 1.66 1.75 1.84 1.93 2.03 2.15 2.28 2.44 2.63 5.92 5.18 4.65 20 1.66 1.75 1.83 1.93 2.03 2.14 2.27 2.43 2.62 2.85 6.54 5.60 25 1.66 1.74 1.83 1.92 2.02 2.13 2.26 2.42 2.60 2.83 3.14 6.98 30 1.65 1.74 1.82 1.92 2.01 2.13 2.25 2.40 2.59 2.82 3.11 3.51 35 1.65 1.73 1.82 1.91 2.01 2.12 2.25 2.39 2.57 2.80 3.09 3.47 40 1.65 1.73 1.82 1.91 2.00 2.11 2.24 2.38 2.56 2.78 3.06 3.44 50 1.64 1.72 1.81 1.90 1.99 2.10 2.22 2.36 2.53 2.75 3.01 3.37 60 1.63 1.72 1.80 1.89 1.98 2.09 2.20 2.34 2.51 2.71 2.97 3.31 70 1.63 1.71 1.79 1.88 1.97 2.07 2.19 2.32 2.48 2.68 2.93 3.25 80 1.62 1.70 1.78 1.87 1.96 2.06 2.17 2.30 2.46 2.65 2.89 3.19 90 1.61 1.69 1.77 1.86 1.95 2.05 2.16 2.29 2.44 2.62 2.85 3.14 100 1.61 1.69 1.77 1.85 1.94 2.03 2.14 2.27 2.42 2.59 2.81 3.09 110 1.60 1.68 1.76 1.84 1.93 2.02 2.13 2.25 2.39 2.56 2.77 3.04 120 1.60 1.67 1.75 1.83 1.92 2.01 2.11 2.23 2.37 2.54 2.74 2.99 130 1.59 1.67 1.74 1.82 1.91 2.00 2.10 2.22 2.35 2.51 2.71 2.95 140 1.58 1.66 1.74 1.81 1.90 1.99 2.09 2.20 2.33 2.49 2.68 2.91 150 1.58 1.65 1.73 1.81 1.89 1.98 2.07 2.18 2.31 2.46 2.64 2.87 160 1.57 1.65 1.72 1.80 1.88 1.96 2.06 2.17 2.29 2.44 2.61 2.83 180 1.56 1.63 1.71 1.78 1.86 1.94 2.03 2.14 2.26 2.39 2.56 2.76 D2.6 Properties of Ammonia D2.6. Table 10. (continued) Temperature in C Pressure in bar 50 40 30 20 10 0 10 20 30 40 50 200 1.55 1.62 1.69 1.77 1.84 1.92 2.01 2.11 2.22 2.35 2.51 2.69 250 1.52 1.59 1.66 1.73 1.80 1.87 1.95 2.04 2.14 2.26 2.39 2.54 300 1.49 1.56 1.63 1.69 1.76 1.83 1.90 1.98 2.07 2.17 2.28 2.42 400 1.44 1.51 1.57 1.63 1.69 1.74 1.81 1.87 1.95 2.02 2.11 2.21 500 1.40 1.46 1.52 1.57 1.62 1.67 1.73 1.78 1.84 1.91 1.98 2.05 160 180 200 250 300 Pressure in bar 60 Temperature in C 70 80 90 100 110 120 1 2.98 2.89 2.80 2.72 2.65 2.58 2.45 2.33 2.22 2.13 1.92 1.75 5 3.27 3.14 3.02 2.91 2.81 2.72 2.56 2.42 2.30 2.19 1.96 1.78 10 3.71 3.50 3.32 3.17 3.04 2.92 2.71 2.54 2.39 2.26 2.01 1.81 15 4.25 3.94 3.68 3.47 3.29 3.13 2.87 2.66 2.49 2.34 2.06 1.84 20 4.95 4.48 4.11 3.82 3.58 3.37 3.05 2.80 2.60 2.43 2.11 1.87 25 5.89 5.16 4.63 4.23 3.91 3.65 3.24 2.94 2.71 2.52 2.16 1.91 30 7.22 6.05 5.27 4.71 4.29 3.96 3.46 3.10 2.83 2.61 2.21 1.94 35 4.02 7.28 6.10 5.31 4.74 4.31 3.69 3.27 2.95 2.70 2.27 1.97 40 3.97 9.13 7.20 6.05 5.28 4.72 3.95 3.45 3.08 2.80 2.32 2.01 50 3.86 4.60 8.30 6.75 5.77 4.57 3.86 3.38 3.02 2.44 2.08 60 3.77 4.44 5.53 9.22 7.31 5.36 4.35 3.71 3.26 2.57 2.16 70 3.68 4.29 5.26 7.06 14.5 80 3.59 4.16 5.03 6.54 10.1 11.2 13.1 9.85 15.0 140 6.42 4.94 4.09 3.53 2.70 2.23 7.88 5.66 4.53 3.82 2.84 2.31 90 3.52 4.04 4.83 6.12 8.83 33.4 10.1 6.56 5.03 4.15 2.99 2.40 100 3.45 3.94 4.65 5.78 7.93 14.4 13.7 7.72 5.63 4.52 3.14 2.48 110 3.38 3.84 4.48 5.48 7.25 11.6 20.9 9.26 6.33 4.92 3.31 2.57 120 3.31 3.74 4.34 5.23 6.72 9.86 11.4 7.16 5.38 3.48 2.65 130 3.25 3.66 4.21 5.01 6.29 8.73 14.4 8.15 5.89 3.66 2.74 140 3.20 3.58 4.09 4.81 5.93 7.90 37.6 18.9 9.33 6.45 3.84 2.84 150 3.14 3.50 3.97 4.64 5.62 7.26 21.6 25.5 10.8 7.08 4.04 2.93 160 3.09 3.43 3.87 4.48 5.36 6.75 15.8 32.9 12.4 7.77 4.24 3.02 180 3.00 3.30 3.69 4.21 4.92 5.97 10.9 28.6 16.3 9.32 4.65 3.21 200 2.91 3.18 3.53 3.98 4.58 5.41 8.64 18.3 18.8 11.0 5.08 3.40 250 2.72 2.94 3.21 3.54 3.95 4.47 6.09 9.17 13.2 12.5 6.10 3.86 300 2.57 2.75 2.96 3.21 3.52 3.88 4.90 6.45 8.60 9.91 6.72 4.24 400 2.32 2.45 2.60 2.76 2.95 3.17 3.69 4.37 5.18 6.00 6.13 4.54 500 2.14 2.23 2.34 2.46 2.59 2.73 3.06 3.45 3.89 4.33 4.87 4.25 43.5 125 D2.6. Table 11. Isentropic speed of sound ws in ammonia in m/s Pressure in bar Temperature in C 50 40 30 1 1890 1816 5 1891 1818 1746 1675 1603 1531 10 1892 1819 1748 1677 1605 1534 1460 1385 15 1894 1821 1749 1679 1608 1536 1463 1389 1312 20 1895 1822 1751 1681 1610 1539 1466 1392 1316 1236 25 1896 1824 1753 1683 1612 1541 1469 1395 1319 1240 1157 30 1898 1825 1755 1685 1615 1544 1472 1399 1323 1245 1162 1075 35 1899 1827 1757 1687 1617 1546 1475 1402 1327 1249 1167 1081 389.3 20 398.0 10 406.4 0 10 20 30 40 50 60 414.3 422.0 429.4 436.6 443.6 450.4 457.1 407.8 417.2 426.0 434.2 442.1 449.6 410.7 421.1 430.7 439.6 405.9 417.8 428.5 403.0 416.2 402.0 269 270 D2 Properties of Selected Important Pure Substances D2.6. Table 11. (continued) Pressure in bar Temperature in C 50 40 30 20 10 40 1900 1828 1758 1689 1619 50 1903 1831 1762 1693 1624 60 1905 1835 1765 1697 70 1908 1838 1769 1701 80 1911 1841 1772 0 10 20 30 40 50 60 1549 1478 1405 1330 1253 1172 1086 1554 1483 1412 1338 1261 1182 1098 1628 1559 1489 1418 1345 1269 1192 1109 1632 1564 1495 1424 1352 1277 1200 1119 1704 1637 1569 1500 1430 1359 1285 1209 1130 90 1913 1844 1776 1708 1641 1574 1505 1436 1365 1293 1218 1140 100 1916 1846 1779 1712 1645 1578 1511 1442 1372 1300 1226 1150 110 1918 1849 1782 1716 1650 1583 1516 1448 1378 1308 1235 1159 120 1921 1852 1786 1720 1654 1588 1521 1454 1385 1315 1243 1168 130 1923 1855 1789 1723 1658 1592 1526 1459 1391 1322 1251 1177 140 1926 1858 1792 1727 1662 1597 1531 1465 1397 1329 1259 1186 150 1928 1861 1796 1731 1666 1601 1536 1470 1404 1336 1266 1195 160 1931 1864 1799 1734 1670 1606 1541 1476 1410 1342 1274 1203 180 1935 1870 1805 1742 1678 1615 1551 1486 1421 1355 1288 1220 200 1940 1875 1812 1749 1686 1623 1560 1497 1433 1368 1302 1236 250 1952 1889 1827 1766 1705 1644 1583 1522 1461 1399 1336 1273 300 1964 1903 1842 1783 1724 1664 1605 1546 1487 1427 1367 1307 400 1987 1929 1872 1815 1759 1703 1647 1591 1535 1479 1423 1368 500 2010 1954 1900 1846 1792 1738 1685 1632 1579 1526 1474 1422 Pressure in bar Temperature in C 70 80 90 100 110 120 140 160 180 200 250 300 1 463.6 469.9 476.1 482.2 488.1 494.0 505.4 516.4 527.1 537.5 562.2 585.6 5 456.9 463.9 470.6 477.2 483.6 489.8 501.8 513.4 524.5 535.2 560.7 584.5 10 448.0 455.9 463.5 470.7 477.7 484.4 497.3 509.6 521.2 532.4 558.7 583.1 15 438.3 447.4 455.9 463.9 471.6 478.9 492.7 505.7 517.9 529.6 556.7 581.7 20 427.8 438.2 447.8 456.8 465.2 473.1 488.0 501.7 514.6 526.7 554.8 580.4 25 416.0 428.3 439.2 449.2 458.5 467.2 483.1 497.7 511.2 523.8 552.8 579.0 30 402.7 417.3 430.0 441.2 451.5 461.0 478.1 493.6 507.7 520.9 550.8 577.6 35 987.1 405.1 419.9 432.7 444.1 454.5 473.0 489.4 504.3 518.0 548.9 576.3 994.1 40 391.0 408.7 423.5 436.3 447.7 467.7 485.2 500.8 515.1 547.0 575.0 50 1008 909.5 381.7 402.5 419.1 433.2 456.7 476.4 493.7 509.2 543.1 572.4 60 1021 925.9 819.4 375.6 398.8 416.8 445.0 467.4 486.5 503.3 539.3 569.8 70 1034 941.4 839.5 721.7 373.2 397.9 432.4 458.0 479.1 497.4 535.6 567.4 80 1046 956.3 858.3 747.4 611.2 374.6 418.7 448.3 471.7 491.5 531.9 565.0 90 1058 970.5 876.0 770.8 646.6 340.9 403.7 438.3 464.2 485.6 528.4 562.7 100 1069 984.1 892.7 792.4 677.3 529.5 386.7 427.8 456.6 479.8 524.9 560.5 110 1080 997.2 908.6 812.4 704.6 574.3 366.6 416.9 449.1 474.0 521.6 558.5 120 1091 1010 923.7 831.2 729.2 611.0 340.3 405.7 441.6 468.4 518.4 556.5 130 1101 1022 938.2 848.9 751.8 642.5 319.8 394.1 434.2 463.1 515.4 554.7 140 1111 1034 952.1 865.6 772.8 670.5 395.5 382.5 427.1 458.0 512.7 553.1 150 1121 1045 965.4 881.5 792.3 695.7 456.6 372.3 420.5 453.2 510.1 551.5 160 1131 1056 978.2 896.7 810.7 718.7 503.2 367.9 414.6 448.9 507.7 550.2 180 1150 1077 1003 925.1 844.4 759.9 574.4 400.0 407.7 442.2 503.9 548.0 200 1167 1097 1025 951.3 875.0 796.2 629.5 462.6 414.3 439.6 501.3 546.5 250 1208 1143 1077 1010 941.4 872.4 733.1 597.2 494.9 464.7 502.2 546.5 300 1246 1184 1122 1060 935.0 811.3 693.4 592.0 529.2 516.6 552.6 400 1312 1257 1201 1146 1091 1037 930.9 831.8 743.1 670.2 584.0 584.9 500 1370 1319 1268 1218 1168 1119 935.3 854.9 785.3 672.2 638.8 997.6 1024 D2.6 Properties of Ammonia D2.6. Table 12. Thermal conductivity λ of ammonia in mW/(m K) Pressure in bar Temperature in ˚C −50 −40 −30 −20 −10 0 10 20 30 40 50 60 1 722.4 688.1 21.12 21.64 22.24 22.91 23.67 24.49 25.39 26.36 27.39 28.48 25.00 25.87 26.82 27.83 28.91 26.58 27.48 28.46 29.52 28.28 29.20 30.21 30.09 31.02 5 722.9 688.7 655.2 622.4 590.5 559.3 10 723.5 689.3 655.8 623.1 591.2 560.1 529.8 500.1 15 724.1 690.0 656.5 623.9 592.0 560.9 530.6 501.0 472.0 20 724.7 690.6 657.2 624.6 592.7 561.7 531.5 501.9 473.0 444.5 25 725.4 691.3 657.9 625.3 593.5 562.5 532.3 502.8 473.9 445.5 417.4 30 726.0 691.9 658.6 626.0 594.2 563.3 533.1 503.7 474.9 446.5 418.5 390.6 35 726.6 692.6 659.3 626.7 595.0 564.1 534.0 504.6 475.8 447.6 419.6 391.8 40 727.2 693.3 660.0 627.4 595.7 564.9 534.8 505.5 476.8 448.6 420.8 393.1 50 728.5 694.6 661.3 628.9 597.2 566.4 536.5 507.2 478.6 450.6 423.0 395.5 60 729.7 695.9 662.7 630.3 598.7 568.0 538.1 509.0 480.5 452.6 425.1 397.9 70 730.9 697.1 664.0 631.7 600.2 569.5 539.7 510.7 482.3 454.6 427.3 400.3 80 732.2 698.4 665.4 633.1 601.7 571.1 541.3 512.4 484.1 456.5 429.4 402.6 90 733.4 699.7 666.7 634.5 603.1 572.6 543.0 514.1 486.0 458.5 431.5 404.9 100 734.6 701.0 668.1 635.9 604.6 574.1 544.6 515.8 487.7 460.4 433.6 407.2 110 735.8 702.3 669.4 637.3 606.0 575.7 546.2 517.5 489.5 462.3 435.6 409.4 120 737.1 703.6 670.7 638.7 607.5 577.2 547.7 519.1 491.3 464.1 437.6 411.6 130 738.3 704.8 672.0 640.1 608.9 578.7 549.3 520.8 493.0 466.0 439.6 413.7 140 739.5 706.1 673.4 641.4 610.4 580.2 550.9 522.4 494.8 467.8 441.6 415.8 150 740.7 707.4 674.7 642.8 611.8 581.7 552.4 524.1 496.5 469.7 443.5 417.9 160 741.9 708.6 676.0 644.2 613.2 583.1 554.0 525.7 498.2 471.5 445.4 420.0 180 744.3 711.1 678.6 646.9 616.0 586.1 557.0 528.9 501.6 475.0 449.2 424.1 200 746.7 713.6 681.2 649.6 618.8 589.0 560.1 532.1 504.9 478.5 452.9 428.0 250 752.7 719.8 687.6 656.3 625.8 596.2 567.6 539.8 513.0 487.1 461.9 437.6 300 758.5 725.9 694.0 662.8 632.6 603.2 574.9 547.4 520.9 495.3 470.6 446.6 350 764.4 732.0 700.2 669.3 639.2 610.1 582.0 554.8 528.6 503.3 478.9 455.3 400 770.1 737.9 706.4 675.7 645.8 616.9 589.0 562.1 536.1 511.0 486.9 463.7 500 781.5 749.7 718.5 688.2 658.7 630.2 602.6 576.1 550.5 525.9 502.3 479.7 70 80 90 100 110 120 140 160 180 200 250 300 1 29.64 30.85 32.12 33.44 34.81 36.22 39.17 42.25 45.44 48.69 56.92 64.77 5 30.05 31.26 32.51 33.82 35.18 36.59 39.52 42.57 45.74 48.99 57.18 65.01 10 30.63 31.81 33.05 34.35 35.70 37.10 40.00 43.02 46.15 49.37 57.52 65.31 15 31.29 32.45 33.66 34.94 36.28 37.67 40.55 43.50 46.59 49.78 57.87 65.63 20 32.05 33.16 34.35 35.61 36.93 38.32 41.17 44.03 47.07 50.21 58.24 65.96 25 32.94 33.99 35.13 36.36 37.66 39.05 41.87 44.61 47.58 50.67 58.62 66.29 34.01 34.96 36.03 37.21 38.49 39.88 42.65 45.24 48.12 51.16 59.02 66.64 36.11 37.08 38.19 39.44 40.82 43.52 45.93 48.71 51.67 59.43 67.00 Pressure in bar 30 24.20 32.00 Temperature in ˚C 35 363.8 40 365.2 50 368.0 340.0 60 370.8 343.2 314.5 70 373.4 346.3 318.3 288.5 52.86 53.56 52.91 54.20 56.22 62.83 69.86 80 376.0 349.3 321.9 293.2 261.1 60.40 58.51 55.88 56.34 57.89 63.97 70.79 90 378.6 352.2 325.4 297.6 267.4 75.36 65.21 59.50 58.81 59.76 65.20 71.77 100 381.1 355.0 348.7 301.7 272.9 240.1 74.80 63.97 61.68 61.86 66.52 72.81 110 383.5 357.8 331.9 305.5 278.0 248.0 90.02 69.59 65.04 64.21 67.94 73.90 120 385.9 360.5 335.0 309.2 282.6 254.5 76.83 68.98 66.86 69.45 75.05 37.53 38.32 39.33 40.51 41.88 44.50 46.68 49.34 52.22 59.86 67.38 41.72 42.26 43.20 44.48 46.83 48.40 50.74 53.40 60.78 68.16 46.74 46.96 47.97 49.78 50.45 52.35 54.74 61.76 68.98 52.79 120.9 271 272 D2 Properties of Selected Important Pure Substances D2.6. Table 12. (continued) Pressure in bar Temperature in ˚C 70 80 90 100 110 120 140 160 180 200 250 300 130 388.3 363.1 338.0 312.7 286.9 260.3 215.1 86.46 73.65 69.84 71.08 76.26 140 390.6 365.7 340.9 316.1 291.0 265.5 209.5 99.84 79.21 73.19 72.81 77.53 150 392.9 368.2 343.7 319.3 294.9 270.3 216.8 117.8 85.89 76.98 74.67 78.86 160 395.1 370.6 346.5 322.5 298.5 274.7 224.0 141.6 93.96 81.26 76.64 80.25 180 399.5 375.4 351.8 328.4 305.4 282.8 236.2 177.9 113.7 91.55 80.98 83.22 200 403.7 380.0 356.8 334.1 311.8 290.1 246.3 193.2 137.4 103.9 250 413.9 391.0 368.7 347.0 326.1 306.1 266.6 221.9 178.7 139.8 100.5 300 423.5 401.2 379.6 358.7 338.7 319.8 282.9 242.7 204.2 169.2 117.8 106.3 350 432.7 410.8 389.8 369.6 350.2 332.0 296.8 259.4 224.2 191.7 136.3 118.0 400 441.4 419.9 399.4 379.7 360.9 343.2 309.3 273.7 240.7 210.1 154.2 130.4 500 457.9 437.1 417.2 398.3 380.3 363.4 331.1 298.0 267.6 239.7 185.3 155.3 85.86 86.45 95.62 D2.6. Table 13. Dynamic viscosity of ammonia in 106 Pas Pressure in bar Temperature in C 50 40 30 1 328.9 281.3 5 329.5 281.8 244.5 214.7 190.4 170.1 10 330.3 282.4 245.1 215.3 190.9 170.6 153.4 138.4 15 331.0 283.1 245.7 215.8 191.4 171.1 153.8 138.8 125.7 20 331.7 283.8 246.3 216.3 191.9 171.5 154.2 139.3 126.1 114.4 25 332.5 284.4 246.9 216.9 192.4 172.0 154.7 139.7 126.5 114.8 104.2 11.06 30 333.2 285.1 247.4 217.4 192.9 172.4 155.1 140.1 126.9 115.2 104.6 94.79 35 333.9 285.7 248.0 217.9 193.4 172.9 155.5 140.5 127.3 115.6 104.9 95.20 40 334.7 286.4 248.6 218.5 193.8 173.3 155.9 140.9 127.7 116.0 105.3 95.61 50 336.2 287.7 249.8 219.5 194.8 174.2 156.8 141.7 128.5 116.7 106.1 96.40 60 337.6 289.0 251.0 220.6 195.8 175.1 157.6 142.5 129.3 117.5 106.9 97.18 70 339.1 290.3 252.1 221.6 196.8 176.0 158.5 143.3 130.0 118.2 107.6 97.95 80 340.5 291.6 253.3 222.7 197.7 176.9 159.3 144.1 130.8 119.0 108.4 98.71 90 342.0 292.9 254.4 223.7 198.7 177.8 160.1 144.9 131.6 119.7 109.1 99.46 100 343.5 294.2 255.6 224.8 199.6 178.7 161.0 145.7 132.3 120.5 109.8 100.2 110 344.9 295.4 256.8 225.8 200.6 179.6 161.8 146.5 133.1 121.2 110.6 100.9 120 346.4 296.7 257.9 226.9 201.5 180.5 162.6 147.3 133.8 121.9 111.3 101.6 130 347.8 298.0 259.0 227.9 202.5 181.3 163.4 148.0 134.6 122.7 112.0 102.3 140 349.3 299.3 260.2 228.9 203.4 182.2 164.3 148.8 135.3 123.4 112.7 103.0 150 350.7 300.6 261.3 230.0 204.4 183.1 165.1 149.6 136.0 124.1 113.4 103.7 160 352.2 301.9 262.5 231.0 205.3 184.0 165.9 150.3 136.8 124.8 114.1 104.4 180 355.0 304.4 264.7 233.0 207.2 185.7 167.5 151.8 138.2 126.2 115.4 105.8 200 357.9 306.9 267.0 235.1 209.0 187.4 169.1 153.3 139.6 127.5 116.8 107.1 250 365.0 313.2 272.6 240.1 213.6 191.6 173.0 157.0 143.1 130.9 120.0 110.2 300 372.1 319.5 278.2 245.1 218.2 195.8 176.8 160.6 146.5 134.1 123.1 113.3 400 386.1 331.8 289.1 255.0 227.1 203.9 184.4 167.6 153.1 140.4 129.1 119.1 500 400.0 344.0 299.9 264.6 235.8 211.8 191.7 174.4 159.4 146.4 134.8 124.5 8.165 20 8.501 10 8.844 0 9.194 10 20 30 40 50 60 9.549 9.407 9.911 10.28 10.65 11.02 11.40 9.789 10.17 10.56 10.94 11.33 10.04 10.45 10.85 11.25 10.34 10.76 11.18 10.68 11.12 D2.6 Properties of Ammonia D2.6. Table 13. (continued) Pressure in bar 1 Temperature in C 70 80 90 100 110 120 140 160 180 200 250 300 11.78 12.16 12.54 12.93 13.32 13.70 14.48 15.26 16.04 16.82 18.76 20.67 5 11.72 12.11 12.50 12.89 13.29 13.68 14.47 15.25 16.04 16.82 18.76 20.68 10 11.65 12.06 12.46 12.86 13.26 13.65 14.45 15.25 16.04 16.83 18.78 20.70 15 11.60 12.01 12.42 12.82 13.23 13.63 14.44 15.24 16.04 16.83 18.79 20.72 20 11.54 11.97 12.38 12.80 13.21 13.62 14.44 15.24 16.05 16.84 18.81 20.74 25 11.50 11.94 12.36 12.78 13.20 13.62 14.44 15.25 16.06 16.86 18.83 20.76 30 11.47 11.92 12.35 12.78 13.20 13.62 14.45 15.27 16.08 16.88 18.86 20.79 35 86.09 11.92 12.36 12.79 13.21 13.63 14.47 15.29 16.20 16.90 18.88 20.82 40 86.52 11.94 12.38 12.81 13.24 13.66 14.49 15.31 16.13 16.93 18.91 20.85 50 87.37 78.78 12.52 12.93 13.34 13.75 14.58 15.39 16.20 17.01 18.98 20.92 60 88.19 79.68 71.40 13.20 13.55 13.93 14.71 15.51 16.31 17.10 19.07 21.00 70 88.99 80.56 72.41 64.18 13.96 14.23 14.92 15.67 16.45 17.23 19.17 21.08 80 89.78 81.41 73.37 65.37 56.76 14.76 15.22 15.89 16.62 17.38 19.28 21.18 90 90.56 82.23 74.29 66.48 58.32 15.96 15.66 16.18 16.85 17.56 19.41 21.29 100 91.31 83.04 75.18 67.52 59.70 50.67 16.33 16.57 17.12 17.78 19.56 21.40 110 92.06 83.82 76.04 68.51 60.95 52.68 17.45 17.08 17.46 18.04 19.73 21.53 120 92.79 84.59 76.87 69.45 62.10 54.34 19.74 17.76 17.88 18.34 19.92 21.67 130 93.51 85.34 77.67 70.35 63.17 55.78 29.22 18.69 18.39 18.70 20.13 21.82 140 94.22 86.07 78.45 71.21 64.18 57.07 38.28 20.01 19.02 19.12 20.36 21.98 150 94.92 86.79 79.22 72.05 65.13 58.25 42.13 21.96 19.80 19.60 20.61 22.16 160 95.60 87.50 79.96 72.85 66.04 59.34 44.67 24.83 20.75 20.17 20.89 22.34 180 96.95 88.88 81.40 74.40 67.75 61.32 48.27 32.15 23.34 21.56 21.52 22.75 200 98.27 90.21 82.78 75.85 69.33 63.10 50.97 37.77 26.90 23.36 22.26 23.21 250 101.4 93.39 86.02 79.22 72.89 66.97 56.00 45.73 36.10 29.40 24.60 24.58 300 104.4 96.37 89.03 82.28 76.06 70.29 59.87 50.61 42.32 35.47 27.54 26.24 400 110.1 101.9 94.53 87.79 81.63 75.98 65.99 57.46 50.16 44.00 33.91 30.14 500 115.3 107.0 99.54 92.73 86.54 80.88 70.97 62.64 55.63 49.75 39.37 34.18 20 30 40 50 60 D2.6. Table 14. Kinematic viscosity n of ammonia in 107 m2/s Pressure in bar Temperature in C 50 40 30 20 1 4.68 4.08 94.5 5 4.69 4.08 3.61 3.23 2.92 2.66 10 4.70 4.09 3.61 3.23 2.93 2.67 2.45 2.27 15 4.71 4.10 3.62 3.24 2.93 2.68 2.46 2.27 2.11 8.98 9.88 20 4.72 4.11 3.63 3.25 2.94 2.68 2.46 2.28 2.12 1.97 6.91 7.64 25 4.73 4.11 3.64 3.25 2.94 2.69 2.47 2.28 2.12 1.98 1.85 5.73 30 4.74 4.12 3.64 3.26 2.95 2.69 2.48 2.29 2.13 1.98 1.85 1.74 35 4.75 4.13 3.65 3.27 2.96 2.70 2.48 2.29 2.13 1.99 1.86 1.74 40 4.76 4.14 3.66 3.27 2.96 2.70 2.49 2.30 2.14 1.99 1.86 1.75 50 4.77 4.15 3.67 3.29 2.97 2.72 2.50 2.31 2.15 2.00 1.87 1.76 60 4.79 4.17 3.69 3.30 2.99 2.73 2.51 2.32 2.15 2.01 1.88 1.76 103 10 112 0 121 10 130 24.2 140 26.4 151 161 173 184 28.6 30.9 33.2 35.6 13.3 14.5 15.7 17.0 10.8 273 274 D2 Properties of Selected Important Pure Substances D2.6. Table 14. (continued) Pressure in bar Temperature in C 50 40 30 20 70 4.81 4.19 3.70 3.31 80 4.83 4.20 3.71 3.33 10 0 10 20 30 40 50 60 3.00 2.74 2.52 2.33 2.16 2.02 1.89 1.77 3.01 2.75 2.53 2.34 2.17 2.03 1.90 1.78 90 4.85 4.22 3.73 3.34 3.02 2.76 2.54 2.35 2.18 2.04 1.91 1.79 100 4.86 4.23 3.74 3.35 3.03 2.77 2.55 2.36 2.19 2.05 1.92 1.80 110 4.88 4.25 3.76 3.37 3.05 2.78 2.56 2.37 2.20 2.06 1.93 1.81 120 4.90 4.27 3.77 3.38 3.06 2.79 2.57 2.38 2.21 2.06 1.93 1.82 130 4.92 4.28 3.79 3.39 3.07 2.80 2.58 2.39 2.22 2.07 1.94 1.83 140 4.93 4.30 3.80 3.40 3.08 2.81 2.59 2.40 2.23 2.08 1.95 1.83 150 4.95 4.31 3.81 3.42 3.09 2.82 2.60 2.40 2.24 2.09 1.96 1.84 160 4.97 4.33 3.83 3.43 3.10 2.84 2.61 2.41 2.25 2.10 1.97 1.85 180 5.00 4.36 3.86 3.45 3.13 2.86 2.63 2.43 2.26 2.11 1.98 1.87 200 5.04 4.39 3.88 3.48 3.15 2.88 2.65 2.45 2.28 2.13 2.00 1.88 250 5.13 4.47 3.95 3.54 3.21 2.93 2.70 2.50 2.32 2.17 2.04 1.92 300 5.21 4.54 4.02 3.60 3.26 2.98 2.74 2.54 2.36 2.21 2.07 1.95 400 5.38 4.69 4.15 3.72 3.37 3.08 2.83 2.62 2.44 2.28 2.14 2.02 500 5.55 4.84 4.28 3.84 3.47 3.17 2.92 2.70 2.52 2.35 2.21 2.08 160 180 200 Pressure in bar 1 Temperature in C 70 196 80 209 90 221 100 235 110 248 120 262 140 291 322 354 388 250 478 300 578 5 38.1 40.6 43.2 45.9 48.7 51.5 57.5 63.7 70.2 77.0 95.2 115 10 18.3 19.6 21.0 22.4 23.8 25.2 28.2 31.4 34.7 38.1 47.3 57.4 15 11.7 12.6 13.5 14.5 15.5 16.5 18.5 20.6 22.9 25.2 31.4 38.1 10.6 11.3 12.1 13.6 15.3 17.0 18.7 23.4 28.5 10.7 12.0 13.4 14.8 18.6 22.7 11.1 12.3 15.4 18.9 10.4 13.2 16.1 11.4 14.1 20 8.36 9.09 9.82 25 6.36 6.97 7.58 8.19 8.81 9.44 30 5.00 5.54 6.08 6.61 7.14 7.68 8.77 9.89 35 1.63 4.51 5.00 5.48 5.95 6.42 7.38 8.36 9.37 40 1.64 3.72 4.18 4.62 5.05 5.48 6.34 7.21 8.11 9.02 50 1.65 1.55 3.00 3.41 3.79 4.16 4.88 5.60 6.34 7.09 9.06 60 1.66 1.56 1.47 2.56 2.93 3.27 3.91 4.54 5.17 5.81 7.48 9.26 70 1.67 1.57 1.48 1.39 2.28 2.62 3.21 3.78 4.33 4.90 6.35 7.89 80 1.68 1.58 1.49 1.41 1.32 2.11 2.69 3.21 3.71 4.21 5.51 6.87 11.2 90 1.69 1.59 1.50 1.42 1.34 1.67 2.28 2.77 3.23 3.69 4.85 6.08 100 1.70 1.60 1.51 1.43 1.35 1.27 1.95 2.42 2.85 3.27 4.33 5.45 110 1.70 1.61 1.52 1.44 1.36 1.29 1.67 2.13 2.54 29.93 3.91 4.94 120 1.71 1.62 1.53 1.45 1.37 1.30 1.42 1.90 2.28 2.65 3.56 4.51 130 1.72 1.63 1.54 1.46 1.39 1.32 1.21 1.70 2.07 2.42 3.27 4.15 140 1.73 1.63 1.55 1.47 1.40 1.33 1.21 1.54 1.90 2.22 3.02 3.84 150 1.74 1.64 1.56 1.48 1.40 1.34 1.22 1.41 1.75 2.06 2.81 3.58 160 1.75 1.65 1.56 1.49 1.41 1.35 1.24 1.31 1.62 1.91 2.62 3.35 180 1.76 1.67 1.58 1.50 1.43 1.37 1.26 1.23 1.43 1.69 2.32 2.98 200 1.78 1.68 1.59 1.52 1.45 1.38 1.28 1.22 1.32 1.53 2.09 2.68 250 1.81 1.72 1.63 1.55 1.48 1.42 1.32 1.25 1.24 1.32 1.71 2.18 300 1.85 1.75 1.66 1.59 1.52 1.45 1.35 1.28 1.24 1.26 1.50 1.86 400 1.91 1.81 1.72 1.64 1.57 1.51 1.40 1.32 1.27 1.25 1.32 1.53 500 1.97 1.87 1.78 1.70 1.62 1.56 1.45 1.37 1.30 1.27 1.27 1.39 D2.6 Properties of Ammonia D2.6. Table 15. Thermal diffusivity a of ammonia in 107 m2/s Pressure in bar Temperature in ˚C −50 −40 1 2.36 2.26 −30 108 −20 118 −10 128 0 138 10 149 160 172 40 184 50 197 60 211 5 2.36 2.26 2.17 2.07 1.98 1.90 2.36 2.26 2.17 2.08 1.99 1.90 1.81 1.73 15 2.37 2.27 2.17 2.08 1.99 1.90 1.82 1.73 1.64 7.17 8.53 9.86 20 2.37 2.27 2.17 2.08 1.99 1.91 1.82 1.74 1.65 1.56 5.17 6.28 25 2.37 2.27 2.18 2.08 2.00 1.91 1.82 1.74 1.65 1.56 1.47 4.12 30 2.37 2.27 2.18 2.09 2.00 1.91 1.83 1.74 1.66 1.57 1.47 1.37 35 2.38 2.28 2.18 2.09 2.00 1.92 1.83 1.75 1.66 1.57 1.48 1.38 40 2.38 2.28 2.18 2.09 2.00 1.92 1.83 1.75 1.66 1.58 1.48 1.38 50 2.38 2.28 2.19 2.10 2.01 1.93 1.84 1.76 1.67 1.59 1.49 1.40 60 2.39 2.29 2.19 2.10 2.02 1.93 1.85 1.77 1.68 1.60 1.51 1.41 70 2.39 2.29 2.20 2.11 2.02 1.94 1.85 1.77 1.69 1.60 1.52 1.42 80 2.40 2.30 2.20 2.11 2.03 1.94 1.86 1.78 1.70 1.61 1.53 1.44 90 2.40 2.30 2.21 2.12 2.03 1.95 1.87 1.79 1.71 1.62 1.54 1.45 100 2.41 2.31 2.21 2.12 2.04 1.96 1.87 1.79 1.71 1.63 1.55 1.46 110 2.41 2.31 2.22 2.13 2.04 1.96 1.88 1.80 1.72 1.64 1.56 1.47 120 2.41 2.32 2.22 2.13 2.05 1.97 1.89 1.81 1.73 1.65 1.57 1.48 130 2.42 2.32 2.23 2.14 2.05 1.97 1.89 1.81 1.74 1.66 1.58 1.49 140 2.42 2.32 2.23 2.14 2.06 1.98 1.90 1.82 1.74 1.66 1.58 1.50 150 2.43 2.33 2.24 2.15 2.06 1.98 1.90 1.83 1.75 1.67 1.59 1.51 160 2.43 2.33 2.24 2.15 2.07 1.99 1.91 1.83 1.76 1.68 1.60 1.52 180 2.44 2.34 2.25 2.16 2.08 2.00 1.92 1.85 1.77 1.70 1.62 1.54 200 2.45 2.35 2.26 2.17 2.09 2.01 1.93 1.86 1.78 1.71 1.64 1.56 250 2.47 2.37 2.28 2.20 2.12 2.04 1.96 1.89 1.82 1.75 1.68 1.61 300 2.49 2.40 2.30 2.22 2.14 2.06 1.99 1.92 1.85 1.78 1.71 1.65 350 2.51 2.42 2.33 2.24 2.16 2.09 2.02 1.95 1.88 1.81 1.75 1.68 400 2.53 2.44 2.35 2.26 2.19 2.11 2.04 1.97 1.91 1.84 1.78 1.72 500 2.57 2.48 2.39 2.31 2.23 2.16 2.09 2.02 1.96 1.90 1.84 1.78 70 80 1 26.5 30 10 Pressure in bar 23.5 20 29.4 32.4 35.4 38.5 11.7 13.5 15.2 17.0 Temperature in ˚C 225 239 90 255 100 271 110 288 120 305 140 341 160 380 180 421 200 463 250 300 573 685 114 136 5 41.6 44.9 48.2 51.6 55.1 58.8 66.3 74.3 82.6 91.2 10 18.8 20.6 22.4 24.2 26.1 28.0 32.0 36.1 40.3 44.7 56.1 67.5 15 11.2 12.5 13.8 15.1 16.4 17.8 20.5 23.3 26.2 29.2 36.9 44.7 10.5 11.6 12.7 14.8 17.0 19.2 21.5 27.4 33.2 11.4 13.2 15.0 16.9 21.6 26.4 10.7 12.2 13.8 17.8 21.8 10.2 11.6 15.1 18.6 20 7.36 8.43 9.49 25 5.08 6.00 6.91 7.82 8.72 9.63 30 3.54 4.38 5.20 6.00 6.79 7.59 9.16 35 1.27 3.21 3.96 4.70 5.42 6.15 7.55 8.86 40 1.27 2.31 3.03 3.72 4.39 5.06 6.34 7.51 8.71 9.93 13.0 16.1 50 1.29 1.17 1.67 2.32 2.93 3.54 4.66 5.63 6.62 7.63 10.2 12.7 60 1.31 1.19 1.06 1.33 1.93 2.51 3.54 4.38 5.24 6.10 8.29 70 1.32 1.21 1.08 0.92 1.17 1.75 2.74 3.49 4.26 5.02 6.94 8.83 80 1.34 1.23 1.11 0.96 0.76 1.13 2.13 2.83 3.52 4.21 5.93 7.62 90 1.35 1.25 1.13 1.00 0.82 0.53 1.64 2.31 2.95 3.58 5.15 6.69 100 1.37 1.27 1.16 1.03 0.86 0.62 1.22 1.90 2.50 3.08 4.53 5.94 10.5 275 276 D2 Properties of Selected Important Pure Substances D2.6. Table 15. (continued) Temperature in ˚C Pressure in bar 70 80 90 110 1.38 1.28 1.18 1.05 0.91 0.70 0.84 1.55 2.13 2.68 4.02 5.33 120 1.39 1.30 1.20 1.08 0.94 0.77 0.46 1.26 1.83 2.34 3.60 4.83 130 1.41 1.31 1.21 1.10 0.98 0.82 0.18 1.01 1.57 2.06 3.25 4.40 140 1.42 1.33 1.23 1.13 1.01 0.87 0.36 0.79 1.35 1.83 2.96 4.04 150 1.43 1.34 1.25 1.15 1.04 0.91 0.50 0.60 1.17 1.63 2.70 3.73 160 1.44 1.36 1.27 1.17 1.06 0.94 0.61 0.48 1.01 1.45 2.48 3.46 180 1.46 1.38 1.30 1.21 1.11 1.01 0.74 0.46 0.77 1.18 2.12 3.02 200 1.48 1.41 1.32 1.24 1.15 1.06 0.84 0.57 0.65 0.98 1.84 2.67 250 1.53 1.46 1.39 1.31 1.24 1.16 1.00 0.81 0.69 0.77 1.39 2.08 300 1.58 1.51 1.44 1.38 1.31 1.24 1.11 0.96 0.83 0.80 1.15 1.72 350 1.62 1.56 1.49 1.43 1.37 1.31 1.20 1.07 0.96 0.89 1.06 1.51 400 1.66 1.60 1.54 1.48 1.42 1.37 1.27 1.15 1.06 0.99 1.05 1.38 500 1.73 1.67 1.62 1.57 1.52 1.47 1.38 1.28 1.20 1.14 1.10 1.28 100 110 120 140 160 180 200 250 300 D2.6. Table 16. Prandtl number Pr of ammonia Pressure in bar Temperature in ˚C −50 −40 −30 −20 −10 0 10 20 30 40 50 60 1 1.99 1.80 0.879 0.875 0.873 0.874 0.875 0.875 0.876 0.876 0.875 0.874 5 1.99 1.81 1.67 1.56 1.47 1.40 1.03 1.00 0.971 0.952 0.937 0.924 10 1.99 1.81 1.67 1.56 1.47 1.40 1.35 1.31 1.14 1.08 1.03 1.00 15 1.99 1.81 1.67 1.56 1.47 1.41 1.35 1.31 1.28 1.25 1.16 1.09 20 1.99 1.81 1.67 1.56 1.47 1.41 1.35 1.31 1.28 1.27 1.34 1.22 25 1.99 1.81 1.67 1.56 1.48 1.41 1.35 1.31 1.28 1.27 1.26 1.39 30 2.00 1.81 1.67 1.56 1.48 1.41 1.35 1.31 1.28 1.27 1.26 1.27 35 2.00 1.82 1.67 1.56 1.48 1.41 1.35 1.31 1.28 1.26 1.26 1.26 40 2.00 1.82 1.68 1.57 1.48 1.41 1.35 1.31 1.28 1.26 1.26 1.26 50 2.00 1.82 1.68 1.57 1.48 1.41 1.36 1.31 1.28 1.26 1.25 1.26 60 2.01 1.82 1.68 1.57 1.48 1.41 1.36 1.31 1.28 1.26 1.25 1.25 70 2.01 1.83 1.68 1.57 1.48 1.41 1.36 1.31 1.28 1.26 1.25 1.25 80 2.02 1.83 1.69 1.57 1.49 1.41 1.36 1.31 1.28 1.26 1.24 1.24 90 2.02 1.83 1.69 1.58 1.49 1.42 1.36 1.31 1.28 1.26 1.24 1.24 100 2.02 1.84 1.69 1.58 1.49 1.42 1.36 1.31 1.28 1.25 1.24 1.23 110 2.03 1.84 1.69 1.58 1.49 1.42 1.36 1.31 1.28 1.25 1.24 1.23 120 2.03 1.84 1.70 1.58 1.49 1.42 1.36 1.32 1.28 1.25 1.23 1.23 130 2.03 1.85 1.70 1.59 1.49 1.42 1.36 1.32 1.28 1.25 1.23 1.22 140 2.04 1.85 1.70 1.59 1.50 1.42 1.36 1.32 1.28 1.25 1.23 1.22 150 2.04 1.85 1.71 1.59 1.50 1.42 1.36 1.32 1.28 1.25 1.23 1.22 160 2.04 1.86 1.71 1.59 1.50 1.43 1.37 1.32 1.28 1.25 1.23 1.21 180 2.05 1.86 1.71 1.60 1.50 1.43 1.37 1.32 1.28 1.25 1.22 1.21 200 2.06 1.87 1.72 1.60 1.51 1.43 1.37 1.32 1.28 1.25 1.22 1.21 250 2.08 1.88 1.73 1.61 1.52 1.44 1.37 1.32 1.28 1.24 1.22 1.20 300 2.09 1.90 1.74 1.62 1.52 1.44 1.38 1.32 1.28 1.24 1.21 1.19 350 2.11 1.91 1.76 1.63 1.53 1.45 1.38 1.33 1.28 1.24 1.21 1.18 400 2.12 1.93 1.77 1.64 1.54 1.46 1.39 1.33 1.28 1.24 1.21 1.18 500 2.15 1.95 1.79 1.66 1.56 1.47 1.40 1.34 1.28 1.24 1.20 1.17 D2.6 Properties of Ammonia D2.6. Table 16. (continued) Pressure in bar Temperature in ˚C 70 80 90 100 110 120 140 160 180 200 250 300 1 0.873 0.871 0.868 0.865 0.862 0.859 0.853 0.847 0.842 0.838 0.835 0.844 5 0.914 0.905 0.897 0.890 0.883 0.877 0.866 0.857 0.850 0.845 0.839 0.847 10 0.974 0.954 0.937 0.923 0.911 0.900 0.883 0.871 0.861 0.853 0.844 0.850 15 1.05 1.01 0.982 0.960 0.941 0.925 0.901 0.884 0.871 0.862 0.849 0.853 20 1.14 1.08 1.03 1.00 0.974 0.952 0.919 0.898 0.883 0.871 0.855 0.857 25 1.25 1.16 1.10 1.05 1.01 0.980 0.938 0.913 0.894 0.880 0.860 0.861 30 1.41 1.27 1.17 1.10 1.05 1.01 0.957 0.928 0.906 0.889 0.866 0.864 35 1.29 1.41 1.26 1.17 1.10 1.05 0.978 0.944 0.918 0.899 0.871 0.868 40 1.29 1.61 1.38 1.24 1.15 1.08 1.00 0.960 0.930 0.909 0.877 0.871 50 1.28 1.32 1.79 1.47 1.29 1.18 1.05 1.00 0.957 0.929 0.889 0.879 60 1.27 1.31 1.39 1.92 1.51 1.30 1.10 1.04 0.986 0.952 0.902 0.886 70 1.26 1.30 1.37 1.51 1.96 1.50 1.17 1.08 1.02 0.976 0.915 0.894 80 1.25 1.28 1.34 1.46 1.75 1.87 1.26 1.13 1.05 1.00 0.928 0.902 90 1.25 1.27 1.33 1.42 1.64 3.14 1.39 1.20 1.09 1.03 0.942 0.910 100 1.24 1.26 1.31 1.39 1.56 2.07 1.59 1.27 1.14 1.06 0.957 0.918 110 1.23 1.25 1.29 1.37 1.50 1.83 1.98 1.37 1.19 1.09 0.973 0.926 120 1.23 1.25 1.28 1.34 1.45 1.69 3.11 1.51 1.25 1.13 0.989 0.934 130 1.22 1.24 1.27 1.32 1.42 1.60 6.72 1.69 1.32 1.17 1.01 0.943 140 1.22 1.23 1.26 1.30 1.38 1.53 3.38 1.95 1.40 1.22 1.02 0.951 150 1.22 1.22 1.25 1.29 1.35 1.47 2.43 2.33 1.49 1.26 1.04 0.960 160 1.21 1.22 1.24 1.27 1.33 1.43 2.05 2.74 1.60 1.32 1.06 0.969 180 1.20 1.21 1.22 1.25 1.29 1.36 1.70 2.65 1.86 1.43 1.10 0.986 200 1.20 1.20 1.20 1.22 1.26 1.31 1.53 2.16 2.04 1.56 1.14 1.00 250 1.18 1.17 1.17 1.18 1.20 1.22 1.32 1.55 1.80 1.71 1.23 1.05 300 1.17 1.16 1.15 1.15 1.16 1.17 1.22 1.33 1.49 1.56 1.30 1.08 350 1.16 1.15 1.13 1.13 1.13 1.13 1.15 1.22 1.31 1.39 1.30 1.11 400 1.15 1.13 1.12 1.11 1.10 1.10 1.11 1.15 1.21 1.27 1.26 1.11 500 1.14 1.12 1.10 1.08 1.07 1.06 1.05 1.06 1.09 1.11 1.15 1.08 5 1. 2. Bibliography Tillner-Roth R, Harms-Watzenberg F, Baehr HD (1993) Eine neue Fundamentalgleichung für Ammoniak, DKV-Tagungsbericht (20), Nürnberg, Band II/1, 167/181 Baehr HD, Tillner-Roth R (1995) Thermodynamische Eigenschaften umweltverträglicher Kältemittel. Springer, Berlin 3. 4. Tufeu R, Ivanov DY, Garrabos Y, Le Neindre B (1984) Thermal conductivity of ammonia in a large temperature and pressure range including the critical region. Ber Bunsenges Phys Chem 88:422–427 Fenghour A, Wakeham WA, Vesovic V, Watson JTR, Millat J, Vogal E (1995) The viscosity of ammonia. J Phys Chem Ref Data 24:1649–1667 277 278 D2 Properties of Selected Important Pure Substances D2.7 Properties of R134a (1,1,1,2-tetrafluoromethane) Roland Span1 . Rolf Krauss2 1 2 Ruhr-Universität Bochum, Bochum, Germany Universität Stuttgart, Stuttgart, Germany 1 Characteristic Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 4 Reference States of Enthalpy and Entropy . . . . . . . . . . . . . 278 2 Critical Point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 5 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 3 Triple Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 Tables with thermodynamic properties of R134a (1,1,1,2Tetrafluoroethan) were calculated with the reference equation of state established by Tillner-Roth and Baehr [1, 2]. The thermal conductivity and viscosity of R134a were calculated with the corresponding equations by Krauss et al. [3]. The densities required as input to these equations were calculated using the equation by Tillner-Roth and Baehr. p Pressure in bar b r Density in kg/m3 ws Isentropic speed of sound in m/s Isobaric expansion coefficient in 103/K b = v1 (∂v/∂T )p # Temperature in C l Thermal conductivity in mW/m K Z Compression factor Z = p/(rRT) Dynamic viscosity in 106 Pa·s h Specific enthalpy in kJ/kg n Kinematic viscosity n in 107 m2/s s Specific entropy in kJ/(kg K) a Thermal diffusivity in 107 m2/s cp Specific isobaric heat capacity in kJ/(kg K) Pr Prandtl number Pr = cp/l cv Specific isochoric heat v capacity in kJ/(kg K) 3 Specific volume in m /kg 1 Characteristic Quantities e = 102.032 g/mol, specific gas constant Molecular mass M R = 81.488856 J/(kg K). 2 Critical Point [1] pc = 40.56 bar, Tc = 374.18 K (#c = 101.03 C), rc = 508 kg/m3. 3 Triple Point [1] pt = 0.00391 bar, Tt = 169.85 K (#t = 103.3 C), r0t ¼ 1591kg=m3 . 4 Reference States of Enthalpy and Entropy h0 = 200 kJ/kg and s 0 = 1 kJ/(kg K) for saturated liquid at # = 0 C. Properties of R134a (1,1,1,2-tetrafluoromethane) D2.7 D2.7. Table 1. Properties of R134a at p = 1 bar q C r kg/m3 h kJ/kg s kJ/(kg K) cp kJ/(kg K) cv kJ/(kg K) b 103/K ws m/s l mW/(m K) h 106 Pa·s n 107 m2/s Pr – a 107 m2/s 90 1556.0 87.27 0.5019 1.189 0.7921 1.71 1053 – – – – – 85 1542.6 93.22 0.5340 1.193 0.7941 1.74 1027 – – – – – 80 1529.2 99.20 0.5653 1.198 0.7968 1.76 1002 – – – – – 75 1515.6 105.2 0.5960 1.203 0.8002 1.79 977.2 – – – – – 70 1502.0 111.2 0.6261 1.209 0.8040 1.82 952.4 – – – – – 65 1488.3 117.3 0.6556 1.216 0.8083 1.85 927.8 – – – – – 60 1474.5 123.4 0.6845 1.223 0.8128 1.88 903.4 – – – – – 55 1460.5 129.5 0.7130 1.230 0.8175 1.92 879.2 – – – – – 50 1446.5 135.7 0.7409 1.238 0.8225 1.96 855.1 – – – – – 45 1432.2 141.9 0.7684 1.246 0.8276 2.00 831.2 – – – – – 40 1417.8 148.2 0.7955 1.255 0.8328 2.04 807.5 – – – – – 35 1403.2 154.5 0.8223 1.263 0.8382 2.09 783.9 108.9 405.8 2.89 0.614 4.71 30 1388.4 106.8 381.2 0.604 4.54 160.8 0.8486 1.273 0.8438 2.15 760.4 25 5.1594 383.7 1.752 0.7932 0.6886 4.77 146.1 20 5.0401 387.6 1.768 0.7951 0.6932 4.60 147.8 10.01 15 4.9275 391.6 1.783 0.7987 0.6990 4.44 149.5 10 4.8208 395.6 1.799 0.8035 0.7056 4.31 5 4.7196 399.7 1.814 0.8092 0.7128 0 4.6232 403.7 1.829 0.8154 5 4.5312 407.8 1.844 0.8221 10 4.4433 412.0 1.858 15 4.3591 416.1 20 4.2784 25 9.576 2.75 19.2 23.4 0.823 10.14 20.1 25.0 0.806 10.43 10.35 21.0 26.5 0.792 151.1 10.86 10.56 21.9 28.0 0.781 4.19 152.7 11.28 10.76 22.8 29.5 0.772 0.7203 4.07 154.2 11.69 10.97 23.7 31.0 0.765 0.7280 3.97 155.7 12.10 11.17 24.7 32.5 0.759 0.8290 0.7359 3.87 157.2 12.51 11.38 25.6 34.0 0.754 1.873 0.8362 0.7440 3.78 158.7 12.91 11.58 26.6 35.4 0.750 420.3 1.887 0.8435 0.7521 3.69 160.1 13.31 11.78 27.5 36.9 0.746 4.2010 424.5 1.902 0.8510 0.7602 3.61 161.5 13.71 11.98 28.5 38.3 0.744 30 4.1265 428.8 1.916 0.8586 0.7684 3.54 162.9 14.10 12.18 29.5 39.8 0.742 35 4.0549 433.1 1.930 0.8662 0.7767 3.46 164.3 14.49 12.38 30.5 41.3 0.740 40 3.9860 437.5 1.944 0.8740 0.7849 3.40 165.7 14.88 12.58 31.6 42.7 0.739 45 3.9195 441.9 1.958 0.8817 0.7931 3.33 167.1 15.26 12.77 32.6 44.1 0.738 50 3.8554 446.3 1.972 0.8895 0.8014 3.27 168.4 15.63 12.97 33.6 45.6 0.738 55 3.7935 450.8 1.985 0.8974 0.8096 3.21 169.7 16.01 13.16 34.7 47.0 0.738 60 3.7336 455.3 1.999 0.9052 0.8178 3.15 171.0 16.38 13.36 35.8 48.5 0.738 65 3.6758 459.8 2.013 0.9131 0.8260 3.10 172.3 16.74 13.55 36.9 49.9 0.739 70 3.6198 464.4 2.026 0.9209 0.8341 3.04 173.6 17.10 13.74 38.0 51.3 0.740 75 3.5655 469.0 2.040 0.9288 0.8423 2.99 174.8 17.46 13.93 39.1 52.7 0.741 80 3.5130 473.7 2.053 0.9367 0.8504 2.95 176.1 17.82 14.12 40.2 54.1 0.742 85 3.4621 478.4 2.066 0.9445 0.8585 2.90 177.3 18.17 14.31 41.3 55.6 0.744 90 3.4126 483.1 2.079 0.9524 0.8666 2.85 178.6 18.51 14.50 42.5 57.0 0.746 95 3.3647 487.9 2.092 0.9602 0.8747 2.81 179.8 18.86 14.68 43.6 58.4 0.748 100 3.3181 492.7 2.105 0.9681 0.8827 2.77 181.0 19.20 14.87 44.8 59.8 0.750 105 3.2728 497.6 2.118 0.9759 0.8907 2.73 182.2 19.53 15.05 46.0 61.2 0.752 110 3.2288 502.5 2.131 0.9837 0.8987 2.69 183.4 19.86 15.24 47.2 62.5 0.755 115 3.1860 507.4 2.144 0.9915 0.9066 2.65 184.6 20.19 15.42 48.4 63.9 0.757 120 3.1444 512.4 2.157 0.9992 0.9145 2.61 185.7 20.51 15.60 49.6 65.3 0.760 125 3.1038 517.4 2.169 1.007 0.9224 2.58 186.9 20.83 15.79 50.9 66.7 0.763 130 3.0644 522.5 2.182 1.015 0.9303 2.54 188.0 21.15 15.97 52.1 68.0 0.766 135 3.0259 527.6 2.194 1.022 0.9381 2.51 189.2 21.46 16.15 53.4 69.4 0.769 140 2.9885 532.7 2.207 1.030 0.9459 2.48 190.3 21.77 16.33 54.6 70.7 0.773 145 2.9519 537.9 2.219 1.038 0.9537 2.44 191.4 22.08 16.51 55.9 72.1 0.776 150 2.9163 543.1 2.232 1.045 0.9614 2.41 192.6 22.38 16.68 57.2 73.4 0.779 155 2.8476 553.6 2.256 1.061 0.9768 2.35 194.8 – – – 9.930 – – 279 280 D2 Properties of Selected Important Pure Substances D2.7. Table 1. (continued) q C r kg/m3 h kJ/kg s kJ/(kg K) cp kJ/(kg K) cv kJ/(kg K) b 103/K ws m/s l mW/(m K) h 106 Pa·s n 107 m2/s Pr – a 107 m2/s 160 2.8476 553.6 2.256 1.061 0.9768 2.35 194.8 – – – – – 165 2.8145 558.9 2.269 1.068 0.9845 2.32 195.9 – – – – – 170 2.7822 564.3 2.281 1.076 0.9921 2.30 197.0 – – – – – 175 2.7506 569.7 2.293 1.083 0.9997 2.27 198.0 – – – – – 180 2.7198 575.1 2.305 1.091 1.007 2.24 199.1 – – – – – l0 mW/(m K) h0 106 Pa·s n0 107 m2/s D2.7. Table 2. Properties of the saturated liquid r0 kg/m3 h0 kJ/kg s0 kJ/(kg K) cp0 kJ/(kg K) cv0 kJ/(kg K) b0 103/K ws0 m/s 90 0.01524 1555.8 87.23 0.5020 1.189 85 0.02399 1542.5 93.18 0.5341 1.193 0.7920 1.71 1052 – – – – – 0.7940 1.74 1027 – – – – 80 0.03672 1529.0 99.16 0.5654 – 1.198 0.7968 1.76 1002 – – – – 75 0.05478 1515.5 105.2 – 0.5961 1.204 0.8002 1.79 976.8 – – – – 70 0.07981 1501.9 – 111.2 0.6262 1.210 0.8040 1.82 952.0 – – – – 65 – 0.11380 1488.2 117.3 0.6557 1.216 0.8082 1.85 927.4 – – – – – 60 0.15906 1474.3 123.4 0.6846 1.223 0.8127 1.88 903.0 – – – – – 55 0.21828 1460.4 129.5 0.7131 1.230 0.8175 1.92 878.8 – – – – – 50 0.29451 1446.3 135.7 0.7410 1.238 0.8224 1.96 854.7 – – – – – 45 0.39117 1432.1 141.9 0.7685 1.246 0.8276 2.00 830.9 – – – – – 40 0.51209 1417.7 148.1 0.7956 1.255 0.8328 2.05 807.2 – – – – – 35 0.66144 1403.1 154.4 0.8223 1.264 0.8382 2.09 783.7 108.9 405.6 2.89 0.614 4.71 30 0.84378 1388.4 160.8 0.8486 1.273 0.8438 2.15 760.3 106.8 381.1 2.75 0.604 4.54 25 1.0640 1373.4 167.2 0.8746 1.283 0.8494 2.20 737.0 104.6 358.4 2.61 0.594 4.39 20 1.3273 1358.3 173.6 0.9002 1.293 0.8551 2.27 713.8 102.4 337.2 2.48 0.583 4.26 15 1.6394 1342.8 180.1 0.9256 1.304 0.8609 2.33 690.7 100.2 317.4 2.36 0.572 4.13 10 2.0060 1327.1 186.7 0.9506 1.316 0.8669 2.41 667.6 98.06 298.9 2.25 0.562 4.01 5 2.4334 1311.1 193.3 0.9754 1.328 0.8729 2.49 644.6 95.87 281.6 2.15 0.551 3.90 0 2.9280 1294.8 200.0 1.000 1.341 0.8791 2.58 621.6 93.67 265.3 2.05 0.539 3.80 5 3.4966 1278.1 206.8 1.024 1.355 0.8854 2.69 598.7 91.46 249.9 1.96 0.528 3.70 10 4.1461 1261.0 213.6 1.048 1.370 0.8918 2.80 575.7 89.25 235.4 1.87 0.516 3.61 15 4.8837 1243.4 220.5 1.072 1.387 0.8983 2.93 552.7 87.02 221.7 1.78 0.505 3.53 20 5.7171 1225.3 227.5 1.096 1.405 0.9050 3.07 529.6 84.78 208.7 1.70 0.493 3.46 25 6.6538 1206.7 234.5 1.120 1.425 0.9119 3.24 506.5 82.53 196.3 1.63 0.480 3.39 30 7.7020 1187.5 241.7 1.144 1.446 0.9189 3.43 483.2 80.27 184.6 1.55 0.467 3.33 35 8.8698 1167.5 249.0 1.167 1.471 0.9262 3.64 359.9 77.98 173.4 1.49 0.454 3.27 40 10.166 1146.7 256.4 1.190 1.498 0.9336 3.90 436.4 75.69 162.7 1.42 0.440 3.22 45 11.599 1125.1 263.9 1.214 1.530 0.9414 4.20 412.8 73.37 152.5 1.36 0.426 3.18 50 13.179 1102.3 271.6 1.237 1.566 0.9494 4.56 389.0 71.05 142.7 1.29 0.412 3.14 55 14.915 1078.3 279.5 1.261 1.609 0.9579 5.00 364.9 68.71 133.2 1.24 0.396 3.12 60 16.818 1052.9 287.5 1.285 1.660 0.9668 5.55 340.5 66.36 124.1 1.18 0.380 3.10 65 18.898 1025.6 295.8 1.309 1.723 0.9764 6.25 315.7 64.02 115.2 1.12 0.362 3.10 70 21.168 996.25 304.3 1.333 1.804 0.9869 7.19 290.3 61.69 106.6 1.07 0.343 3.12 75 23.641 964.09 313.1 1.358 1.911 0.9988 8.48 264.1 59.39 98.13 1.02 0.322 3.16 80 26.332 928.24 322.4 1.384 2.065 1.013 10.4 236.6 57.15 89.69 0.966 0.298 3.24 85 29.258 887.16 332.2 1.410 2.306 1.031 13.6 207.4 54.99 81.15 0.915 0.269 3.40 90 32.442 837.83 342.9 1.439 2.756 1.056 19.9 175.9 52.93 72.22 0.862 0.229 3.76 95 35.912 772.70 355.2 1.472 3.938 1.094 37.4 141.2 51.21 62.34 0.807 0.168 100 39.724 651.18 373.3 1.519 101.0 55.59 48.63 0.747 0.049 q C p bar 17.59 1.174 254 a0 107 m2/s Pr0 – 4.79 15.4 D2.7 Properties of R134a (1,1,1,2-tetrafluoromethane) D2.7. Table 3. Properties of the saturated vapor q C p bar r00 kg/m3 h00 kJ/kg s00 kJ/(kg K) cp00 kJ/(kg K) cv00 kJ/(kg K) b00 103/K ws00 m/s l00 mW/(m K) h00 106 Pa·s n00 107 m2/s a00 107 m2/s Pr00 – 90 0.01524 0.10236 342.8 1.897 0.6173 0.5341 5.53 131.0 – – – – – 85 0.02399 0.15697 345.8 1.877 0.6294 0.5457 5.40 132.6 – – – – – 80 0.03672 0.23429 348.8 1.858 0.6417 0.5573 5.29 134.0 – – – – – 75 0.05478 0.34116 351.9 1.841 0.6540 0.5689 5.19 135.5 – – – – – 70 0.07981 0.48568 355.0 1.826 0.6665 0.5806 5.09 136.8 – – – – – 65 0.11380 0.67728 358.2 1.813 0.6793 0.5923 5.01 138.2 – – – – – 60 0.15906 0.92676 361.3 1.801 0.6924 0.6040 4.94 139.4 – – – – – 55 0.21828 1.2463 364.5 1.790 0.7058 0.6159 4.89 140.6 – – – – – 50 0.29451 1.6496 367.7 1.781 0.7197 0.6280 4.84 141.7 – – – – – 45 0.39117 2.1518 370.8 1.772 0.7341 0.6402 4.81 142.7 – – – – – 40 0.51209 2.7695 374.0 1.764 0.7490 0.6526 4.80 143.6 – – – – 35 0.66144 3.5209 377.2 1.758 0.7646 0.6652 4.79 144.5 8.704 9.507 27.0 32.3 0.835 30 0.84378 4.4259 380.3 1.751 0.7809 0.6781 4.81 145.2 9.142 9.719 22.0 26.5 0.830 25 1.0640 5.5059 383.4 1.746 0.7979 0.6912 4.83 145.8 9.656 9.946 18.1 22.0 0.822 20 1.3273 6.7845 386.6 1.741 0.8158 0.7046 4.87 146.3 10.11 10.16 15.0 18.3 0.820 15 1.6394 8.2870 389.6 1.737 0.8346 0.7183 4.93 146.6 10.57 10.38 12.5 15.3 0.819 10 2.0060 10.041 392.7 1.733 0.8544 0.7322 5.01 146.9 11.03 10.59 10.5 12.9 0.821 5 2.4334 12.077 395.7 1.730 0.8752 0.7464 5.11 147.0 11.49 10.81 8.95 10.9 0.823 0 2.9280 14.428 398.6 1.727 0.8972 0.7608 5.22 146.9 11.96 11.02 7.64 9.24 5 3.4966 17.131 401.5 1.724 0.9206 0.7755 5.36 146.7 12.43 11.24 6.56 7.88 0.832 10 4.1461 20.226 404.3 1.722 0.9455 0.7904 5.53 146.4 12.92 11.46 5.67 6.76 0.839 15 4.8837 23.758 407.1 1.720 0.9721 0.8056 5.72 145.9 13.42 11.68 4.92 5.81 0.846 20 5.7171 27.780 409.7 1.718 1.001 0.8210 5.95 145.1 13.93 11.91 4.29 5.01 0.856 25 6.6538 32.350 412.3 1.716 1.032 0.8367 6.22 144.3 14.46 12.14 3.75 4.33 0.867 30 7.7020 37.535 414.8 1.714 1.065 0.8527 6.54 143.2 15.01 12.38 3.30 3.75 0.879 35 8.8698 43.416 417.2 1.713 1.103 0.8691 6.92 141.9 15.58 12.63 2.91 3.25 0.894 40 10.166 50.085 419.4 1.711 1.145 0.8858 7.36 140.3 16.19 12.89 2.57 2.82 0.911 45 11.599 57.657 421.5 1.709 1.192 0.9029 7.90 138.6 16.84 13.17 2.28 2.45 0.932 50 13.179 66.272 423.4 1.707 1.246 0.9205 8.55 136.6 17.54 13.47 2.03 2.12 0.957 55 14.915 76.104 425.2 1.705 1.310 0.9387 9.36 134.3 18.30 13.79 1.81 1.84 0.987 60 16.818 87.379 426.6 1.702 1.387 0.9577 10.4 131.7 19.14 14.15 1.62 1.58 1.03 – 0.827 65 18.898 100.40 427.8 1.699 1.482 0.9775 11.7 128.7 20.09 14.56 1.45 1.35 1.07 70 21.168 115.57 428.6 1.696 1.605 0.9986 13.4 125.5 21.17 15.04 1.30 1.14 1.14 75 23.641 133.49 429.0 1.691 1.771 1.021 15.9 121.8 22.44 15.60 1.17 0.949 1.23 80 26.332 155.08 428.8 1.685 2.012 1.046 19.5 117.7 24.00 16.31 1.05 0.769 1.37 85 29.258 181.85 427.8 1.677 2.397 1.074 25.4 113.1 26.01 17.23 0.947 0.597 1.59 90 32.442 216.76 425.4 1.666 3.121 1.107 36.6 107.9 28.88 18.53 0.855 0.427 2.00 95 35.912 267.14 420.7 1.649 5.019 1.149 66.5 101.9 36.49 20.70 0.775 0.272 100 39.724 373.01 407.7 1.611 58.45 26.26 0.704 0.062 25.35 1.218 390 93.95 2.85 11.4 D2.7. Table 4. Density r of R134a in kg/m3 Temperature in C Pressure in bar 70 60 50 40 30 20 1 1502 1474 1446 1418 1388 5 1503 1475 1447 1419 1389 1359 1328 1296 1261 10 1504 1476 1448 1420 1391 1361 1330 1298 1264 1228 1189 15 1504 1477 1449 1421 1392 1362 1331 1299 1266 1230 1192 1151 20 1505 1478 1450 1422 1393 1364 1333 1301 1268 1233 1195 1155 5.040 10 4.821 0 4.623 10 4.443 20 4.278 23.74 30 4.127 22.55 40 3.986 21.53 49.00 281 282 D2 Properties of Selected Important Pure Substances D2.7. Table 4. (continued) Temperature in C Pressure in bar 70 60 50 40 30 20 10 0 10 20 30 40 25 1506 1479 1451 1423 1395 1365 1335 1303 1270 1236 1199 1159 30 1507 1480 1452 1424 1396 1367 1336 1305 1272 1238 1202 1162 35 1508 1481 1453 1425 1397 1368 1338 1307 1274 1241 1205 1166 40 1508 1482 1454 1427 1398 1369 1339 1309 1277 1243 1207 1169 45 1509 1482 1455 1428 1399 1371 1351 1310 1279 1245 1210 1173 50 1510 1483 1456 1429 1401 1372 1343 1312 1281 1248 1213 1176 60 1512 1485 1458 1431 1403 1375 1346 1316 1284 1252 1218 1182 70 1513 1487 1460 1433 1405 1377 1348 1319 1288 1257 1223 1188 80 1515 1488 1462 1435 1408 1380 1351 1322 1292 1261 1228 1194 90 1516 1490 1464 1437 1410 1382 1354 1325 1296 1265 1233 1200 100 1518 1492 1466 1439 1412 1385 1357 1328 1299 1269 1238 1205 110 1519 1493 1467 1441 1414 1387 1360 1331 1302 1273 1242 1210 120 1521 1495 1469 1443 1417 1390 1362 1334 1306 1276 1246 1215 140 1524 1498 1473 1447 1421 1394 1367 1340 1312 1284 1254 1224 160 1526 1501 1476 1451 1425 1399 1372 1346 1318 1291 1262 1233 180 1529 1504 1479 1454 1429 1403 1377 1351 1324 1297 1269 1241 200 1532 1507 1483 1458 1433 1408 1382 1356 1330 1303 1276 1249 220 1535 1510 1486 1461 1437 1412 1387 1361 1335 1309 1283 1256 240 1537 1513 1489 1465 1440 1416 1391 1366 1341 1315 1289 1263 260 1540 1516 1492 1468 1444 1420 1395 1371 1346 1321 1296 1270 280 1543 1519 1495 1471 1448 1424 1400 1375 1351 1326 1301 1276 300 1545 1522 1498 1475 1451 1427 1404 1380 1356 1331 1307 1283 Temperature in C Pressure in bar 1 50 60 70 80 90 3.855 3.734 3.620 3.513 3.413 100 3.318 110 3.229 120 3.144 130 3.064 140 2.988 160 180 2.848 2.720 5 20.62 19.81 19.07 18.41 17.79 17.23 16.70 16.21 15.75 15.32 14.54 13.84 10 45.88 43.35 41.22 39.37 37.75 36.29 34.98 33.79 32.70 31.69 29.89 28.31 68.19 64.07 60.67 57.78 55.27 53.05 51.07 49.28 46.15 43.48 94.89 88.00 82.61 78.18 74.43 71.17 68.30 63.44 59.42 98.53 93.42 89.05 81.90 76.19 15 1104 20 1109 1057 73.45 25 1114 1064 1004 138.5 122.8 112.4 104.7 30 1119 1071 1014 940.6 173.9 150.6 136.5 126.3 118.4 111.9 101.7 35 1124 1077 1022 954.9 856.4 206.8 176.9 159.3 146.9 137.3 123.0 112.6 40 1128 1082 1030 967.2 882.8 677.8 234.0 200.3 180.2 166.0 146.2 132.4 45 1132 1088 1037 978.2 902.5 782.9 341.9 254.7 220.2 198.8 171.3 153.4 50 1136 1093 1044 988.0 918.7 822.1 607.8 335.3 270.0 236.8 198.7 175.7 60 1144 1103 1057 1005 944.7 869.5 764.6 591.2 415.9 334.3 261.6 224.4 70 1151 1112 1068 1020 965.5 901.3 821.9 717.3 582.4 460.5 336.0 278.7 80 1158 1120 1078 1033 983.0 925.8 859.1 779.0 682.4 576.8 418.6 337.9 998.2 104.5 93.88 90 1165 1128 1088 1045 946.1 887.3 820.0 742.8 657.5 499.7 399.5 100 1171 1135 1097 1056 1012 963.4 910.2 850.9 785.1 713.5 569.7 460.1 110 1177 1142 1105 1066 1024 978.6 929.5 876.0 817.7 755.2 626.3 516.0 120 1182 1148 1113 1075 1035 992.2 946.4 897.1 844.3 788.2 671.9 565.5 140 1193 1161 1127 1092 1055 1016 974.8 931.6 886.2 838.7 740.5 645.4 160 1203 1172 1140 1107 1072 1036 998.4 959.4 918.8 876.9 790.8 705.7 180 1212 1182 1152 1120 1087 1054 1019 982.7 945.7 907.7 830.1 753.0 200 1221 1192 1162 1132 1101 1069 1036 968.6 933.6 862.3 791.4 1003 D2.7 Properties of R134a (1,1,1,2-tetrafluoromethane) D2.7. Table 4. (continued) Temperature in C Pressure in bar 50 60 70 80 90 100 110 120 130 140 160 180 988.6 220 1229 1201 1173 1143 1114 1083 1052 1021 955.9 889.6 823.7 240 1237 1210 1182 1154 1125 1096 1067 1037 1006 975.5 913.3 851.4 260 1244 1218 1191 1164 1136 1108 1080 1051 1022 993.1 934.2 875.7 280 1251 1225 1199 1173 1146 1120 1092 1065 1037 1009 952.9 897.3 300 1258 1233 1207 1182 1156 1130 1104 1077 1050 1024 969.9 916.7 D2.7. Table 5. Compression factor Z of R 134a Temperature in C Pressure in bar 70 60 50 40 30 20 10 0 10 20 30 40 1 0.004 0.004 0.004 0.004 0.004 0.962 0.967 0.972 0.975 0.978 0.981 0.983 5 0.020 0.020 0.019 0.019 0.018 0.018 0.018 0.017 0.017 0.882 0.897 0.910 10 0.040 0.039 0.038 0.037 0.036 0.036 0.035 0.035 0.034 0.034 0.034 0.800 15 0.060 0.058 0.057 0.056 0.054 0.053 0.053 0.052 0.051 0.051 0.051 0.051 20 0.080 0.078 0.076 0.074 0.072 0.071 0.070 0.069 0.068 0.068 0.068 0.068 25 0.100 0.097 0.095 0.092 0.090 0.089 0.087 0.086 0.085 0.085 0.084 0.085 30 0.120 0.117 0.114 0.111 0.108 0.106 0.105 0.103 0.102 0.101 0.101 0.101 35 0.140 0.136 0.132 0.129 0.126 0.124 0.122 0.120 0.119 0.118 0.118 0.118 40 0.160 0.155 0.151 0.148 0.144 0.142 0.139 0.137 0.136 0.135 0.134 0.134 45 0.180 0.175 0.170 0.166 0.162 0.159 0.156 0.154 0.153 0.151 0.151 0.150 50 0.200 0.194 0.189 0.184 0.180 0.177 0.174 0.171 0.169 0.168 0.167 0.167 60 0.240 0.233 0.226 0.221 0.216 0.212 0.208 0.205 0.202 0.201 0.199 0.199 70 0.279 0.271 0.264 0.257 0.251 0.246 0.242 0.238 0.235 0.233 0.232 0.231 80 0.319 0.309 0.301 0.293 0.287 0.281 0.276 0.272 0.268 0.266 0.264 0.263 90 0.359 0.348 0.338 0.330 0.322 0.316 0.310 0.305 0.301 0.298 0.295 0.294 100 0.398 0.386 0.375 0.366 0.357 0.350 0.344 0.338 0.334 0.330 0.327 0.325 110 0.437 0.424 0.412 0.402 0.393 0.384 0.377 0.371 0.366 0.362 0.359 0.356 120 0.477 0.462 0.449 0.438 0.428 0.419 0.411 0.404 0.398 0.394 0.390 0.387 140 0.555 0.538 0.523 0.509 0.497 0.487 0.477 0.469 0.462 0.457 0.452 0.448 160 0.633 0.614 0.596 0.581 0.567 0.554 0.544 0.534 0.526 0.519 0.513 0.509 180 0.711 0.689 0.669 0.651 0.636 0.622 0.609 0.599 0.589 0.581 0.574 0.568 200 0.789 0.764 0.742 0.722 0.704 0.689 0.675 0.663 0.652 0.642 0.634 0.628 220 0.866 0.839 0.814 0.792 0.773 0.755 0.740 0.726 0.714 0.703 0.694 0.686 240 0.943 0.913 0.886 0.862 0.841 0.822 0.805 0.789 0.776 0.764 0.753 0.745 260 1.020 0.987 0.958 0.932 0.909 0.888 0.869 0.852 0.837 0.824 0.812 0.802 280 1.096 1.061 1.030 1.002 0.976 0.953 0.933 0.915 0.898 0.884 0.871 0.860 300 1.173 1.135 1.101 1.071 1.043 1.019 0.997 0.977 0.959 0.943 0.929 0.917 Temperature in C Pressure in bar 50 60 70 80 90 100 110 120 130 140 160 180 1 0.985 0.987 0.988 0.989 0.990 0.991 0.992 0.993 0.993 0.994 0.995 0.996 5 0.921 0.930 0.937 0.944 0.950 0.955 0.959 0.963 0.966 0.969 0.974 0.978 10 0.828 0.850 0.868 0.883 0.895 0.906 0.915 0.924 0.931 0.937 0.948 0.956 15 0.052 0.752 0.787 0.814 0.835 0.854 0.869 0.883 0.894 0.904 0.921 0.934 283 284 D2 Properties of Selected Important Pure Substances D2.7. Table 5. (continued) Temperature in C Pressure in bar 50 60 70 80 90 100 110 120 130 140 160 180 20 0.068 0.070 0.685 0.732 0.768 0.796 0.819 0.839 0.855 0.870 0.893 0.912 25 0.085 0.087 0.089 0.627 0.688 0.731 0.765 0.792 0.815 0.834 0.865 0.889 30 0.102 0.103 0.106 0.111 0.583 0.655 0.704 0.741 0.771 0.796 0.836 0.865 35 0.118 0.120 0.122 0.127 0.138 0.557 0.634 0.686 0.725 0.757 0.806 0.842 40 0.135 0.136 0.139 0.144 0.153 0.194 0.547 0.623 0.676 0.716 0.775 0.818 45 0.151 0.152 0.155 0.160 0.168 0.189 0.422 0.551 0.622 0.672 0.744 0.795 50 0.167 0.169 0.171 0.176 0.184 0.200 0.263 0.465 0.564 0.627 0.713 0.771 60 0.199 0.200 0.203 0.207 0.215 0.227 0.251 0.317 0.439 0.533 0.650 0.724 70 0.231 0.232 0.234 0.238 0.245 0.255 0.273 0.305 0.366 0.451 0.590 0.680 80 0.262 0.263 0.265 0.269 0.275 0.284 0.298 0.321 0.357 0.412 0.541 0.641 90 0.293 0.294 0.296 0.299 0.305 0.313 0.325 0.343 0.369 0.407 0.510 0.610 100 0.324 0.325 0.326 0.329 0.334 0.341 0.352 0.367 0.388 0.416 0.497 0.589 110 0.355 0.355 0.356 0.359 0.363 0.370 0.379 0.392 0.409 0.433 0.498 0.577 120 0.385 0.385 0.386 0.388 0.392 0.398 0.406 0.418 0.433 0.452 0.506 0.575 140 0.446 0.444 0.444 0.446 0.449 0.453 0.460 0.469 0.481 0.496 0.536 0.587 160 0.505 0.503 0.502 0.502 0.504 0.508 0.513 0.521 0.530 0.542 0.573 0.614 180 0.564 0.561 0.559 0.559 0.559 0.562 0.566 0.572 0.579 0.589 0.614 0.647 200 0.622 0.618 0.615 0.614 0.614 0.615 0.618 0.622 0.629 0.636 0.657 0.684 220 0.680 0.675 0.671 0.669 0.667 0.668 0.670 0.673 0.677 0.684 0.701 0.723 240 0.737 0.731 0.726 0.723 0.721 0.720 0.721 0.723 0.726 0.731 0.745 0.763 260 0.794 0.787 0.781 0.776 0.773 0.771 0.771 0.772 0.774 0.778 0.788 0.804 280 0.850 0.842 0.835 0.829 0.825 0.823 0.821 0.821 0.822 0.824 0.832 0.845 300 0.906 0.896 0.889 0.882 0.877 0.873 0.871 0.869 0.869 0.871 0.876 0.886 D2.7. Table 6. Specific enthalpy h of R134 a in kJ/kg Temperature in C Pressure in bar 70 60 50 40 30 20 10 0 10 20 30 40 1 111.2 123.4 135.7 148.2 160.8 387.6 395.6 403.7 412.0 420.3 428.8 437.5 5 111.4 123.6 135.9 148.3 160.9 173.8 186.8 200.0 213.6 411.6 421.2 430.6 10 111.6 123.8 136.1 148.5 161.1 173.9 186.9 200.2 213.7 227.5 241.7 419.9 15 111.8 124.0 136.2 148.7 161.3 174.1 187.1 200.3 213.8 227.6 241.7 256.3 20 112.0 124.2 136.4 148.9 161.5 174.2 187.2 200.4 213.9 227.6 241.7 256.2 25 112.2 124.4 136.6 149.1 161.6 174.4 187.4 200.5 214.0 227.7 241.7 256.2 30 112.5 124.6 136.8 149.2 161.8 174.6 187.5 200.7 214.1 227.7 241.7 256.1 35 112.7 124.8 137.0 149.4 162.0 174.7 187.6 200.8 214.2 227.8 241.8 256.1 40 112.9 125.0 137.2 149.6 162.2 174.9 187.8 200.9 214.3 227.9 241.8 256.1 45 113.1 125.2 137.4 149.8 162.4 175.1 187.9 201.0 214.4 227.9 241.8 256.0 50 113.3 125.4 137.6 150.0 162.5 175.2 188.1 201.2 214.5 228.0 241.9 256.0 60 113.7 125.8 138.0 150.4 162.9 175.6 188.4 201.5 214.7 228.2 242.0 256.0 70 114.2 126.2 138.4 150.8 163.3 175.9 188.7 201.7 214.9 228.4 242.1 256.1 80 114.6 126.7 138.8 151.2 163.6 176.3 189.1 202.0 215.2 228.6 242.2 256.1 D2.7 Properties of R134a (1,1,1,2-tetrafluoromethane) D2.7. Table 6. (continued) Temperature in C Pressure in bar 70 60 50 40 30 20 10 0 10 20 30 40 90 115.0 127.1 139.2 151.6 164.0 176.6 189.4 202.3 215.5 228.8 242.4 256.2 100 115.5 127.5 139.7 152.0 164.4 177.0 189.7 202.6 215.7 229.0 242.5 256.3 110 115.9 127.9 140.1 152.3 164.8 177.3 190.0 202.9 216.0 229.3 242.7 256.4 120 116.3 128.3 140.5 152.7 165.1 177.7 190.4 203.2 216.3 229.5 242.9 256.6 140 117.2 129.2 141.3 153.5 165.9 178.4 191.1 203.9 216.9 230.0 243.4 256.9 160 118.1 130.0 142.1 254.4 166.7 179.2 191.8 204.6 217.5 230.6 243.8 257.3 180 118.9 130.9 143.0 155.2 167.5 179.9 192.5 205.2 218.1 231.1 244.3 257.7 200 119.8 131.8 143.8 156.0 168.3 180.7 193.2 205.9 218.8 231.7 244.9 258.2 220 120.7 132.6 144.7 156.8 169.1 181.5 194.0 206.6 219.4 232.3 245.4 258.7 240 121.6 133.5 145.5 157.7 169.9 182.3 194.7 207.4 220.1 233.0 246.0 259.2 260 122.5 134.4 146.4 158.5 170.7 183.1 195.5 208.1 220.8 233.6 246.6 259.8 280 123.4 135.3 147.2 159.3 171.5 183.9 196.3 208.8 221.5 234.3 247.3 260.3 300 124.3 136.1 148.1 160.2 172.4 184.7 197.1 209.6 222.2 235.0 247.9 260.9 Temperature in C Pressure in bar 1 50 60 70 80 90 100 110 120 130 140 160 180 446.3 455.3 464.4 473.7 483.1 492.7 502.5 512.4 522.5 532.7 553.6 575.1 5 440.1 449.6 459.2 468.9 478.8 488.7 498.7 508.9 519.2 529.6 550.9 572.7 10 430.9 441.5 452.0 462.4 472.8 483.2 493.7 504.2 514.8 525.6 547.3 569.5 15 271.5 431.3 443.4 454.9 466.1 477.2 488.2 499.2 510.2 521.3 543.6 566.2 20 271.4 287.3 432.1 445.8 458.4 470.4 482.2 493.8 505.3 516.8 539.7 562.9 25 271.2 286.9 303.8 433.4 448.9 462.6 475.5 487.9 500.0 512.0 535.7 559.4 30 271.0 286.6 303.1 321.4 435.8 453.1 467.8 481.3 494.3 506.9 531.5 555.8 35 270.9 286.3 302.6 320.3 341.3 440.0 458.5 473.9 487.9 501.3 527.1 552.1 40 270.8 286.1 302.2 319.5 339.1 370.7 446.3 465.1 480.9 495.4 522.4 548.3 45 270.7 285.9 301.8 318.7 337.4 360.8 426.2 454.3 472.9 488.9 517.6 544.4 50 270.6 285.7 301.4 318.0 336.2 357.2 391.0 440.1 463.7 481.7 512.4 540.3 60 270.5 285.4 300.8 317.0 334.2 353.1 375.4 405.9 440.5 465.2 501.4 531.9 70 270.4 285.1 300.3 316.1 332.8 350.6 370.1 392.7 419.7 447.2 489.7 523.1 80 270.3 284.9 299.9 315.5 331.7 348.7 367.0 386.9 409.1 433.1 478.0 514.2 90 270.3 284.8 299.6 314.9 330.8 347.3 364.7 383.3 403.2 424.4 467.6 505.7 100 270.3 284.7 299.4 314.5 330.1 346.2 363.0 380.7 399.3 418.9 459.5 498.0 110 270.4 284.6 299.2 314.1 329.5 345.3 361.7 378.7 396.5 415.0 453.4 491.3 120 270.5 284.6 299.1 313.8 329.0 344.6 360.6 377.2 394.3 412.1 448.8 485.7 140 270.7 284.6 298.9 313.4 328.3 343.4 359.0 374.9 391.2 408.0 442.4 477.5 160 270.9 284.8 298.9 313.2 327.8 342.7 357.9 373.3 389.1 405.2 438.2 471.9 180 271.2 285.0 298.9 313.1 327.5 342.2 357.1 372.2 387.6 403.3 435.3 467.9 200 271.6 285.3 299.1 313.2 327.4 341.9 356.5 371.4 386.5 401.9 433.1 465.0 220 272.1 285.6 299.4 313.3 327.4 341.7 356.2 370.9 385.8 400.8 431.5 462.8 240 272.5 286.0 299.7 313.5 327.5 341.6 356.0 370.5 385.2 400.1 430.3 461.1 260 273.0 286.4 300.0 313.7 327.6 341.7 355.9 370.3 384.8 399.6 429.4 459.8 280 273.5 286.9 300.4 314.1 327.9 341.8 355.9 370.2 384.6 399.2 428.7 458.8 300 274.1 287.4 300.8 314.4 328.2 342.0 356.0 370.2 384.5 399.0 428.3 458.0 285 286 D2 Properties of Selected Important Pure Substances D2.7. Table 7. Specific entropy s of R134a in kJ/(kg K) Temperature in C Pressure in bar 70 60 50 40 30 20 10 0 10 20 30 40 1 0.6261 0.6845 0.7409 0.7955 0.8486 1.768 1.799 1.829 1.858 1.887 1.916 1.944 5 0.6256 0.6840 0.7404 0.7950 0.8480 0.8996 0.9501 0.9996 1.048 1.734 1.766 1.797 10 0.6250 0.6834 0.7397 0.7942 0.8472 0.8988 0.9492 0.9986 1.047 1.095 1.143 1.713 15 0.6244 0.6827 0.7390 0.7935 0.8465 0.8980 0.9483 0.9976 1.046 1.094 1.141 1.189 20 0.6238 0.6821 0.7384 0.7928 0.8457 0.8972 0.9474 0.9967 1.045 1.093 1.140 1.187 25 0.6232 0.6815 0.7377 0.7921 0.8450 0.8964 0.9466 0.9957 1.044 1.092 1.139 1.186 30 0.6226 0.6809 0.7371 0.7914 0.8442 0.8956 0.9457 0.9948 1.043 1.090 1.137 1.184 35 0.6220 0.6802 0.7364 0.7907 0.8435 0.8948 0.9448 0.9938 1.042 1.089 1.136 1.183 40 0.6214 0.6796 0.7357 0.7901 0.8427 0.8940 0.9440 0.9929 1.041 1.088 1.135 1.181 45 0.6208 0.6790 0.7351 0.7894 0.8420 0.8932 0.9432 0.9920 1.040 1.087 1.134 1.180 50 0.6203 0.6784 0.7345 0.7887 0.8413 0.8924 0.9423 0.9911 1.039 1.086 1.132 1.178 60 0.6191 0.6772 0.7332 0.7873 0.8398 0.8909 0.9407 0.9893 1.037 1.084 1.130 1.176 70 0.6180 0.6760 0.7319 0.7860 0.8384 0.8894 0.9391 0.9876 1.035 1.082 1.128 1.173 80 0.6168 0.6748 0.7307 0.7847 0.8370 0.8879 0.9375 0.9859 1.033 1.080 1.125 1.171 90 0.6157 0.6736 0.7294 0.7834 0.8356 0.8864 0.9359 0.9842 1.031 1.078 1.123 1.168 100 0.6146 0.6724 0.7282 0.7821 0.8343 0.8850 0.9344 0.9825 1.030 1.076 1.121 1.166 110 0.6134 0.6713 0.7270 0.7808 0.8329 0.8836 0.9328 0.9809 1.028 1.074 1.119 1.164 120 0.6123 0.6701 0.7258 0.7795 0.8316 0.8822 0.9313 0.9793 1.026 1.072 1.117 1.161 140 0.6101 0.6678 0.7234 0.7770 0.8290 0.8794 0.9284 0.9762 1.023 1.068 1.113 1.157 160 0.6080 0.6656 0.7210 0.7746 0.8264 0.8767 0.9255 0.9732 1.020 1.065 1.110 1.153 180 0.6058 0.6634 0.7187 0.7722 0.8239 0.8740 0.9228 0.9702 1.016 1.062 1.106 1.149 200 0.6037 0.6612 0.7164 0.7698 0.8214 0.8714 0.9200 0.9673 1.013 1.059 1.103 1.146 220 0.6017 0.6590 0.7142 0.7675 0.8190 0.8689 0.9174 0.9646 1.011 1.055 1.099 1.142 240 0.5996 0.6569 0.7120 0.7652 0.8166 0.8664 0.9148 0.9618 1.008 1.052 1.096 1.139 260 0.5976 0.6548 0.7098 0.7629 0.8143 0.8640 0.9122 0.9592 1.005 1.049 1.093 1.136 280 0.5956 0.6527 0.7077 0.7607 0.8120 0.8616 0.9098 0.9566 1.002 1.047 1.090 1.132 300 0.5936 0.6507 0.7056 0.7585 0.8097 0.8592 0.9073 0.9540 0.9995 1.044 1.087 1.129 Temperature in C Pressure in bar 50 60 70 80 90 100 110 120 130 140 160 180 1 1.972 1.999 2.026 2.053 2.079 2.105 2.131 2.157 2.182 2.207 2.256 2.305 5 1.826 1.856 1.884 1.912 1.939 1.966 1.993 2.019 2.045 2.070 2.121 2.170 10 1.748 1.781 1.812 1.841 1.870 1.899 1.926 1.954 1.980 2.007 2.058 2.108 15 1.237 1.723 1.759 1.792 1.823 1.853 1.883 1.911 1.939 1.966 2.018 2.070 20 1.235 1.283 1.709 1.748 1.783 1.816 1.847 1.877 1.906 1.934 1.988 2.041 25 1.233 1.281 1.331 1.700 1.744 1.781 1.815 1.847 1.878 1.907 1.963 2.017 30 1.231 1.278 1.327 1.380 1.698 1.745 1.784 1.819 1.852 1.882 1.941 1.996 35 1.229 1.276 1.324 1.375 1.434 1.702 1.751 1.791 1.826 1.859 1.920 1.977 40 1.227 1.274 1.322 1.371 1.426 1.512 1.713 1.762 1.801 1.837 1.901 1.959 45 1.226 1.272 1.319 1.368 1.420 1.483 1.656 1.729 1.775 1.814 1.882 1.943 50 1.224 1.270 1.317 1.364 1.415 1.472 1.561 1.688 1.747 1.791 1.864 1.927 60 1.221 1.266 1.312 1.358 1.407 1.458 1.517 1.595 1.682 1.743 1.829 1.897 70 1.218 1.263 1.308 1.353 1.400 1.448 1.500 1.558 1.626 1.693 1.794 1.869 80 1.215 1.260 1.304 1.349 1.394 1.440 1.488 1.540 1.595 1.654 1.760 1.842 90 1.213 1.257 1.300 1.344 1.389 1.434 1.480 1.527 1.577 1.629 1.732 1.818 100 1.210 1.254 1.297 1.340 1.384 1.428 1.472 1.518 1.565 1.612 1.709 1.795 110 1.207 1.251 1.294 1.337 1.380 1.423 1.466 1.510 1.554 1.600 1.691 1.776 D2.7 Properties of R134a (1,1,1,2-tetrafluoromethane) D2.7. Table 7. (continued) Temperature in C Pressure in bar 50 60 70 80 90 100 110 120 130 140 160 180 120 1.205 1.248 1.291 1.333 1.376 1.418 1.460 1.503 1.546 1.590 1.676 1.760 140 1.200 1.243 1.285 1.327 1.368 1.410 1.451 1.492 1.533 1.574 1.655 1.734 160 1.196 1.238 1.280 1.321 1.362 1.402 1.442 1.482 1.522 1.561 1.639 1.715 180 1.192 1.234 1.275 1.316 1.356 1.396 1.435 1.474 1.513 1.551 1.627 1.701 200 1.188 1.230 1.271 1.311 1.351 1.390 1.429 1.467 1.505 1.543 1.617 1.688 220 1.184 1.226 1.266 1.306 1.346 1.384 1.423 1.461 1.498 1.535 1.608 1.678 240 1.181 1.222 1.262 1.302 1.341 1.379 1.417 1.455 1.492 1.528 1.600 1.669 260 1.177 1.218 1.258 1.298 1.337 1.375 1.412 1.449 1.486 1.522 1.593 1.661 280 1.174 1.215 1.255 1.294 1.332 1.370 1.408 1.444 1.481 1.516 1.586 1.654 300 1.171 1.211 1.251 1.290 1.328 1.366 1.403 1.440 1.476 1.511 1.580 1.647 D2.7. Table 8. Specific isobaric heat capacity cp of R134a in kJ/(kg K) Temperature in C Pressure in bar 70 60 50 40 30 20 10 0 10 20 30 40 1 1.209 1.223 1.238 1.255 1.273 0.7951 0.8035 0.8154 0.8290 0.8435 0.8586 0.8740 5 1.209 1.222 1.237 1.254 1.272 1.292 1.314 1.340 1.370 0.9635 0.9494 0.9468 10 1.208 1.222 1.236 1.253 1.270 1.290 1.312 1.337 1.366 1.401 1.443 1.134 15 1.208 1.221 1.235 1.252 1.269 1.289 1.310 1.335 1.363 1.396 1.437 1.489 20 1.207 1.220 1.235 1.250 1.268 1.287 1.308 1.332 1.359 1.391 1.430 1.479 25 1.207 1.219 1.234 1.249 1.267 1.285 1.306 1.330 1.356 1.387 1.424 1.471 30 1.206 1.219 1.233 1.248 1.265 1.284 1.304 1.327 1.353 1.383 1.419 1.463 35 1.205 1.218 1.232 1.247 1.264 1.282 1.303 1.325 1.350 1.379 1.414 1.455 40 1.205 1.217 1.231 1.246 1.263 1.281 1.301 1.323 1.347 1.376 1.409 1.448 45 1.204 1.217 1.230 1.246 1.262 1.280 1.299 1.321 1.345 1.372 1.404 1.442 50 1.204 1.216 1.230 1.245 1.261 1.278 1.297 1.318 1.342 1.369 1.399 1.436 60 1.203 1.215 1.228 1.243 1.259 1.276 1.294 1.314 1.337 1.362 1.391 1.425 70 1.202 1.214 1.227 1.241 1.256 1.273 1.291 1.311 1.332 1.356 1.383 1.414 80 1.201 1.212 1.225 1.239 1.254 1.271 1.288 1.307 1.328 1.351 1.376 1.405 90 1.200 1.211 1.224 1.238 1.253 1.268 1.285 1.304 1.324 1.346 1.370 1.397 100 1.199 1.210 1.223 1.236 1.251 1.266 1.283 1.300 1.320 1.341 1.364 1.389 110 1.198 1.209 1.221 1.235 1.249 1.264 1.280 1.297 1.316 1.336 1.358 1.382 120 1.197 1.208 1.220 1.233 1.247 1.262 1.278 1.295 1.313 1.332 1.353 1.376 140 1.195 1.206 1.218 1.230 1.244 1.258 1.273 1.289 1.306 1.324 1.344 1.365 160 1.193 1.204 1.215 1.228 1.241 1.254 1.269 1.284 1.300 1.317 1.335 1.355 180 1.192 1.202 1.213 1.225 1.238 1.251 1.265 1.280 1.295 1.311 1.328 1.346 200 1.190 1.200 1.211 1.223 1.235 1.248 1.261 1.275 1.290 1.305 1.321 1.338 220 1.189 1.198 1.209 1.221 1.233 1.245 1.258 1.272 1.286 1.300 1.315 1.331 240 1.187 1.197 1.207 1.219 1.230 1.242 1.255 1.268 1.281 1.295 1.310 1.325 260 1.186 1.195 1.206 1.217 1.228 1.240 1.252 1.265 1.278 1.291 1.305 1.319 280 1.185 1.194 1.204 1.215 1.226 1.237 1.249 1.262 1.274 1.287 1.300 1.314 300 1.183 1.192 1.202 1.213 1.224 1.235 1.247 1.259 1.271 1.283 1.296 1.310 287 288 D2 Properties of Selected Important Pure Substances D2.7. Table 8. (continued) Temperature in C Pressure in bar 50 60 70 80 90 100 110 120 130 140 160 180 1 0.8895 0.9052 0.9209 0.9367 0.9524 0.9681 0.9837 0.9992 1.015 1.030 1.061 1.091 5 0.9500 0.9565 0.9651 0.9751 0.9862 0.9979 1.010 1.023 1.036 1.049 1.077 1.104 10 1.079 1.054 1.042 1.039 1.040 1.044 1.050 1.058 1.067 1.077 1.099 1.122 15 1.560 1.248 1.172 1.134 1.114 1.104 1.100 1.100 1.103 1.109 1.123 1.142 20 1.545 1.643 1.465 1.302 1.228 1.188 1.166 1.154 1.148 1.146 1.152 1.164 25 1.532 1.619 1.764 1.731 1.436 1.319 1.258 1.224 1.203 1.192 1.184 1.189 30 1.520 1.599 1.722 1.970 2.003 1.556 1.398 1.319 1.274 1.247 1.221 1.216 35 1.509 1.580 1.687 1.880 2.455 2.175 1.642 1.459 1.369 1.316 1.265 1.246 40 1.498 1.564 1.659 1.815 2.168 9.404 2.187 1.684 1.499 1.405 1.315 1.280 45 1.489 1.550 1.634 1.764 2.016 2.912 4.459 2.096 1.689 1.520 1.374 1.317 50 1.480 1.537 1.613 1.724 1.917 2.382 5.675 2.976 1.979 1.672 1.443 1.359 60 1.465 1.514 1.577 1.663 1.792 2.015 2.510 3.641 2.933 2.123 1.615 1.454 70 1.451 1.495 1.549 1.619 1.714 1.854 2.082 2.473 2.848 2.546 1.820 1.562 80 1.439 1.478 1.525 1.584 1.659 1.759 1.899 2.097 2.334 2.433 1.997 1.672 90 1.428 1.464 1.505 1.556 1.617 1.694 1.793 1.918 2.063 2.179 2.059 1.764 100 1.418 1.451 1.488 1.532 1.584 1.647 1.722 1.811 1.910 2.000 2.015 1.818 110 1.409 1.440 1.474 1.513 1.558 1.610 1.670 1.739 1.812 1.882 1.937 1.830 120 1.401 1.429 1.461 1.496 1.536 1.580 1.631 1.686 1.744 1.799 1.861 1.814 140 1.387 1.412 1.439 1.468 1.500 1.535 1.573 1.613 1.653 1.692 1.747 1.751 160 1.375 1.397 1.421 1.446 1.474 1.502 1.533 1.564 1.595 1.624 1.672 1.690 180 1.365 1.385 1.406 1.429 1.452 1.477 1.502 1.528 1.554 1.578 1.619 1.641 200 1.356 1.374 1.394 1.414 1.435 1.457 1.479 1.501 1.523 1.544 1.580 1.603 220 1.348 1.365 1.383 1.401 1.420 1.440 1.460 1.479 1.499 1.517 1.550 1.573 240 1.341 1.357 1.373 1.391 1.408 1.426 1.444 1.462 1.479 1.496 1.526 1.549 260 1.334 1.349 1.365 1.381 1.397 1.414 1.430 1.447 1.463 1.478 1.507 1.530 280 1.328 1.343 1.358 1.373 1.388 1.404 1.419 1.434 1.449 1.464 1.491 1.513 300 1.323 1.337 1.351 1.365 1.380 1.395 1.409 1.424 1.438 1.451 1.477 1.499 D2.7. Table 9. Specific isochoric heat capacity cv of R134a in kJ/(kg K) Temperature in C Pressure in bar 70 60 50 40 30 20 10 0 10 20 30 40 1 0.8040 0.8128 0.8225 0.8328 0.8438 0.6932 0.7056 0.7203 0.7359 0.7521 0.7684 0.7849 5 0.8042 0.8129 0.8225 0.8329 0.8438 0.8551 0.8669 0.8790 0.8917 0.8052 0.8074 0.8155 10 0.8043 0.8130 0.8226 0.8330 0.8438 0.8551 0.8668 0.8790 0.8916 0.9047 0.9187 0.8824 15 0.8044 0.8131 0.8228 0.8331 0.8439 0.8552 0.8668 0.8789 0.8914 0.9045 0.9182 0.9329 20 0.8046 0.8132 0.8229 0.8332 0.8440 0.8552 0.8668 0.8788 0.8912 0.9042 0.9178 0.9323 25 0.8047 0.8134 0.8230 0.8333 0.8440 0.8552 0.8668 0.8787 0.8911 0.9040 0.9174 0.9317 30 0.8048 0.8135 0.8231 0.8334 0.8441 0.8553 0.8668 0.8787 0.8910 0.9037 0.9171 0.9311 35 0.8050 0.8136 0.8232 0.8334 0.8442 0.8553 0.8668 0.8786 0.8909 0.9035 0.9167 0.9306 40 0.8051 0.8137 0.8233 0.8335 0.8443 0.8553 0.8668 0.8786 0.8908 0.9034 0.9164 0.9301 45 0.8053 0.8139 0.8234 0.8336 0.8443 0.8554 0.8668 0.8786 0.8907 0.9032 0.9162 0.9297 50 0.8054 0.8140 0.8236 0.8337 0.8444 0.8555 0.8668 0.8785 0.8906 0.9030 0.9159 0.9293 D2.7 Properties of R134a (1,1,1,2-tetrafluoromethane) D2.7. Table 9. (continued) Temperature in C Pressure in bar 70 60 50 40 30 20 10 0 10 20 30 40 60 0.8057 0.8143 0.8238 0.8340 0.8446 0.8556 0.8669 0.8785 0.8905 0.9028 0.9155 0.9286 70 0.8060 0.8146 0.8241 0.8342 0.8448 0.8557 0.8670 0.8785 0.8904 0.9026 0.9151 0.9281 80 0.8063 0.8148 0.8243 0.8344 0.8450 0.8559 0.8671 0.8785 0.8903 0.9024 0.9148 0.9276 90 0.8066 0.8151 0.8246 0.8346 0.8452 0.8560 0.8672 0.8786 0.8903 0.9023 0.9145 0.9271 100 0.8069 0.8154 0.8248 0.8349 0.8454 0.8562 0.8673 0.8787 0.8903 0.9022 0.9143 0.9268 110 0.8072 0.8157 0.8251 0.8351 0.8456 0.8564 0.8674 0.8787 0.8903 0.9021 0.9142 0.9265 120 0.8075 0.8160 0.8254 0.8354 0.8458 0.8566 0.8676 0.8788 0.8903 0.9021 0.9140 0.9263 140 0.8082 0.8166 0.8260 0.8359 0.8463 0.8570 0.8679 0.8791 0.8905 0.9021 0.9139 0.9259 160 0.8088 0.8172 0.8265 0.8365 0.8468 0.8574 0.8683 0.8794 0.8906 0.9021 0.9138 0.9257 180 0.8095 0.8179 0.8271 0.8370 0.8473 0.8579 0.8687 0.8797 0.8909 0.9023 0.9139 0.9256 200 0.8101 0.8185 0.8278 0.8376 0.8478 0.8583 0.8691 0.8800 0.8912 0.9025 0.9140 0.9256 220 0.8108 0.8191 0.8284 0.8382 0.8484 0.8588 0.8695 0.8804 0.8915 0.9027 0.9141 0.9257 240 0.8115 0.8198 0.8290 0.8388 0.8489 0.8594 0.8700 0.8809 0.8919 0.9030 0.9144 0.9258 260 0.8122 0.8205 0.8296 0.8394 0.8495 0.8599 0.8705 0.8813 0.8923 0.9034 0.9146 0.9260 280 0.8129 0.8211 0.8303 0.8400 0.8501 0.8604 0.8710 0.8818 0.8927 0.9037 0.9149 0.9263 300 0.8135 0.8218 0.8309 0.8406 0.8506 0.8610 0.8715 0.8822 0.8931 0.9041 0.9153 0.9266 Temperature in C Pressure in bar 1 50 60 70 80 90 100 110 120 130 140 160 180 0.8014 0.8178 0.8341 0.8504 0.8666 0.8827 0.8987 0.9145 0.9303 0.9459 0.9768 1.007 5 0.8265 0.8389 0.8522 0.8660 0.8802 0.8946 0.9091 0.9238 0.9385 0.9532 0.9827 1.012 10 0.8717 0.8727 0.8791 0.8883 0.8990 0.9107 0.9232 0.9361 0.9493 0.9628 0.9903 1.018 15 0.9490 0.9266 0.9158 0.9158 0.9209 0.9289 0.9385 0.9492 0.9607 0.9728 0.9981 1.024 20 0.9479 0.9657 0.9765 0.9537 0.9481 0.9499 0.9556 0.9635 0.9729 0.9833 1.006 1.031 25 0.9470 0.9640 0.9844 1.018 0.9852 0.9756 0.9751 0.9792 0.9860 0.9944 1.015 1.037 30 0.9461 0.9626 0.9816 1.007 1.047 1.010 0.9985 0.9969 1.000 1.006 1.023 1.044 35 0.9453 0.9613 0.9794 1.002 1.043 1.063 1.028 1.017 1.016 1.019 1.032 1.051 40 0.9446 0.9602 0.9775 0.9981 1.029 1.151 1.070 1.041 1.033 1.032 1.041 1.057 45 0.9440 0.9592 0.9759 0.9951 1.020 1.070 1.139 1.071 1.052 1.046 1.050 1.064 50 0.9434 0.9583 0.9745 0.9926 1.015 1.049 1.139 1.108 1.073 1.061 1.059 1.071 60 0.9424 0.9568 0.9721 0.9888 1.008 1.031 1.064 1.114 1.111 1.090 1.077 1.083 70 0.9415 0.9555 0.9702 0.9859 1.003 1.022 1.045 1.074 1.101 1.105 1.092 1.095 80 0.9408 0.9544 0.9687 0.9837 0.9995 1.017 1.036 1.057 1.080 1.097 1.102 1.104 90 0.9401 0.9535 0.9674 0.9819 0.9970 1.013 1.030 1.048 1.067 1.084 1.103 1.110 100 0.9396 0.9528 0.9663 0.9804 0.9949 1.010 1.026 1.042 1.059 1.075 1.100 1.113 110 0.9392 0.9521 0.9654 0.9791 0.9933 1.008 1.023 1.038 1.054 1.069 1.096 1.113 120 0.9388 0.9516 0.9647 0.9781 0.9919 1.006 1.020 1.035 1.050 1.065 1.091 1.112 140 0.9382 0.9507 0.9635 0.9765 0.9897 1.003 1.017 1.031 1.045 1.058 1.085 1.108 160 0.9378 0.9501 0.9626 0.9753 0.9882 1.001 1.014 1.028 1.041 1.054 1.080 1.104 180 0.9376 0.9497 0.9620 0.9744 0.9871 0.9998 1.013 1.026 1.039 1.052 1.077 1.101 200 0.9374 0.9494 0.9615 0.9738 0.9862 0.9988 1.011 1.024 1.037 1.050 1.075 1.099 220 0.9374 0.9493 0.9613 0.9734 0.9856 0.9980 1.010 1.023 1.035 1.048 1.073 1.097 240 0.9375 0.9492 0.9611 0.9731 0.9852 0.9974 1.010 1.022 1.034 1.047 1.072 1.096 260 0.9376 0.9492 0.9610 0.9729 0.9849 0.9970 1.009 1.021 1.034 1.046 1.071 1.095 280 0.9377 0.9493 0.9610 0.9729 0.9848 0.9968 1.009 1.021 1.033 1.045 1.070 1.094 300 0.9380 0.9495 0.9611 0.9729 0.9847 0.9966 1.009 1.021 1.033 1.045 1.069 1.093 289 290 D2 Properties of Selected Important Pure Substances D2.7. Table 10. Isobaric expansion coefficient b of R134a in 103/K Temperature in C Pressure in bar 70 60 50 40 30 20 10 0 10 20 30 40 1 1.82 1.88 1.96 2.04 2.15 4.60 4.31 4.07 3.87 3.69 3.54 3.40 5 1.81 1.88 1.95 2.04 2.13 2.25 2.40 2.57 2.79 5.44 4.88 4.47 10 1.81 1.87 1.94 2.02 2.12 2.24 2.38 2.55 2.76 3.03 3.39 7.21 15 1.80 1.86 1.93 2.01 2.11 2.22 2.36 2.52 2.72 2.98 3.32 3.80 20 1.79 1.85 1.92 2.00 2.10 2.20 2.34 2.49 2.69 2.94 3.26 3.70 25 1.79 1.85 1.91 1.99 2.08 2.19 2.32 2.47 2.66 2.89 3.20 3.61 30 1.78 1.84 1.91 1.98 2.07 2.17 2.30 2.45 2.63 2.85 3.14 3.53 35 1.78 1.83 1.90 1.97 2.06 2.16 2.28 2.42 2.60 2.81 3.09 3.45 40 1.77 1.82 1.89 1.96 2.05 2.15 2.26 2.40 2.57 2.78 3.04 3.38 45 1.76 1.82 1.88 1.95 2.03 2.13 2.24 2.38 2.54 2.74 2.99 3.31 50 1.76 1.81 1.87 1.94 2.02 2.12 2.23 2.36 2.51 2.71 2.94 3.24 60 1.74 1.80 1.86 1.92 2.00 2.09 2.19 2.32 2.46 2.64 2.86 3.13 70 1.73 1.78 1.84 1.91 1.98 2.06 2.16 2.28 2.42 2.58 2.78 3.02 80 1.72 1.77 1.83 1.89 1.96 2.04 2.13 2.24 2.37 2.52 2.71 2.93 90 1.71 1.76 1.81 1.87 1.94 2.02 2.11 2.21 2.33 2.47 2.64 2.84 100 1.70 1.75 1.80 1.85 1.92 1.99 2.08 2.18 2.29 2.42 2.58 2.76 110 1.69 1.73 1.78 1.84 1.90 1.97 2.05 2.14 2.25 2.38 2.52 2.69 120 1.68 1.72 1.77 1.82 1.88 1.95 2.03 2.12 2.22 2.33 2.47 2.62 140 1.66 1.70 1.74 1.79 1.85 1.91 1.98 2.06 2.15 2.25 2.37 2.51 160 1.64 1.68 1.72 1.76 1.81 1.87 1.94 2.01 2.09 2.18 2.28 2.40 180 1.62 1.65 1.69 1.74 1.78 1.84 1.90 1.96 2.03 2.12 2.21 2.31 200 1.60 1.63 1.67 1.71 1.75 1.80 1.86 1.92 1.98 2.06 2.14 2.23 220 1.58 1.61 1.65 1.69 1.73 1.77 1.82 1.88 1.94 2.00 2.08 2.16 240 1.57 1.60 1.63 1.66 1.70 1.74 1.79 1.84 1.89 1.95 2.02 2.09 260 1.55 1.58 1.61 1.64 1.67 1.71 1.76 1.80 1.85 1.91 1.97 2.03 280 1.53 1.56 1.59 1.62 1.65 1.69 1.73 1.77 1.81 1.86 1.92 1.98 300 1.52 1.54 1.57 1.60 1.63 1.66 1.70 1.74 1.78 1.82 1.87 1.93 Temperature in C Pressure in bar 50 60 70 80 90 1 3.27 3.15 3.04 2.95 2.85 5 4.15 3.89 3.67 3.48 3.31 10 6.06 5.32 4.79 4.39 15 4.50 8.26 6.74 20 4.34 5.36 25 4.19 5.09 6.72 30 4.06 4.86 6.22 9.22 18.9 11.4 35 3.94 4.66 5.83 8.10 15.7 21.0 40 3.83 4.49 5.50 7.31 11.8 20.4 12.3 45 3.73 4.33 5.21 6.71 9.85 22.5 55.0 18.3 11.8 50 3.64 4.18 4.97 6.23 8.59 14.9 67.4 31.0 15.9 11.0 60 3.47 3.94 4.57 5.52 7.04 9.91 17.0 36.0 28.4 16.9 70 3.33 3.73 4.26 5.00 6.09 7.83 10.9 16.9 24.0 21.3 11.6 7.67 80 3.20 3.55 4.00 4.60 5.43 6.63 8.46 11.3 15.2 17.8 13.2 8.74 11.0 13.2 13.0 9.44 10.3 11.5 9.56 11.2 110 120 130 140 160 180 2.77 2.69 2.61 2.54 2.48 2.35 2.24 3.16 3.03 2.92 2.81 2.71 2.54 2.40 4.06 3.79 3.57 3.37 3.21 3.06 2.81 2.61 5.79 5.14 4.64 4.26 3.94 3.69 3.47 3.11 2.84 8.36 6.84 5.87 5.19 4.68 4.28 3.96 3.46 3.10 7.81 6.52 5.66 5.03 4.55 3.87 3.39 8.58 7.02 6.01 5.29 4.34 3.71 9.05 7.33 6.23 4.88 4.07 7.43 5.52 4.47 8.99 6.27 4.92 7.13 5.40 15.0 10.0 100 123 12.2 9.16 90 3.09 3.39 3.78 4.28 4.94 5.83 7.07 8.80 100 2.99 3.26 3.60 4.02 4.56 5.25 6.16 7.34 8.79 110 2.89 3.14 3.43 3.80 4.25 4.81 5.51 6.38 7.40 8.50 9.23 9.91 6.49 9.14 D2.7 Properties of R134a (1,1,1,2-tetrafluoromethane) D2.7. Table 10. (continued) Temperature in C Pressure in bar 50 60 70 80 90 120 2.81 3.03 3.29 3.61 3.99 140 2.66 2.84 3.06 3.30 3.59 160 2.54 2.69 2.86 3.06 180 2.43 2.56 2.70 200 2.33 2.44 2.57 220 2.25 2.34 240 2.17 260 2.10 280 300 100 110 120 130 140 160 180 4.46 5.02 5.69 6.46 7.28 8.54 8.45 3.93 4.32 4.76 5.25 5.75 6.64 6.99 3.29 3.55 3.83 4.15 4.49 4.84 5.48 5.85 2.87 3.05 3.25 3.48 3.72 3.97 4.22 4.70 5.02 2.71 2.86 3.02 3.20 3.39 3.58 3.78 4.15 4.41 2.45 2.57 2.70 2.83 2.98 3.13 3.29 3.44 3.73 3.95 2.26 2.35 2.45 2.56 2.67 2.79 2.92 3.05 3.17 3.41 3.60 2.18 2.26 2.35 2.44 2.54 2.64 2.75 2.85 2.96 3.15 3.31 2.04 2.11 2.18 2.26 2.34 2.42 2.51 2.60 2.69 2.78 2.94 3.07 1.98 2.04 2.11 2.17 2.24 2.32 2.39 2.47 2.55 2.62 2.76 2.88 D2.7. Table 11. Isentropic speed of sound ws in R134a in m/s Temperature in C Pressure in bar 70 60 50 40 30 20 10 0 10 20 30 40 1 952.4 903.4 855.1 807.5 760.4 147.8 151.1 154.2 157.2 160.1 162.9 165.7 5 954.3 905.4 857.3 809.8 762.9 716.4 669.9 623.4 576.5 147.8 152.1 156.1 10 956.6 907.9 859.9 812.7 766.1 719.8 673.7 627.6 581.3 534.2 486.1 140.9 15 958.8 910.3 862.6 815.6 769.2 723.2 677.5 631.8 585.9 539.5 492.1 443.3 20 961.1 912.8 865.2 818.4 772.3 726.6 681.2 635.9 590.5 544.6 498.0 450.1 25 963.4 915.2 867.8 821.3 775.4 729.9 684.9 640.0 595.0 549.7 503.8 456.8 30 965.6 917.6 870.4 824.1 778.4 733.3 688.5 643.9 599.4 554.6 509.4 463.2 35 967.8 920.0 873.0 826.9 781.4 736.5 692.1 647.9 603.8 559.5 514.8 469.5 40 970.0 922.3 875.6 829.6 784.4 739.8 695.6 651.8 608.0 564.3 520.2 475.6 45 972.2 924.7 878.1 832.3 787.3 743.0 699.1 655.6 612.3 568.9 525.4 481.5 50 974.4 927.1 880.6 835.1 790.3 746.2 702.6 659.4 616.4 573.5 530.6 487.3 60 978.8 931.7 885.6 840.4 796.1 752.4 709.4 666.8 624.5 582.5 540.5 498.4 70 983.1 936.3 890.5 845.7 801.8 758.6 716.0 674.0 632.4 591.2 550.1 509.1 80 987.3 940.8 895.4 850.9 807.3 764.6 722.5 681.1 640.1 599.6 559.3 519.3 90 991.5 945.3 900.2 856.0 812.9 770.5 728.9 688.0 647.6 607.7 568.3 529.1 100 995.6 949.7 904.9 861.1 818.3 776.3 735.2 694.8 655.0 615.7 576.9 538.6 110 999.7 954.1 909.6 866.1 823.6 782.1 741.3 701.4 662.1 623.4 585.3 547.7 120 1004 958.4 914.2 871.0 828.9 787.7 747.4 707.9 669.1 631.0 593.5 556.5 140 1012 966.9 923.2 880.7 839.2 798.7 759.1 720.5 682.6 645.5 609.1 573.4 160 1020 975.3 932.1 890.1 849.2 809.4 770.5 732.6 695.6 659.4 624.0 589.4 180 1027 983.4 940.7 899.3 858.9 819.7 781.5 744.3 708.1 672.7 638.2 604.5 200 1035 991.4 949.2 908.2 868.4 829.8 792.2 755.7 720.1 685.5 651.7 618.9 220 1042 999.3 957.5 917.0 877.7 839.6 802.6 766.7 731.7 697.8 664.8 632.7 240 1050 1007 965.6 925.6 886.8 849.2 812.7 777.3 743.0 709.7 677.3 646.0 260 1057 1015 973.6 934.0 895.6 858.5 822.6 787.7 753.9 721.2 689.4 658.7 280 1064 1022 981.4 942.2 904.3 867.6 832.1 797.8 764.5 732.3 701.1 671.0 300 1071 1029 989.1 950.3 912.8 876.6 841.5 807.6 774.8 743.1 712.4 682.8 291 292 D2 Properties of Selected Important Pure Substances D2.7. Table 11. (continued) Temperature in C Pressure in bar 50 60 70 80 90 100 110 120 130 140 160 180 1 168.4 171.0 173.6 176.1 178.6 181.0 183.4 185.7 188.0 190.3 194.8 199.1 5 159.8 163.2 166.6 169.7 172.8 175.7 178.5 181.3 183.9 186.5 191.5 196.4 10 146.9 152.0 156.7 160.9 164.9 168.6 172.1 175.4 178.6 181.7 187.5 192.9 15 392.1 138.0 145.0 150.9 156.1 160.9 165.2 169.3 173.0 176.6 183.3 189.4 20 400.3 347.1 129.9 138.9 146.2 152.3 157.8 162.7 167.2 171.4 179.1 185.9 25 408.2 356.8 300.4 123.2 134.3 142.7 149.7 155.8 161.2 166.1 174.8 182.4 30 415.7 366.1 312.5 250.4 118.9 131.6 140.8 148.3 154.8 160.5 170.5 179.0 35 423.0 374.8 323.6 266.5 192.7 117.7 130.9 140.4 148.2 154.9 166.2 175.6 40 430.1 383.1 333.9 280.5 217.3 108.9 119.4 132.0 141.5 149.3 162.0 172.3 45 436.9 391.1 343.6 293.0 236.2 163.2 106.0 123.2 134.7 143.7 157.9 169.2 50 443.5 398.8 352.7 304.5 252.1 191.1 113.9 115.1 128.3 138.4 154.1 166.3 60 456.1 413.2 369.7 325.0 278.5 229.0 175.1 127.3 121.6 130.7 147.8 161.3 70 468.0 426.8 385.2 343.2 300.5 256.9 212.3 169.3 139.5 133.0 144.7 158.2 80 479.4 439.5 399.6 359.7 319.8 279.8 240.2 202.3 170.1 150.5 147.0 157.6 90 490.2 451.6 413.1 374.9 337.1 299.7 263.3 228.7 198.0 174.4 156.1 160.4 100 500.6 463.0 425.8 389.1 352.9 317.6 283.4 251.1 221.9 197.7 170.3 166.8 110 510.6 473.9 437.8 402.3 367.6 333.8 301.4 270.8 242.9 218.9 186.9 176.4 120 520.2 484.4 449.3 414.9 381.3 348.8 317.7 288.5 261.7 238.2 203.9 188.1 140 538.4 504.2 470.7 438.0 406.4 376.0 347.0 319.7 294.6 272.0 236.2 214.2 160 555.5 522.5 490.4 459.2 429.1 400.2 372.8 346.9 323.0 301.3 265.4 240.5 180 571.7 539.8 508.8 478.8 449.9 422.3 396.0 371.3 348.4 327.3 291.7 265.4 200 587.0 556.0 526.1 497.1 469.3 442.6 417.4 393.5 371.3 350.9 315.8 288.6 220 601.6 571.5 542.3 514.3 487.3 461.5 437.1 414.0 392.5 372.6 337.9 310.4 240 615.6 586.2 557.8 530.5 504.3 479.3 455.5 433.1 412.1 392.6 358.4 330.7 260 628.9 600.2 572.5 545.9 520.4 496.0 472.9 451.0 430.5 411.4 377.6 349.9 280 641.8 613.7 586.6 560.6 535.6 511.9 489.3 467.9 447.8 429.1 395.7 368.0 300 654.2 626.6 600.1 574.6 550.2 526.9 504.8 483.9 464.2 445.8 412.8 385.1 D2.7. Table 12. Thermal conductivity l of R134a in mW/(m K) Temperature in C Pressure in bar 35 30 25 15 10 5 0 5 10 20 30 1 108.9 106.8 5 109.1 107.0 104.8 102.6 100.4 10.43 10.86 11.28 11.69 12.10 12.51 13.31 14.10 98.22 96.02 93.80 91.56 89.31 13.80 10 109.3 107.2 105.0 102.9 14.53 100.7 98.50 96.31 94.10 91.89 89.65 85.12 80.47 15 109.5 107.4 105.3 20 109.7 107.6 105.5 103.1 100.9 98.77 96.59 94.40 92.20 89.99 85.50 80.91 103.3 101.2 99.04 96.87 94.70 92.52 90.32 85.88 81.34 25 109.9 107.8 30 110.1 108.1 105.7 103.6 101.4 99.30 97.15 95.00 92.83 90.65 86.25 81.76 105.9 103.8 101.7 99.56 97.43 95.29 93.14 90.97 86.61 35 110.3 82.18 108.3 106.2 104.1 101.9 99.83 97.70 95.57 93.44 91.29 86.97 82.58 40 45 110.5 108.5 106.4 104.3 102.2 100.1 97.97 95.86 93.74 91.61 87.32 82.98 110.7 108.7 106.6 104.5 102.4 100.3 98.24 96.14 94.03 91.92 87.67 83.37 50 110.9 108.9 106.8 104.8 102.7 100.6 98.51 96.42 94.33 92.23 88.01 83.75 60 111.3 109.3 107.3 105.2 103.2 101.1 99.03 96.97 94.90 92.83 88.68 84.50 9.576 20 10.01 D2.7 Properties of R134a (1,1,1,2-tetrafluoromethane) D2.7. Table 12. (continued) Temperature in C Pressure in bar 35 30 70 111.8 109.6 80 112.2 110.1 90 112.6 100 110 25 20 15 10 5 0 5 10 20 30 107.7 105.7 103.6 101.6 108.1 106.1 104.1 102.1 100.0 97.51 95.47 93.42 89.33 85.22 98.03 96.02 94.00 89.97 110.5 108.5 106.5 104.5 102.5 100.5 85.92 98.55 96.56 94.57 90.59 86.60 113.0 110.9 108.9 107.0 105.0 103.0 113.4 111.3 109.2 107.4 105.4 103.5 101.0 99.06 97.09 95.12 91.19 87.26 101.5 99.56 97.61 95.66 91.78 120 113.8 111.7 109.7 107.8 105.9 103.9 102.0 100.0 87.91 98.12 96.19 92.36 88.54 140 114.5 112.5 110.5 108.6 106.7 104.8 102.9 101.0 97.23 93.48 89.75 160 115.3 113.3 111.3 109.3 107.5 105.7 103.8 101.9 100.1 98.22 94.55 90.91 180 116.0 114.1 112.1 110.1 108.3 106.5 104.6 102.8 101.0 99.19 95.59 92.03 200 116.8 114.8 112.9 110.9 109.0 107.3 105.5 103.7 101.9 100.1 96.59 93.10 220 117.5 115.5 113.6 111.7 109.8 108.0 106.3 104.5 102.8 101.0 97.56 94.13 240 118.2 116.3 114.4 112.5 110.6 108.8 107.1 105.3 103.6 101.9 98.49 95.13 260 118.9 117.0 115.1 113.2 111.4 109.6 107.8 106.1 104.4 102.8 99.40 96.10 280 119.5 117.7 115.8 114.0 112.1 110.3 108.5 106.9 105.2 103.6 100.3 97.03 300 120.2 118.3 116.5 114.7 112.9 111.1 109.3 107.6 106.0 104.4 101.1 97.94 99.54 99.11 Temperature in C Pressure in bar 40 50 60 70 80 90 100 110 120 130 140 150 1 14.88 15.63 16.38 17.10 17.82 18.51 19.20 19.86 20.51 21.15 21.77 22.38 5 15.24 15.95 16.65 17.34 18.02 18.69 19.34 19.99 20.62 21.24 21.85 22.44 10 16.15 16.72 17.32 17.92 18.53 19.14 19.74 20.33 20.92 21.50 22.07 22.63 15 76.18 71.27 18.48 18.87 19.33 19.83 20.34 20.86 21.38 21.90 22.42 22.93 20 76.68 71.86 66.82 20.55 20.59 20.84 21.19 21.59 22.01 22.45 22.90 23.35 25 77.17 72.44 67.51 62.34 22.90 22.39 22.38 22.56 22.83 23.16 23.51 23.88 30 77.64 72.99 68.17 63.15 57.89 25.35 24.18 23.89 23.90 24.04 24.26 24.53 35 78.11 73.53 68.81 63.92 58.83 53.53 27.49 25.82 25.30 25.16 25.18 25.31 40 78.56 74.05 69.42 64.65 59.72 54.64 51.74 29.01 27.22 26.56 26.30 26.23 45 79.00 74.56 70.01 65.35 60.55 55.65 50.56 36.40 30.04 28.36 27.65 27.31 50 79.43 75.05 70.58 66.01 61.34 56.59 51.74 46.99 34.39 30.79 29.29 28.58 60 80.27 76.00 71.67 67.27 62.81 58.31 53.84 49.34 44.31 37.45 33.64 31.83 70 81.08 76.91 72.70 68.45 64.16 59.86 55.61 51.43 47.42 43.08 38.63 35.55 80 81.86 77.78 73.68 69.55 65.41 61.28 57.20 53.26 49.47 45.94 42.41 39.19 90 82.61 78.61 74.61 70.59 66.58 62.59 58.66 54.86 51.26 47.90 44.85 41.99 100 83.34 79.42 75.50 71.58 67.68 63.82 60.01 56.33 52.83 49.58 46.65 44.05 110 84.05 80.20 76.35 72.53 68.73 64.97 61.28 57.69 54.28 51.11 48.21 45.67 120 84.74 80.95 77.18 73.43 69.72 66.05 62.46 58.97 55.64 52.52 49.65 47.08 140 86.05 82.38 78.74 75.14 71.57 68.07 64.64 61.31 58.12 55.10 52.29 49.72 160 87.31 83.74 80.21 76.72 73.29 69.92 66.62 63.43 60.35 57.42 54.67 52.12 180 88.51 85.03 81.59 78.21 74.88 71.62 68.44 65.36 62.38 59.54 56.84 54.33 200 89.65 86.25 82.91 79.61 76.38 73.22 70.14 67.14 64.25 61.49 58.85 56.37 220 90.76 87.43 84.16 80.94 77.80 74.72 71.72 68.81 66.00 63.30 60.72 58.28 240 91.82 88.56 85.36 82.21 79.14 76.14 73.21 70.37 67.63 64.99 62.47 60.07 260 92.84 89.64 86.51 83.43 80.42 77.48 74.63 71.85 69.17 66.59 64.11 61.75 280 93.83 90.69 87.61 84.59 81.65 78.77 75.97 73.26 70.63 68.10 65.66 63.34 300 94.79 91.70 88.68 85.72 82.82 80.00 77.26 74.59 72.02 69.53 67.14 64.85 293 294 D2 Properties of Selected Important Pure Substances D2.7. Table 13. Dynamic viscosity of R134a in 106 Pa·s Temperature in C Pressure in bar 1 15 11.58 20 25 30 35 40 45 50 55 60 65 70 11.78 11.98 12.18 12.38 12.58 12.77 12.97 13.16 13.36 13.55 13.74 11.88 12.08 12.28 12.47 12.67 12.86 13.05 13.24 13.44 13.63 13.82 13.43 13.61 13.79 13.97 13.95 14.11 14.27 5 221.7 10 223.6 210.3 197.6 185.5 173.9 15 225.5 212.2 199.6 187.5 175.9 164.7 154.0 143.5 133.3 20 227.4 214.1 201.5 189.4 177.9 166.8 156.1 145.7 135.7 125.7 115.9 25 229.3 216.0 203.4 191.4 179.8 168.8 158.2 147.9 138.0 128.2 118.6 108.9 30 231.1 217.9 205.3 193.2 181.8 170.8 160.2 150.0 140.2 130.6 121.1 111.8 35 232.9 219.7 207.1 195.1 183.7 172.7 162.2 152.1 142.3 132.9 123.6 114.4 40 234.8 221.5 208.9 197.0 185.6 174.7 164.2 154.1 144.4 135.1 125.9 117.0 45 236.6 223.3 210.8 198.8 187.4 176.5 166.1 156.1 146.5 137.2 128.2 119.4 50 238.4 225.1 212.6 200.6 189.2 178.4 168.0 158.1 148.5 139.3 130.4 121.7 60 241.9 228.7 216.1 204.2 192.8 182.0 171.7 161.8 152.4 143.3 134.5 126.0 70 245.4 232.2 219.6 207.7 196.4 185.6 175.3 165.5 156.1 147.1 138.5 130.1 80 248.9 235.6 223.1 211.1 199.8 189.1 178.8 169.1 159.7 150.8 142.2 134.0 90 252.4 239.1 226.5 214.5 203.2 192.5 182.3 172.5 163.2 154.3 145.8 137.7 100 255.8 242.5 229.8 217.9 206.6 195.8 185.6 175.9 166.6 157.8 149.3 141.3 110 259.2 245.8 233.2 221.2 209.9 199.1 188.9 179.2 170.0 161.1 152.7 144.7 120 262.5 249.1 236.5 224.5 213.1 202.4 192.2 182.5 173.2 164.4 156.0 148.0 140 269.2 255.7 243.0 230.9 219.5 208.7 198.5 188.8 179.5 170.8 162.4 154.4 160 275.8 262.2 249.3 237.2 225.8 214.9 204.7 194.9 185.7 176.9 168.5 160.5 180 282.3 268.6 255.6 243.4 231.9 221.0 210.7 200.9 191.6 182.8 174.4 166.4 200 288.7 274.9 261.9 249.6 238.0 227.0 216.6 206.7 197.4 188.5 180.1 172.1 220 295.1 281.1 268.0 255.6 243.9 232.9 222.4 212.5 203.1 194.1 185.7 177.6 240 301.4 287.4 274.1 261.6 249.8 238.7 228.1 218.1 208.6 199.7 191.1 183.0 260 307.7 293.5 280.2 267.5 255.6 244.4 233.7 223.7 214.1 205.1 196.5 188.3 280 314.0 299.7 286.2 273.4 261.4 250.1 239.3 229.2 219.5 210.4 201.7 193.5 300 320.2 305.8 292.1 279.3 267.1 255.7 244.8 234.6 224.9 215.7 206.9 198.6 12.88 13.06 13.25 14.83 Temperature in C Pressure in bar 75 80 90 95 100 105 110 115 120 130 140 150 1 13.93 14.12 14.50 14.68 14.87 15.05 15.24 15.42 15.60 15.97 16.33 16.68 5 14.00 14.19 14.57 14.75 14.94 15.12 15.30 15.48 15.67 16.03 16.38 16.74 10 14.16 14.34 14.70 14.88 15.06 15.24 15.42 15.60 15.78 16.13 16.48 16.83 15 14.43 14.59 14.93 15.10 15.27 15.44 15.61 15.78 15.95 16.30 16.64 16.98 20 14.92 15.04 15.31 15.45 15.60 15.75 15.90 16.06 16.21 16.53 16.86 17.18 25 15.91 15.94 16.01 16.11 16.21 16.33 16.46 16.59 16.86 17.15 17.45 30 102.3 99.08 92.58 17.19 17.01 16.94 16.94 16.98 17.04 17.12 17.32 17.55 17.81 35 105.3 96.08 75.48 19.50 18.55 18.18 18.00 17.92 17.89 17.95 18.08 18.27 40 108.1 99.23 80.49 69.46 51.23 20.95 19.87 19.33 19.06 18.82 18.79 18.86 45 110.7 102.1 84.55 75.04 64.06 46.14 24.51 22.02 20.99 20.06 19.73 19.62 50 113.2 104.8 88.06 79.38 70.05 59.30 44.07 28.78 24.56 21.96 21.00 20.60 60 117.8 109.8 94.08 86.27 78.35 70.24 61.74 52.48 42.53 29.42 25.24 23.53 70 122.1 114.3 99.25 91.95 84.73 77.52 70.30 63.13 55.89 41.99 32.69 28.24 80 126.1 118.4 103.9 96.90 90.08 83.39 76.81 70.29 64.04 52.07 41.79 34.76 90 129.9 122.4 108.1 101.4 94.80 88.43 82.22 76.18 70.32 59.37 49.64 41.76 100 133.5 126.1 112.1 105.5 99.09 92.92 86.96 81.20 75.64 65.19 55.97 48.07 D2.7 Properties of R134a (1,1,1,2-tetrafluoromethane) D2.7. Table 13. (continued) Temperature in C Pressure in bar 75 80 90 95 100 105 110 115 120 130 140 150 110 137.0 129.7 115.8 109.3 103.1 120 140.4 133.1 119.4 112.9 106.8 100.9 97.04 91.24 85.66 80.29 70.24 61.23 53.52 95.18 89.73 84.50 74.72 65.92 140 146.8 139.6 126.0 119.7 113.7 107.9 102.3 58.22 97.04 91.97 82.53 73.99 66.41 160 152.9 145.7 132.3 126.0 120.0 114.3 108.8 103.6 180 158.8 151.6 138.1 131.9 125.9 120.2 114.8 109.6 104.7 98.61 89.33 80.93 73.41 95.48 87.14 200 164.5 157.2 143.8 137.5 131.5 125.9 120.4 115.3 110.3 101.2 79.64 92.83 85.32 220 170.0 162.7 149.2 142.9 136.9 131.2 125.8 120.6 115.7 106.5 240 175.3 168.0 154.4 148.1 142.1 136.4 130.9 125.7 120.8 111.5 103.2 98.14 90.60 260 180.6 173.2 159.5 153.2 147.1 141.4 135.9 130.7 125.7 116.4 107.9 100.3 280 185.7 178.3 164.5 158.1 152.0 146.2 140.7 135.4 130.4 121.0 112.5 104.8 300 190.8 183.3 169.4 162.9 156.8 150.9 145.4 140.1 135.0 125.6 117.0 109.2 95.56 D2.7. Table 14. Kinematic viscosity n of R134a in 107 m2/s Temperature in C Pressure in bar 1 15 20 25 30 35 40 45 50 55 60 65 70 26.6 27.5 28.5 29.5 30.5 31.6 32.6 33.6 34.7 35.8 36.9 38.0 5 1.78 5.01 5.22 5.44 5.66 5.88 6.11 6.33 6.56 6.78 7.01 7.24 10 1.79 1.71 1.64 1.56 1.49 2.63 2.76 2.89 3.01 3.14 3.26 3.39 15 1.81 1.72 1.65 1.57 1.50 1.43 1.36 1.30 1.24 1.90 2.00 2.09 20 1.82 1.74 1.66 1.58 1.51 1.44 1.38 1.31 1.25 1.19 1.13 1.42 25 1.83 1.75 1.67 1.60 1.53 1.46 1.39 1.33 1.27 1.20 1.14 1.08 30 1.84 1.76 1.68 1.61 1.54 1.47 1.40 1.34 1.28 1.22 1.16 1.10 35 1.85 1.77 1.69 1.62 1.55 1.48 1.42 1.35 1.29 1.23 1.18 1.12 40 1.86 1.78 1.71 1.63 1.56 1.49 1.43 1.37 1.31 1.25 1.19 1.14 45 1.87 1.79 1.72 1.64 1.57 1.51 1.44 1.38 1.32 1.26 1.21 1.15 50 1.89 1.80 1.73 1.65 1.58 1.52 1.45 1.39 1.33 1.27 1.22 1.17 60 1.91 1.83 1.75 1.68 1.61 1.54 1.48 1.41 1.36 1.30 1.25 1.19 70 1.93 1.85 1.77 1.70 1.63 1.56 1.50 1.44 1.38 1.32 1.27 1.22 80 1.95 1.87 1.79 1.72 1.65 1.58 1.52 1.46 1.40 1.35 1.29 1.24 90 1.97 1.89 1.81 1.74 1.67 1.60 1.54 1.48 1.42 1.37 1.32 1.27 100 1.99 1.91 1.83 1.76 1.69 1.63 1.56 1.50 1.45 1.39 1.34 1.29 110 2.01 1.93 1.85 1.78 1.71 1.65 1.58 1.52 1.47 1.41 1.36 1.31 120 2.03 1.95 1.87 1.80 1.73 1.67 1.60 1.54 1.49 1.43 1.38 1.33 140 2.07 1.99 1.91 1.84 1.77 1.71 1.64 1.58 1.53 1.47 1.42 1.37 160 2.11 2.03 1.95 1.88 1.81 1.74 1.68 1.62 1.56 1.51 1.46 1.41 180 2.15 2.07 1.99 1.92 1.85 1.78 1.72 1.66 1.60 1.55 1.49 1.45 200 2.19 2.11 2.03 1.96 1.88 1.82 1.75 1.69 1.64 1.58 1.53 1.48 220 2.23 2.15 2.07 1.99 1.92 1.85 1.79 1.73 1.67 1.62 1.56 1.51 240 2.27 2.18 2.10 2.03 1.96 1.89 1.82 1.76 1.71 1.65 1.60 1.55 260 2.31 2.22 2.14 2.07 1.99 1.92 1.86 1.80 1.74 1.68 1.63 1.58 280 2.35 2.26 2.18 2.10 2.03 1.96 1.89 1.83 1.77 1.72 1.66 1.61 300 2.38 2.30 2.21 2.14 2.06 1.99 1.93 1.87 1.81 1.75 1.70 1.65 295 296 D2 Properties of Selected Important Pure Substances D2.7. Table 14. (continued) Temperature in C Pressure in bar 1 75 80 90 95 39.1 40.2 42.5 43.6 100 44.8 105 46.0 110 47.2 115 48.4 120 49.6 130 140 150 52.1 54.6 57.2 10.2 10.7 11.2 5 7.48 7.71 8.19 8.43 8.67 8.92 9.16 9.41 9.66 10 3.52 3.64 3.89 4.02 4.15 4.28 4.41 4.54 4.67 4.93 5.20 5.47 15 2.19 2.28 2.46 2.55 2.64 2.73 2.82 2.92 3.01 3.19 3.38 3.56 20 1.50 1.59 1.74 1.81 1.89 1.96 2.03 2.11 2.18 2.32 2.47 2.61 25 1.02 1.15 1.30 1.37 1.43 1.50 1.56 1.62 1.68 1.81 1.93 2.05 30 1.04 0.984 0.988 1.06 1.13 1.19 1.24 1.30 1.36 1.46 1.57 1.67 35 1.06 1.01 0.881 0.820 0.897 0.960 1.02 1.07 1.12 1.22 1.32 1.41 40 1.08 1.03 0.912 0.847 0.756 0.786 0.849 0.902 0.951 1.04 1.13 1.22 45 1.10 1.04 0.937 0.880 0.818 0.736 0.717 0.775 0.824 0.911 0.992 1.07 50 1.11 1.06 0.959 0.907 0.852 0.794 0.725 0.693 0.733 0.813 0.887 0.959 60 1.14 1.09 0.996 0.949 0.901 0.854 0.808 0.761 0.719 0.707 0.755 0.810 70 1.17 1.12 1.03 0.984 0.940 0.897 0.855 0.816 0.779 0.721 0.710 0.736 80 1.19 1.15 1.06 1.01 0.973 0.933 0.894 0.856 0.822 0.763 0.725 0.717 90 1.22 1.17 1.08 1.04 1.00 0.964 0.927 0.891 0.858 0.799 0.755 0.729 100 1.24 1.19 1.11 1.07 1.03 0.991 0.955 0.921 0.889 0.830 0.784 0.752 110 1.26 1.22 1.13 1.09 1.05 1.02 0.982 0.948 0.917 0.859 0.811 0.775 120 1.28 1.24 1.15 1.11 1.08 1.04 1.01 0.973 0.942 0.885 0.836 0.797 140 1.32 1.28 1.19 1.16 1.12 1.08 1.05 1.02 0.987 0.931 0.882 0.841 160 1.36 1.32 1.23 1.20 1.16 1.12 1.09 1.06 1.03 0.972 0.923 0.880 180 1.40 1.35 1.27 1.23 1.20 1.16 1.13 1.10 1.07 1.01 0.960 0.916 200 1.43 1.39 1.31 1.27 1.23 1.20 1.16 1.13 1.10 1.04 0.994 0.950 220 1.47 1.42 1.34 1.30 1.26 1.23 1.20 1.16 1.13 1.08 1.03 0.982 240 1.50 1.46 1.37 1.33 1.30 1.26 1.23 1.20 1.16 1.11 1.06 1.01 260 1.53 1.49 1.40 1.36 1.33 1.29 1.26 1.23 1.20 1.14 1.09 1.04 280 1.57 1.52 1.43 1.40 1.36 1.32 1.29 1.26 1.22 1.17 1.12 1.07 300 1.60 1.55 1.47 1.43 1.39 1.35 1.32 1.28 1.25 1.20 1.14 1.10 5 0 5 10 20 30 29.5 31.0 32.5 34.0 36.9 39.8 D2.7. Table 15. Thermal diffusivity a of R134a in 107 m2/s Temperature in C Pressure in bar 35 30 1 0.614 0.604 25 23.4 20 25.0 15 26.5 10 28.0 5 0.615 0.605 0.595 0.584 0.574 0.563 0.552 0.540 0.529 0.517 6.03 6.78 10 0.617 0.607 0.596 0.586 0.575 0.564 0.554 0.542 0.531 0.519 0.495 0.469 15 0.618 0.608 0.598 0.587 0.577 0.566 0.555 0.544 0.533 0.522 0.498 0.472 20 0.619 0.609 0.599 0.589 0.578 0.568 0.557 0.546 0.535 0.524 0.501 0.476 25 0.620 0.610 0.600 0.590 0.580 0.570 0.559 0.548 0.537 0.526 0.503 0.479 30 0.621 0.612 0.602 0.592 0.582 0.571 0.561 0.550 0.539 0.528 0.506 0.482 35 0.622 0.613 0.603 0.593 0.583 0.573 0.562 0.552 0.541 0.531 0.508 0.485 40 0.624 0.614 0.604 0.595 0.585 0.574 0.564 0.554 0.543 0.533 0.511 0.488 45 0.625 0.615 0.606 0.596 0.586 0.576 0.566 0.556 0.545 0.535 0.513 0.491 50 0.626 0.617 0.607 0.597 0.587 0.578 0.567 0.557 0.547 0.537 0.515 0.493 D2.7 Properties of R134a (1,1,1,2-tetrafluoromethane) D2.7. Table 15. (continued) Temperature in C Pressure in bar 35 30 25 20 15 10 5 0 5 10 20 30 60 0.628 0.619 0.610 0.600 0.590 0.581 0.571 0.561 0.551 0.541 0.520 0.499 70 0.631 0.621 0.612 0.603 0.593 0.583 0.574 0.564 0.554 0.544 0.524 0.504 80 0.633 0.623 0.614 0.605 0.596 0.586 0.577 0.567 0.558 0.548 0.528 0.508 90 0.635 0.626 0.617 0.608 0.598 0.589 0.580 0.570 0.561 0.551 0.532 0.513 100 0.637 0.628 0.619 0.610 0.601 0.592 0.583 0.573 0.564 0.555 0.536 0.517 110 0.640 0.630 0.621 0.612 0.603 0.594 0.585 0.576 0.567 0.558 0.540 0.521 120 0.642 0.632 0.623 0.615 0.606 0.597 0.588 0.579 0.570 0.561 0.543 0.525 140 0.646 0.637 0.628 0.619 0.611 0.602 0.593 0.585 0.576 0.567 0.550 0.533 160 0.650 0.641 0.632 0.623 0.615 0.607 0.598 0.590 0.581 0.573 0.556 0.539 180 0.654 0.645 0.636 0.627 0.619 0.611 0.603 0.595 0.587 0.578 0.562 0.546 200 0.657 0.649 0.640 0.631 0.623 0.615 0.607 0.599 0.591 0.584 0.568 0.552 220 0.661 0.652 0.644 0.636 0.627 0.619 0.612 0.604 0.596 0.588 0.573 0.558 240 0.664 0.656 0.648 0.639 0.631 0.623 0.616 0.608 0.601 0.593 0.578 0.563 260 0.668 0.660 0.651 0.643 0.635 0.627 0.619 0.612 0.605 0.598 0.583 0.568 280 0.671 0.663 0.655 0.647 0.639 0.631 0.623 0.616 0.609 0.602 0.587 0.573 300 0.674 0.666 0.658 0.650 0.643 0.635 0.627 0.620 0.613 0.606 0.592 0.578 100 110 120 130 140 150 Temperature in C Pressure in bar 1 40 50 60 70 80 90 42.7 45.6 48.5 51.3 54.1 57.0 59.8 62.5 65.3 68.0 70.7 73.4 10.0 10.7 11.3 11.8 12.4 13.0 13.6 14.2 5 7.48 8.14 8.79 9.42 10 2.91 3.38 3.79 4.17 4.53 4.88 5.21 5.53 5.85 6.16 6.47 6.76 15 0.445 0.414 2.02 2.36 2.66 2.93 3.19 3.43 3.66 3.89 4.10 4.31 20 0.449 0.419 0.385 1.34 1.67 1.93 2.16 2.37 2.56 2.75 2.92 3.09 25 0.453 0.424 0.392 0.352 0.955 1.27 1.51 1.71 1.89 2.06 2.22 2.36 30 0.457 0.429 0.398 0.362 0.312 0.728 1.03 1.25 1.43 1.59 1.74 1.87 35 0.460 0.434 0.404 0.371 0.328 0.255 0.611 0.889 1.09 1.25 1.39 1.52 40 0.464 0.438 0.410 0.378 0.340 0.286 0.081 0.567 0.807 0.983 1.13 1.25 45 0.467 0.442 0.415 0.385 0.351 0.306 0.222 0.239 0.563 0.762 0.915 1.04 50 0.470 0.446 0.420 0.392 0.360 0.321 0.264 0.136 0.345 0.576 0.740 0.871 60 0.477 0.454 0.429 0.404 0.376 0.344 0.307 0.257 0.206 0.307 0.474 0.614 70 0.482 0.460 0.438 0.414 0.389 0.362 0.333 0.301 0.267 0.260 0.330 0.442 80 0.488 0.467 0.445 0.423 0.400 0.376 0.351 0.326 0.303 0.288 0.302 0.359 90 0.493 0.473 0.452 0.431 0.410 0.388 0.366 0.345 0.326 0.313 0.313 0.336 100 0.498 0.478 0.459 0.438 0.418 0.398 0.378 0.359 0.343 0.331 0.327 0.337 110 0.502 0.484 0.465 0.445 0.426 0.407 0.389 0.372 0.356 0.345 0.339 0.343 120 0.507 0.489 0.470 0.452 0.434 0.416 0.398 0.382 0.368 0.357 0.350 0.350 140 0.515 0.498 0.481 0.463 0.447 0.430 0.414 0.400 0.387 0.376 0.369 0.365 160 0.523 0.506 0.490 0.474 0.458 0.443 0.428 0.414 0.402 0.392 0.384 0.379 180 0.530 0.514 0.498 0.483 0.468 0.454 0.440 0.427 0.415 0.405 0.397 0.391 200 0.537 0.521 0.506 0.491 0.477 0.463 0.450 0.438 0.427 0.417 0.408 0.402 220 0.543 0.528 0.513 0.499 0.486 0.472 0.460 0.448 0.437 0.427 0.419 0.412 240 0.549 0.534 0.520 0.506 0.493 0.480 0.468 0.457 0.446 0.437 0.428 0.421 260 0.554 0.540 0.526 0.513 0.500 0.488 0.476 0.465 0.455 0.445 0.437 0.429 280 0.559 0.546 0.532 0.520 0.507 0.495 0.483 0.473 0.462 0.453 0.445 0.437 300 0.564 0.551 0.538 0.525 0.513 0.502 0.490 0.480 0.470 0.460 0.452 0.444 297 298 D2 Properties of Selected Important Pure Substances D2.7. Table 16. Prandtl number Pr of R 134a Temperature in C Pressure in bar 15 20 25 30 35 40 45 50 55 60 65 70 1 0.750 0.746 0.744 0.742 0.740 0.739 0.738 0.738 0.738 0.738 0.739 0.740 5 3.53 0.830 0.814 0.802 0.794 0.787 0.781 0.777 0.774 0.772 0.770 0.769 10 3.54 3.46 3.39 3.33 3.27 0.905 0.875 0.854 0.839 0.828 0.819 0.813 15 3.54 3.47 3.39 3.33 3.27 3.22 3.18 3.14 3.12 0.942 0.909 0.886 20 3.55 3.47 3.40 3.33 3.27 3.22 3.17 3.13 3.11 3.09 3.10 1.06 25 3.55 3.47 3.40 3.33 3.27 3.22 3.17 3.13 3.10 3.07 3.07 3.08 30 3.56 3.48 3.41 3.34 3.27 3.22 3.17 3.12 3.09 3.06 3.05 3.05 35 3.56 3.48 3.41 3.34 3.28 3.22 3.17 3.12 3.08 3.05 3.03 3.02 40 3.57 3.49 3.41 3.34 3.28 3.22 3.17 3.12 3.08 3.04 3.02 3.00 45 3.58 3.50 3.42 3.35 3.28 3.22 3.17 3.12 3.07 3.04 3.01 2.98 50 3.58 3.50 3.42 3.35 3.29 3.22 3.17 3.12 3.07 3.03 3.00 2.97 60 3.60 3.51 3.43 3.36 3.29 3.23 3.17 3.12 3.07 3.03 2.99 2.95 70 3.61 3.52 3.45 3.37 3.30 3.24 3.18 3.12 3.07 3.02 2.98 2.94 80 3.62 3.54 3.46 3.38 3.31 3.25 3.18 3.13 3.07 3.02 2.98 2.94 90 3.64 3.55 3.47 3.39 3.32 3.25 3.19 3.13 3.08 3.03 2.98 2.94 100 3.65 3.56 3.48 3.41 3.33 3.26 3.20 3.14 3.08 3.03 2.98 2.94 110 3.67 3.58 3.50 3.42 3.34 3.28 3.21 3.15 3.09 3.04 2.99 2.94 120 3.68 3.59 3.51 3.43 3.36 3.29 3.22 3.16 3.10 3.05 2.99 2.94 140 3.71 3.62 3.54 3.46 3.38 3.31 3.24 3.18 3.12 3.06 3.01 2.96 160 3.74 3.65 3.57 3.48 3.41 3.33 3.27 3.20 3.14 3.08 3.03 2.97 180 3.78 3.68 3.60 3.51 3.43 3.36 3.29 3.22 3.16 3.10 3.05 2.99 200 3.81 3.71 3.63 3.54 3.46 3.39 3.32 3.25 3.19 3.12 3.07 3.01 220 3.84 3.75 3.66 3.57 3.49 3.42 3.34 3.28 3.21 3.15 3.09 3.03 240 3.88 3.78 3.69 3.60 3.52 3.44 3.37 3.30 3.24 3.17 3.11 3.06 260 3.91 3.81 3.72 3.63 3.55 3.47 3.40 3.33 3.26 3.20 3.14 3.08 280 3.94 3.85 3.75 3.66 3.58 3.50 3.43 3.36 3.29 3.22 3.16 3.11 300 3.98 3.88 3.79 3.70 3.61 3.53 3.46 3.38 3.32 3.25 3.19 3.13 Temperature in C Pressure in bar 75 80 90 95 100 105 110 115 120 130 140 150 1 0.741 0.742 0.746 0.748 0.750 0.752 0.755 0.757 0.760 0.766 0.773 0.779 5 0.768 0.768 0.769 0.769 0.771 0.772 0.773 0.775 0.777 0.782 0.787 0.793 10 0.807 0.804 0.799 0.797 0.797 0.796 0.796 0.797 0.798 0.801 0.804 0.809 15 0.869 0.856 0.839 0.833 0.829 0.826 0.823 0.822 0.821 0.821 0.823 0.826 20 0.993 0.951 0.902 0.886 0.875 0.866 0.859 0.854 0.850 0.845 0.844 0.845 25 3.14 1.20 1.02 0.979 0.949 0.927 0.911 0.898 0.889 0.876 0.870 0.867 30 3.07 3.15 1.36 1.18 1.09 1.03 0.993 0.966 0.945 0.918 0.902 0.894 35 3.03 3.07 3.46 2.11 1.47 1.25 1.14 1.08 1.03 0.976 0.945 0.927 40 3.00 3.02 3.19 3.58 9.31 2.03 1.50 1.29 1.18 1.06 1.00 0.970 45 2.97 2.98 3.06 3.22 3.69 7.68 3.00 1.82 1.46 1.20 1.08 1.03 50 2.95 2.95 2.98 3.05 3.23 3.70 5.32 3.57 2.13 1.41 1.20 1.10 60 2.93 2.91 2.89 2.90 2.93 3.00 3.14 3.38 3.49 2.30 1.59 1.32 70 2.91 2.88 2.84 2.83 2.82 2.83 2.85 2.88 2.91 2.78 2.15 1.66 80 2.90 2.87 2.81 2.79 2.77 2.75 2.74 2.73 2.71 2.65 2.40 2.00 90 2.90 2.86 2.79 2.76 2.74 2.71 2.69 2.66 2.63 2.56 2.41 2.17 100 2.89 2.85 2.78 2.75 2.72 2.69 2.66 2.63 2.59 2.51 2.40 2.23 D2.7 Properties of R134a (1,1,1,2-tetrafluoromethane) D2.7. Table 16. (continued) Temperature in C Pressure in bar 75 80 90 95 100 105 110 115 120 130 140 150 110 2.90 2.85 2.78 2.74 2.71 2.67 2.64 2.61 2.57 2.49 2.39 2.26 120 2.90 2.86 2.78 2.74 2.70 2.67 2.63 2.60 2.56 2.48 2.39 2.28 140 2.91 2.86 2.78 2.74 2.70 2.66 2.63 2.59 2.55 2.48 2.39 2.30 160 2.92 2.88 2.79 2.75 2.71 2.67 2.63 2.59 2.56 2.48 2.41 2.33 180 2.94 2.89 2.80 2.76 2.72 2.68 2.64 2.60 2.56 2.49 2.42 2.35 200 2.96 2.91 2.82 2.77 2.73 2.69 2.65 2.61 2.58 2.51 2.44 2.37 220 2.98 2.93 2.84 2.79 2.75 2.71 2.67 2.63 2.59 2.52 2.45 2.39 240 3.00 2.95 2.86 2.81 2.77 2.73 2.69 2.65 2.61 2.54 2.47 2.41 260 3.03 2.97 2.88 2.83 2.79 2.75 2.71 2.67 2.63 2.56 2.49 2.42 280 3.05 3.00 2.90 2.85 2.81 2.77 2.73 2.69 2.65 2.58 2.51 2.45 300 3.07 3.02 2.92 2.87 2.83 2.79 2.75 2.71 2.67 2.60 2.53 2.47 5 1. Bibliography Tillner-Roth R, Baehr HD (1994) An international standard formulation of the thermodynamic properties of 1,1,1,2-tetrafluoroethane (HFC-134a). J Phys Chem Ref Data 23:657–729 2. 3. Baehr HD, Tillner-Roth R (1995) Thermodynamische Eigenschaften umweltverträglicher Kältemittel. Springer, Berlin Krauss RJ, Luettmer-Strathmann J, Sengers JV, Stephan K (1993) Transport properties of 1,1,1,2-tetrafluoroethane (R134a). Int J Thermophys 14:951–988 299 D3 Properties of Pure Fluid Substances D3.1 Liquids and Gases Michael Kleiber1 . Ralph Joh2 1 2 Uhde GmbH, Bad Soden, Germany Siemens AG, Frankfurt, Germany In the previous edition, this section containing thermophysical data of 275 compounds had been supplemented by correlations for temperature-dependent properties in order to give a better opportunity for interpolation and, with the appropriate caution, extrapolation. With the help of these correlations, the user can make use of the data in process simulation programs. Most of the data points given in the tables have been obtained by regression of experimental data from the literature or the relevant databanks. During this regression, a careful evaluation of the data has been performed, and outliers have been removed from the database. The equations listed below have been used for this regression. The final correlations are at least valid in the temperature range where data points are given in the tables. Although the correlations are usually suitable for extrapolation, one should be careful to go beyond this range. Especially when polynoms are used, a plausible curvature should be maintained (see > Chap. D1). In comparison to the previous German edition of the VDI Heat Atlas, for the liquid density, the liquid viscosity, the enthalpy of vaporization and the specific heat capacities of liquids and ideal gases the new PPDS equations have been used. Currently, these equations seem to be the most accurate ones and show a reasonable extrapolation behavior. For the vapor pressure, the 2.5-5-form of the Wagner equation is used, which performs slightly better than the well established 3-6-form. Whenever it was possible, high-precision equations of state have been used to obtain artificial data points as the basis for the regression. On the other hand, many values for transport properties, especially for gases, have been obtained by the estimation methods described in > Chap. D1. In general, all the values and correlations are not the absolutely correct ones but refer to the best possible data according to the knowledge of the authors. Like all data collections, also this one cannot claim completeness or absolute reliability. The authors are grateful for hints on mistakes and general improvements of this chapter. The correlation equations for the temperature-dependent properties are: Liquid density rliq kg=m3 ¼ rc T 0:35 T 2=3 þ A 1 þB 1 Tc Tc kg=m3 4=3 T T þC 1 þD 1 Tc Tc VDI-GVC (ed.), VDI Heat Atlas, DOI 10.1007/978-3-540-77877-6_12, # Springer-Verlag Berlin Heidelberg 2010 ð1Þ Dynamic viscosity of liquids " # C T 1=3 C T 4=3 þB ¼ E exp A Pa s T D T D ð2Þ When Eq. (2) is programmed, it must be taken care that the term in brackets (C T)/(T D) sometimes turns out to be negative, so that it makes sense to write in these cases and CT T D CT T D 1=3 T C 1=3 ¼ T D 4=3 T C 1=3 C T ¼ T D T D ð2aÞ Dynamic viscosity of gases 2 3 4 T T T T þD þE ¼AþB þC Pa s K K K K Thermal conductivity of liquids 2 3 4 l T T T T þD þE ¼AþB þC W=mK K K K K ð3Þ ð4Þ Thermal conductivity of gases 2 3 4 l T T T T þD þE ¼AþB þC W=mK K K K K ð5Þ Surface tension 2 3 s T BþCðT=Tc ÞþDðT =Tc Þ þE ðT =Tc Þ ¼A 1 N=m Tc ð6Þ Vapor pressure " ps T c T T 1:5 T 2:5 A 1 ln ¼ þC 1 þB 1 pc T Tc Tc Tc 5 # T þD 1 Tc ð7Þ Specific heat capacity of liquids A T T 2 cPliq ¼R þ B þ C 1 þ D 1 Tc Tc 1 TTc 3 4 ! T T þE 1 þF 1 Tc Tc ð8Þ 302 D3 Properties of Pure Fluid Substances Equation (8) reduces to a polynomial if the first parameter A is set to 0. For many substances, only few data points are known so that it is not justified to fit all the parameters. In these cases, extrapolation beyond the range of validity should be avoided. Enthalpy of vaporization " T 1=3 T 2=3 T þB 1 þC 1 Dhv ¼RTc A 1 Tc Tc Tc # ð9Þ T 2 T 6 þD 1 þE 1 Tc Tc Specific heat capacity of ideal gases 2 cPid T A ¼ B þ ðC BÞ 1 R AþT AþT 2 3 !# ð10Þ T T T þG þF DþE AþT AþT AþT The symbols are explained in > Chap. D1. If the data points are recalculated from the parameters, small deviations due to approximation errors of the parameters might occur. D3.1. Table 1. Caloric and critical data Substance Formula Molecular Melting weight temperature g/mol C Enthalpy of fusion J/g Boiling point at 1.013 bar C Enthalpy of vaporization at 1.013 bar J/g Critical Critical temperature pressure K bar Critical density Acentric kg/m3 factor Elements Xenon Xe 131.29 111.9 17.5 108.1 95.6 289.73 58.42 1103 0.004 Krypton Kr 83.80 157.4 19.6 153.4 107.1 209.48 55.25 910 0.001 Argon Ar 39.95 189.4 29.6 185.9 161.1 150.69 48.63 536 0.002 Neon Ne 20.18 248.6 16.3 246.1 85.8 44.49 26.79 482 0.039 Helium He 0.384 Air 4.00 271.4 12.5 268.9 20.8 5.20 2.27 70 28.96 210.1 25.7 194.2 191.9 132.53 37.86 343 0.038 Hydrogen H2 2.02 259.3 58.1 252.8 459.2 33.19 13.15 30 0.219 Nitrogen N2 28.01 210.1 25.7 195.8 199.2 126.19 33.96 313 0.037 Oxygen O2 32.00 218.8 13.9 183.0 213.1 154.60 50.46 427 0.022 Sulfur S 32.06 115.3 53.9 444.2 277.4 1312.95 182.08 203 0.246 Fluorine F2 38.00 219.7 13.4 188.1 174.3 144.41 52.40 593 0.051 Chlorine Cl2 70.91 101.0 90.3 34.0 288.0 416.96 79.91 577 0.087 Bromine Br2 159.82 7.3 66.1 58.7 186.5 584.15 103.00 1183 0.129 Iodine I2 253.80 113.7 61.1 184.4 165.3 819.15 116.54 1637 0.112 Hydrogen fluoride HF 20.01 83.4 228.9 19.5 380.5 461.15 64.80 290 0.381 Hydrogen chloride HCl 36.46 114.3 54.9 85.1 448.3 324.65 83.10 450 0.131 Hydrogen bromide HBr Hydrogen iodide HI Hydrogen cyanide Anorganic compounds 80.92 86.9 29.7 66.6 220.3 363.15 85.52 809 0.073 127.91 50.9 22.5 35.4 158.4 423.85 83.10 1049 0.038 HCN 27.02 13.3 311.0 25.7 998.6 456.65 53.90 194 0.410 Water H2O 18.02 0.0 333.1 100.0 2256.6 647.10 220.64 322 0.344 Hydrogen sulfide H2S 34.08 85.5 69.7 60.3 546.5 373.10 89.99 349 0.100 0.256 Ammonia NH3 17.03 77.8 332.2 33.3 1369.2 405.50 113.59 225 Nitric oxide NO 30.01 161.0 76.7 151.8 452.6 180.15 64.80 517 0.583 Nitrogen dioxide NO2 46.01 11.3 318.4 21.2 720.5 431.15 101.32 558 0.851 Nitrous oxide N2O 44.01 90.9 148.6 88.5 374.4 309.52 72.45 454 0.162 Dinitrogentetroxide N2O4 92.01 11.3 159.2 21.3 358.4 431.10 101.32 1115 0.853 Cyanogen C2N2 52.04 27.9 155.8 21.1 448.8 400.15 59.78 267 0.279 Phosphorus trichloride PCl3 137.33 92.0 51.6 75.0 216.9 563.15 56.70 528 0.220 Cyanogen chloride ClCN 61.47 6.5 185.3 12.8 435.1 449.05 59.90 377 0.323 Silane SiH4 32.12 184.7 20.8 112.0 374.5 269.75 48.40 242 0.093 Tetrachlorosilane SiCl4 169.90 68.8 45.1 57.2 165.4 507.05 35.90 521 0.232 Liquids and Gases D3.1 D3.1. Table 1. (continued) Substance Formula Melting Molecular temperature weight g/mol C Enthalpy of fusion J/g Boiling point at 1.013 bar C Enthalpy of vaporization at 1.013 bar J/g 191.5 214.7 Carbon monoxide CO 28.01 205.0 30.0 Carbon dioxide CO2 44.01 56.6 204.9 Carbon suboxide C3O2 68.03 112.2 79.4 6.4 Carbonyl sulfide COS 60.07 138.9 78.7 Phosgene CCl2O 98.92 127.9 58.0 Carbon disulfide CS2 76.14 111.6 Sulfur dioxide SO2 64.06 Sulfur trioxide SO3 80.06 Sulfuryl chloride Cl2SO2 134.97 54.1 Sulfur hexafluoride SF6 146.05 50.8 34.4 Critical Critical temperature pressure bar K Critical density Acentric kg/m3 factor 132.86 34.98 304 304.13 73.77 468 0.050 0.224 363.8 427.58 69.44 383 0.522 50.2 309.0 378.77 63.69 447 0.098 7.7 249.3 455.05 56.74 521 0.201 57.7 46.2 353.3 552.05 79.00 476 0.121 73.2 115.5 10.0 389.1 430.64 78.76 525 0.255 16.8 94.1 44.5 509.0 490.85 82.10 631 0.424 69.4 222.1 545.05 46.10 577 0.176 318.88 37.66 742 0.215 Organic compounds containing sulfur Methyl mercaptan CH4S 48.11 123.0 122.7 6.0 511.0 469.95 72.30 332 0.158 Ethyl mercaptan C2H6S 62.13 147.9 80.1 35.0 432.5 499.15 54.90 300 0.188 Dimethyl sulfide C2H6S 62.13 98.0 37.4 437.1 503.00 55.30 309 0.195 Diethyl sulfide C4H10S 90.19 103.9 132.0 92.2 352.4 557.15 39.60 284 0.290 Thiophene C4H4S 84.14 38.3 60.4 84.2 375.8 579.35 56.90 384 0.197 Halogenated hydrocarbons Fluoromethane (R41) CH3F 34.03 141.9 145.4 78.4 487.8 317.28 59.06 319 0.200 Difluoromethane (R32) CH2F2 52.02 136.1 99.2 51.7 382.0 351.26 57.83 424 0.277 Trifluoromethane (R23) CHF3 70.01 155.2 58.0 82.1 238.7 299.75 48.69 526 0.258 Tetrafluoromethane (R14) CF4 88.00 183.7 8.1 128.1 133.6 227.55 37.40 629 0.178 Methyl chloride 50.49 97.8 129.7 24.1 428.1 416.25 66.80 353 0.154 CH3Cl Methylene chloride CH2Cl2 84.93 95.1 54.2 39.8 333.9 510.05 60.80 459 0.198 Chloroform CHCl3 119.38 63.5 79.9 61.1 247.5 536.45 55.54 508 0.229 Carbon tetrachloride CCl4 153.82 22.9 16.5 76.7 194.2 556.35 45.60 557 0.193 Bromomethane CH3Br 94.94 93.6 63.0 3.6 255.2 467.05 80.00 609 0.191 Dibromomethane CH2Br2 173.85 52.5 43.2 97.0 194.4 611.05 71.70 779 0.209 Tribromomethane CHBr3 252.75 8.2 45.9 Tetrabromomethane CBr4 331.65 92.0 Chlorodifluoromethane (R22) CHClF2 86.47 157.4 Dichlorofluoromethane (R21) CHCl2F 102.92 Chlorotrifluoromethane (R13) CClF3 Dichlorodifluoromethane (R12) 149.2 149.3 696.05 60.90 883 0.156 189.3 120.6 724.80 96.31 1009 0.584 47.7 40.8 234.0 369.28 49.88 520 0.221 135.0 51.0 8.8 242.2 451.55 51.84 525 0.205 104.46 181.0 33.5 81.4 150.0 302.05 38.70 579 0.172 CCl2F2 120.91 158.0 34.2 29.8 166.2 385.12 41.36 565 0.179 Trichlorofluoromethane (R11) CCl3F 137.37 111.1 50.2 23.6 181.8 471.06 43.94 565 0.188 Ethyl fluoride (R161) C2H5F 48.06 143.3 124.8 37.7 418.3 375.30 50.28 293 0.220 Ethyl chloride C2H5Cl 64.52 136.4 69.0 12.3 383.0 460.35 52.70 323 0.192 Ethyl bromide C2H5Br 108.97 118.6 53.8 38.4 249.6 503.75 62.30 507 0.252 1,1-Dichloroethane C2H4Cl2 98.96 97.0 79.5 57.1 296.7 523.05 50.70 412 0.233 1,2-Dichloroethane C2H4Cl2 98.96 35.7 89.2 83.6 323.7 561.60 53.70 450 0.285 1,2-Dibromoethane C2H4Br2 187.87 9.8 58.3 131.5 191.3 650.20 54.77 718 0.207 1,1,1-Trifluoroethane (R143a) C2H3F3 84.04 111.4 73.7 47.2 226.7 345.86 37.62 431 0.262 1,1,1-Trichloroethane C2H3Cl3 133.41 30.0 17.6 74.1 223.0 545.05 43.00 475 0.217 1,1,2,2-Tetrachloroethane C2H2Cl4 167.85 43.9 54.6 145.9 225.5 645.05 40.90 517 0.253 Pentachloroethane C2HCl5 202.29 29.0 56.1 160.4 191.5 646.00 34.80 548 0.337 Hexachloroethane C2Cl6 236.74 186.8 41.2 695.05 33.40 575 0.238 303 304 D3 Properties of Pure Fluid Substances D3.1. Table 1. (continued) Substance Formula Melting Molecular temperature weight g/mol C Enthalpy of fusion J/g Boiling point at 1.013 bar C Enthalpy of vaporization at 1.013 bar J/g Critical Critical temperature pressure bar K Critical density Acentric kg/m3 factor 1,1,2,2C2Cl4F2 Tetrachlorodifluoroethane 203.83 24.9 18.2 93.0 156.8 551.05 34.34 581 0.290 1,1,2Trichlorotrifluoroethane C2Cl3F3 187.38 36.3 13.2 47.6 144.3 487.21 33.92 560 0.253 1,2C2Cl2F4 Dichlorotetrafluoroethane 170.92 92.5 8.8 3.6 135.7 418.85 32.60 581 0.252 1-Chloropropane C3H7Cl 78.54 122.9 70.6 46.5 354.7 503.15 45.80 318 0.227 1-Chlorobutane C4H9Cl 92.57 123.1 89.0 78.7 327.7 542.00 36.80 309 0.226 1-Chloropentane C5H11Cl 106.60 99.0 108.5 314.3 568.05 33.50 303 0.318 Chlorotrifluoroethene C2ClF3 116.47 158.1 47.7 28.8 224.2 379.15 40.53 549 0.242 Vinyl chloride C2H3Cl 62.50 153.9 75.9 13.8 353.5 432.05 56.70 349 0.100 1,1-Dichloroethene C2H2Cl2 96.94 122.6 67.2 31.7 269.6 482.05 51.90 433 0.272 Trichloroethene C2HCl3 131.39 84.9 86.2 242.4 571.05 49.10 513 0.210 Tetrachloroethene C2Cl4 165.83 22.4 63.1 121.0 210.5 620.05 44.90 669 0.214 Fluorobenzene C6H5F 96.10 42.3 117.6 85.2 329.4 560.05 45.51 357 0.248 Chlorobenzene C6H5Cl 112.56 45.3 84.9 131.9 316.4 632.35 45.19 366 0.250 Bromobenzene C6H5Br 157.01 30.8 67.7 156.0 239.4 670.20 45.19 485 0.251 Iodobenzene C6H5I 204.01 31.4 47.8 188.3 200.4 721.20 45.19 581 0.247 m-Chlorotoluene C7H7Cl 126.59 48.0 162.8 312.1 660.75 39.54 347 0.307 Benzyl chloride C7H7Cl 126.59 39.0 179.5 324.1 686.05 39.10 352 0.314 n-Alkanes Methane CH4 16.04 182.5 58.7 161.5 510.8 190.56 45.99 163 0.011 Ethane C2H6 30.07 182.9 95.1 88.6 489.5 305.32 48.72 206 0.100 Propane C3H8 44.10 187.7 79.9 42.1 426.1 369.82 42.48 221 0.152 n-Butane C4H10 58.12 138.4 80.2 0.5 385.9 425.13 37.96 228 0.201 n-Pentane C5H12 72.15 129.8 116.4 36.1 357.7 469.66 33.69 235 0.252 n-Hexane C6H14 86.18 95.4 151.8 68.7 334.9 507.79 30.42 223 0.300 n-Heptane C7H16 100.21 90.6 140.2 98.4 316.7 541.23 27.74 225 0.346 n-Octane C8H18 114.23 56.9 181.6 125.6 302.1 569.57 25.07 228 0.394 n-Nonane C9H20 128.26 53.5 120.6 150.8 288.5 594.55 22.82 234 0.444 n-Decane C10H22 142.29 29.6 201.8 174.1 276.3 617.70 21.01 234 0.488 n-Undecane C11H24 156.31 25.6 141.9 195.9 270.2 639.05 19.50 237 0.530 n-Dodecane C12H26 170.34 9.5 216.3 216.3 256.2 658.10 18.18 238 0.574 n-Tridecane C13H28 184.37 5.3 154.6 235.4 252.0 675.05 16.80 238 0.618 n-Tetradecane C14H30 198.39 6.0 227.2 253.5 242.5 693.05 15.70 239 0.643 n-Pentadecane C15H32 212.42 10.0 162.8 270.6 237.7 708.05 14.80 239 0.685 n-Hexadecane C16H34 226.45 18.3 235.6 286.7 231.6 723.05 14.00 240 0.717 n-Heptadecane C17H36 240.47 22.0 167.0 302.4 228.9 736.05 13.40 241 0.769 n-Octadecane C18H38 254.50 28.3 242.5 316.2 219.5 747.05 12.70 240 0.811 n-Nonadecane C19H40 268.53 32.0 170.6 330.1 214.2 758.05 12.10 240 0.852 n-Eicosane C20H42 282.56 36.5 247.3 343.7 204.8 769.63 11.28 234 0.875 Isobutane C4H10 58.12 159.6 78.1 11.7 365.4 407.81 36.29 226 0.184 2-Methyl butane C5H12 72.15 159.9 71.4 27.8 343.6 460.35 33.78 237 0.228 2,2-Dimethyl propane C5H12 72.15 16.6 43.6 9.5 315.5 433.74 31.96 238 0.196 2-Methyl pentane C6H14 86.18 153.6 72.7 60.2 323.0 497.70 30.43 236 0.280 3-Methyl pentane C6H14 86.18 162.9 61.5 63.3 326.6 504.65 31.20 234 0.270 2,2-Dimethyl butane C6H14 86.18 98.9 6.7 49.7 307.5 489.00 31.00 241 0.234 2,3-Dimethyl butane C6H14 86.18 128.0 9.3 57.9 317.6 500.00 31.51 240 0.248 Isoalkanes Liquids and Gases D3.1 D3.1. Table 1. (continued) Substance Formula Melting Molecular temperature weight g/mol C Enthalpy of fusion J/g Boiling point at 1.013 bar C Enthalpy of vaporization at 1.013 bar J/g Critical Critical temperature pressure bar K Critical density Acentric kg/m3 factor Olefins Ethylene C2H4 28.05 169.1 119.4 103.8 482.7 282.35 50.42 214 0.087 Propylene C3H6 42.08 85.4 71.4 47.7 439.5 365.57 46.65 223 0.141 1-Butene C4H8 56.11 185.4 68.6 6.3 392.2 419.29 40.06 238 0.192 1-Pentene C5H10 70.14 165.1 84.7 30.0 362.2 464.75 35.60 235 0.237 1-Hexene C6H12 84.16 139.9 111.1 63.5 339.1 504.05 31.40 238 0.280 93.7 319.5 537.40 29.20 244 0.344 136.4 121.3 306.4 567.05 26.80 240 0.392 34.4 489.5 393.15 50.90 243 0.132 1-Heptene C7H14 98.19 118.9 1-Octene C8H16 112.22 101.8 Propadiene C3H4 40.06 136.4 1,2-Butadiene C4H6 54.09 136.3 128.7 10.9 440.5 452.00 43.60 246 0.166 1,3-Butadiene C4H6 54.09 108.9 147.6 4.5 416.3 425.15 42.77 245 0.190 1,2-Pentadiene C5H8 68.12 137.4 111.0 44.8 398.6 500.05 38.00 247 0.154 trans-1,3-Pentadiene C5H8 68.12 87.4 104.9 42.0 392.2 500.05 37.40 247 0.116 1,4-Pentadiene C5H8 68.12 148.3 89.2 26.0 359.5 479.00 37.40 225 0.084 2,3-Pentadiene C5H8 68.12 125.7 95.8 48.3 407.4 497.00 38.00 231 0.218 Acetylene C2H2 26.04 80.9 144.8 308.35 61.39 230 0.190 Propyne C3H4 40.06 102.8 133.5 23.1 554.9 402.40 56.30 244 0.211 2-Butyne C4H6 54.09 32.3 170.7 27.0 492.0 473.20 48.70 245 0.238 1-Butyne C4H6 54.09 125.8 111.5 8.1 459.8 440.00 46.00 260 0.247 Cyclopropane C3H6 42.08 127.6 129.3 32.8 473.4 397.95 54.95 259 0.133 Cyclobutane C4H8 56.11 90.7 19.4 12.5 427.8 459.90 49.80 267 0.185 Cyclopentane C5H10 70.14 93.9 8.7 49.2 387.3 511.70 45.25 270 0.196 Methyl cyclopentane C6H12 84.16 142.4 82.3 71.8 347.6 532.75 37.90 264 0.231 Ethyl cyclopentane C7H14 98.19 138.5 70.0 103.4 326.6 569.50 34.00 262 0.270 Propyl cyclopentane C8H16 112.22 117.4 89.4 131.0 310.9 596.00 30.20 262 0.327 Butyl cyclopentane C9H18 126.24 108.0 89.6 Pentyl cyclopentane C10H20 140.27 83.0 Hexyl cyclopentane C11H22 154.30 73.0 Cyclohexane C6H12 84.16 6.5 Methyl cyclohexane C7H14 98.19 126.6 68.8 100.9 320.1 572.15 34.71 267 0.235 Ethyl cyclohexane C8H16 112.22 111.4 74.3 131.9 305.6 609.15 30.40 261 0.246 Acetylene and derivatives Naphthenes 32.6 156.4 286.7 621.00 27.20 261 0.372 180.5 278.1 656.20 24.67 257 0.329 203.1 273.0 660.10 21.38 259 0.476 80.7 356.1 553.60 40.75 273 0.209 Propyl cyclohexane C9H18 126.24 94.9 82.1 156.7 288.7 639.20 28.07 265 0.260 Butyl cyclohexane C10H20 140.27 74.8 100.9 181.0 278.2 667.00 25.70 263 0.274 Pentyl cyclohexane C11H22 154.30 72.9 203.7 275.8 667.85 22.04 264 0.430 Hexyl cyclohexane C12H24 168.32 45.3 224.7 270.6 693.60 22.60 249 0.468 Cyclopentene C5H8 68.12 135.1 49.4 44.3 396.6 507.00 48.00 278 0.196 Cyclohexene C6H10 82.15 103.5 40.1 83.0 371.3 560.45 43.50 282 0.211 Benzene C6H6 78.11 5.5 126.3 80.1 393.7 562.01 49.01 306 0.210 Toluene C7H8 92.14 95.0 72.0 110.6 360.8 591.75 41.26 292 0.266 Ethyl benzene C8H10 106.17 94.9 86.5 136.2 336.8 617.05 36.13 283 0.304 Propyl benzene C9H12 120.19 99.6 77.1 159.2 313.1 638.35 31.96 274 0.344 Butyl benzene C10H14 134.22 87.9 83.6 183.3 301.5 660.50 28.90 270 0.394 Pentyl benzene C11H16 148.25 75.1 102.8 205.6 286.5 679.90 26.04 270 0.438 Hexyl benzene C12H18 162.28 61.2 113.4 226.2 274.4 698.00 23.80 274 0.479 o-Xylene C8H10 106.17 25.3 128.1 144.4 347.6 630.25 37.32 287 0.312 m-Xylene C8H10 106.17 47.9 109.0 139.1 342.3 617.05 35.41 283 0.327 Aromatic compounds 305 306 D3 Properties of Pure Fluid Substances D3.1. Table 1. (continued) Substance Formula Melting Molecular temperature weight g/mol C Enthalpy of fusion J/g Boiling point at 1.013 bar C Enthalpy of vaporization at 1.013 bar J/g Critical Critical temperature pressure bar K Critical density Acentric kg/m3 factor p-Xylene C8H10 106.17 13.3 161.2 138.4 339.8 616.25 35.11 281 0.322 1,2,3-Trimethyl benzene C9H12 120.19 25.4 68.1 176.2 335.4 664.50 34.54 290 0.367 1,2,4-Trimethyl benzene C9H12 120.19 43.9 109.7 169.4 328.2 649.05 32.32 280 0.378 1,3,5-Trimethyl benzene C9H12 120.19 44.8 79.2 164.7 326.1 637.30 31.27 278 0.399 1,2,3,4-Tetramethyl benzene C10H14 134.22 6.3 83.7 205.1 321.1 693.00 31.10 283 0.417 1,2,3,5-Tetramethyl benzene C10H14 134.22 23.7 79.9 198.1 317.4 679.00 29.70 279 0.424 1,2,4,5-Tetramethyl benzene C10H14 134.22 79.3 156.5 196.7 317.9 676.00 29.00 279 0.422 Pentamethyl benzene C11H16 148.25 54.4 83.2 231.5 312.7 719.20 28.70 276 0.464 Hexamethyl benzene C12H18 162.28 165.5 127.2 263.5 311.5 758.00 27.70 274 0.496 Styrene C8H8 104.15 30.6 105.1 145.4 355.7 636.05 38.40 296 0.295 Isopropyl benzene C9H12 120.19 96.0 61.0 152.4 310.7 631.05 32.09 277 0.327 Biphenyl C12H10 154.21 69.2 120.5 255.3 315.5 789.00 38.50 310 0.365 Diphenyl methane C13H12 168.24 25.3 108.2 264.6 292.7 760.00 27.10 299 0.482 Triphenyl methane C19H16 244.34 92.2 90.0 359.5 245.5 865.00 22.00 325 0.574 Tetraphenyl methane C25H20 320.43 288.1 469.7 221.6 983.00 17.90 332 0.679 Naphthalene C10H8 128.17 80.3 148.1 218.0 338.5 748.45 40.50 315 0.304 1-Methylnaphthalene C11H10 142.20 30.5 48.8 244.5 327.3 772.00 36.00 306 0.342 2-Methylnaphthalene C11H10 142.20 34.6 85.2 241.6 325.1 761.00 35.00 306 0.378 1-Ethylnaphthalene C12H12 156.23 13.9 104.3 258.2 312.1 776.00 33.20 300 0.407 2-Ethylnaphthalene C12H12 156.23 7.3 94.1 258.4 307.3 771.00 31.70 300 0.421 Alcohols Methanol CH4O 32.04 97.7 100.3 64.5 1102.0 513.38 82.16 282 0.563 Ethanol C2H6O 46.07 114.1 107.0 78.3 850.1 513.90 61.48 276 0.644 1-Propanol C3H8O 60.10 126.3 89.4 97.2 696.9 536.75 51.75 274 0.621 1-Butanol C4H10O 74.12 89.4 126.4 117.8 585.3 563.05 44.23 270 0.591 1-Pentanol C5H12O 88.15 77.6 111.1 137.9 500.4 586.15 38.80 270 0.591 1-Hexanol C6H14O 102.18 44.6 150.7 157.7 448.7 611.35 35.10 268 0.578 1-Heptanol C7H16O 116.20 34.1 156.4 176.6 401.2 632.60 30.58 267 0.567 1-Octanol C8H18O 130.23 15.6 172.8 195.3 368.5 652.55 28.60 266 0.593 Isopropanol C3H8O 60.10 87.9 90.0 82.2 677.2 508.25 47.62 273 0.663 2-Methyl-1-propanol C4H10O 74.12 108.0 85.3 107.9 564.0 547.75 43.00 272 0.590 3-Methyl-1-butanol C5H12O 88.15 117.3 75.0 131.3 500.5 577.25 39.30 270 0.595 Ethylene glycol C2H6O2 62.07 13.1 160.4 197.1 867.5 719.15 82.00 325 0.513 1,3-Propylene glycol C3H8O2 76.09 26.8 93.3 214.1 733.7 724.05 95.00 351 0.738 Glycerol C3H8O3 92.09 18.3 198.5 287.7 718.6 850.05 75.00 349 0.512 Cyclohexanol C6H12O 100.16 23.5 17.8 160.9 451.7 650.05 42.60 311 0.370 Benzyl alcohol C7H8O 108.14 15.3 83.0 204.5 454.3 720.15 45.01 323 0.362 o-Cresol C7H8O 108.14 31.0 146.3 190.8 423.1 697.55 50.10 383 0.433 m-Cresol C7H8O 108.14 12.3 99.0 202.2 445.2 705.85 45.60 347 0.448 p-Cresol C7H8O 108.14 34.8 117.5 202.0 445.3 704.65 51.50 391 0.509 Phenol C6H6O 94.11 41.0 122.3 181.9 489.5 694.25 61.30 411 0.442 Formic acid CH2O2 46.02 8.5 275.9 100.6 480.7 588.05 58.10 368 0.316 Acetic acid C2H4O2 60.05 16.8 195.3 117.9 397.9 591.95 57.86 334 0.463 Propionic acid C3H6O2 74.08 20.8 143.9 141.2 419.4 600.85 46.17 318 0.576 Phenols Carboxylic acids Butyric acid C4H8O2 88.11 5.3 131.5 163.7 402.6 615.75 40.64 302 0.681 Valeric acid C5H10O2 102.13 29.4 71.7 175.6 395.3 634.05 38.90 304 0.647 Liquids and Gases D3.1 D3.1. Table 1. (continued) Substance Formula Melting Molecular temperature weight g/mol C Enthalpy of fusion J/g Boiling point at 1.013 bar C Enthalpy of vaporization at 1.013 bar J/g Critical Critical temperature pressure bar K Critical density Acentric kg/m3 factor Caproic acid C6H12O2 116.16 3.8 132.6 204.5 394.0 660.20 33.08 281 Acetic anhydride C4H6O3 102.09 73.0 102.8 139.5 394.5 606.05 40.00 352 0.454 Propionic anhydride C6H10O3 130.14 45.1 167.0 326.9 623.00 32.70 329 0.560 Chloroacetic acid C2H3ClO2 94.50 60.0 130.2 189.0 523.8 686.05 57.80 428 0.546 Dichloroacetic acid C2H2Cl2O2 128.94 13.5 95.7 193.9 379.5 686.05 51.70 487 0.555 Trichloroacetic acid C2HCl3O2 163.39 57.0 36.0 197.7 302.7 688.05 48.10 529 0.549 0.730 Ketones Ketene C2H2O 42.04 151.1 Acetone C3H6O 58.08 94.8 99.4 49.7 461.0 370.05 58.10 292 0.125 56.1 501.7 508.10 46.92 274 0.306 Methyl ethyl ketone C4H8O 72.11 86.8 Diethyl ketone C5H10O 86.13 39.0 116.3 79.6 441.2 535.55 41.50 270 0.323 134.6 101.9 393.3 561.00 37.40 256 Dipropyl ketone C7H14O 114.19 0.345 32.6 162.9 144.2 327.8 602.00 29.20 263 Acetophenone C8H8O 0.412 120.15 19.7 85.7 202.4 367.4 709.50 38.40 311 0.364 Benzophenone C13H10O 182.22 48.3 92.8 305.6 301.0 830.05 33.52 321 0.500 Ethers Dimethyl ether C2H6O 46.07 141.5 107.2 24.8 470.5 400.30 53.41 277 0.188 Diethyl ether C4H10O 74.12 116.4 97.0 34.5 357.7 466.63 36.51 264 0.283 Dipropyl ether C6H14O 102.18 123.3 105.4 90.0 310.4 530.60 30.28 268 0.369 Methyl propyl ether C4H10O 74.12 139.2 103.5 38.9 363.5 476.30 38.01 269 0.277 Ethyl propyl ether C5H12O 88.15 127.6 95.2 63.8 312.9 500.20 33.70 260 0.347 Ethylene oxide C2H4O 44.05 112.5 117.4 10.5 587.1 469.15 71.90 314 0.197 Furane C4H4O 68.08 85.6 55.9 31.4 400.2 490.15 55.00 312 0.203 1,4-Dioxane C4H8O2 88.11 11.8 145.7 101.4 389.5 587.05 52.08 370 0.279 Formaldehyde CH2O 30.03 92.0 234.8 19.1 769.2 408.05 65.90 261 0.281 Acetaldehyde C2H4O 44.05 123.0 73.1 20.3 595.7 466.05 55.50 286 0.262 Paraldehyde C6H12O3 132.16 12.7 104.8 124.2 285.1 579.05 35.00 362 0.437 Furfural C5H4O2 96.08 36.6 149.9 161.4 436.1 670.20 56.60 381 0.368 Benzaldehyde C7H6O 106.12 57.1 87.8 178.9 387.0 695.05 46.50 328 0.322 Salicylaldehyde C7H6O2 122.12 1.7 87.6 196.3 373.4 680.00 49.90 357 0.619 Methyl formate C2H4O2 60.05 99.0 125.4 31.8 470.6 487.25 60.00 349 0.255 Ethyl formate C3H6O2 74.08 79.6 124.3 54.0 405.6 508.45 47.40 324 0.276 Propyl formate C4H8O2 88.11 92.9 149.8 81.1 366.1 538.00 40.20 309 0.309 Methyl acetate C3H6O2 74.08 98.0 107.6 56.9 411.8 506.55 47.50 325 0.331 Ethyl acetate C4H8O2 88.11 83.5 118.9 77.1 366.2 523.20 38.30 308 0.361 Propyl acetate C5H10O2 102.13 95.0 109.7 101.5 336.1 549.75 33.60 296 0.390 Methyl propionate C4H8O2 88.11 87.6 114.6 79.5 368.4 530.60 40.04 312 0.347 Aldehydes Esters Ethyl propionate C5H10O2 102.13 73.9 120.4 99.0 333.8 546.05 33.62 296 0.389 Propyl propionate C6H12O2 116.16 75.9 129.1 122.5 315.1 568.60 30.60 299 0.449 Methyl butyrate C5H10O2 102.13 85.8 112.6 102.7 336.5 554.50 34.73 300 0.378 Ethyl butyrate C6H12O2 116.16 98.1 107.6 121.4 310.9 571.00 29.50 288 0.401 Methyl benzoate C8H8O2 136.15 12.4 71.5 199.4 323.5 693.05 35.90 312 0.415 Ethyl benzoate C9H10O2 150.18 34.8 94.6 213.3 300.3 698.00 31.80 307 0.477 Methyl salicylate C8H8O3 152.15 8.0 117.0 220.6 313.7 709.00 40.90 371 0.581 Amines Methyl amine CH5N 31.06 93.5 197.5 6.4 843.4 430.05 74.60 202 0.282 Ethyl amine C2H7N 45.09 81.0 207.4 16.8 608.8 456.15 56.20 218 0.285 Propyl amine C3H9N 59.11 83.0 256.4 47.6 510.4 496.95 47.40 227 0.280 n-Butyl amine C6H15N 73.14 49.1 202.4 77.5 442.0 531.95 42.00 236 0.329 Dimethyl amine C2H7N 45.09 92.3 131.8 7.0 590.0 437.25 53.40 250 0.298 307 308 D3 Properties of Pure Fluid Substances D3.1. Table 1. (continued) Substance Formula Melting Molecular temperature weight g/mol C Enthalpy of fusion J/g Boiling point at 1.013 bar C Enthalpy of vaporization at 1.013 bar J/g Critical Critical temperature pressure bar K Critical density Acentric kg/m3 factor Trimethyl amine C3H9N 59.11 117.1 110.7 3.1 391.1 433.25 41.02 233 0.206 Diethyl amine C6H15N 73.14 49.9 155.9 55.6 397.2 496.65 37.10 243 0.301 Triethyl amine C6H15N 101.19 114.8 84.2 88.8 304.8 535.15 30.40 260 0.318 Piperidine C5H11N 85.15 10.6 134.1 106.4 394.0 594.00 46.51 277 0.243 Pyridine C6H7N 79.10 41.7 104.7 115.2 447.6 620.00 56.30 311 0.239 Aniline C6H7N 93.13 6.0 113.2 183.9 479.5 699.05 53.10 345 0.378 N-methyl aniline C7H9N 107.16 57.1 88.8 195.6 423.2 701.50 52.00 287 0.475 N,N-dimethyl aniline C8H11N 121.18 2.5 95.4 193.4 352.4 687.20 36.30 261 0.402 0.426 N,N-diethyl aniline C10H15N 149.24 38.1 56.9 216.1 304.4 702.00 28.50 268 Phenylhydrazine C6H8N2 108.14 19.3 151.9 244.0 486.5 761.00 49.10 259 0.535 Diphenyl amine C12H11N 169.23 53.0 110.5 302.4 323.7 817.00 31.80 314 0.530 Nitriles Acetonitrile C2H3N 41.05 43.9 198.9 81.4 778.7 545.55 48.30 237 0.334 Propionitrile C3H5N 55.08 92.9 91.3 97.7 572.2 564.40 41.80 241 0.324 Butyronitrile C4H7N 69.11 111.9 72.7 117.4 500.0 582.30 37.90 249 0.371 Benzonitrile C7H5N 103.12 12.8 105.5 190.8 403.6 699.35 42.15 329 0.367 CH3NO 45.04 2.6 177.2 219.6 1136.0 771.00 78.00 276 0.412 Amides Formamide Nitroderivates Nitromethane CH3NO2 61.04 28.6 159.0 101.2 571.4 588.20 63.10 353 0.347 Nitrobenzene C6H5NO2 123.11 5.8 94.2 210.7 359.7 719.05 44.00 353 0.443 o-Nitrotoluene C7H7NO2 137.14 3.3 83.7 221.5 338.0 720.05 38.00 311 0.480 m-Nitrotoluene C7H7NO2 137.14 16.2 102.5 232.7 343.1 734.05 38.00 311 0.495 p-Nitrotoluene C7H7NO2 137.14 51.7 121.6 238.7 339.9 743.05 32.07 311 0.420 Br2 I2 Bromine Iodine 915.2 C2N2 PCl3 ClCN SiH4 SiCl4 CO CO2 C3O2 Cyanogen Phosphorus trichloride Cyanogen chloride Silane Tetrachlorosilane Carbon monoxide Carbon dioxide Carbon suboxide 1195.8 1148.1 1054.3 1566.7 1611.8 1154.5 384.5 453.5 1658.5 1097.1 927.4 1519.7 1221.9 1613.1 1472.7 N2O4 Dinitrogentetroxide 958.2 907.0 1702.5 1496.5 1018.2 NO2 638.7 833.0 N2O 1109.7 671.5 2640.9 Nitrogen dioxide NO Nitric oxide 884.3 701.9 2752.5 931.0 2857.0 1887.2 Nitrous oxide H2S NH3 H2O Water Hydrogen sulfide 1000.0 HCN Ammonia 716.3 HI Hydrogen cyanide 2006.9 916.3 Hydrogen iodide 2115.2 1009.6 HBr 1090.6 HCl Hydrogen bromide 1002.2 Hydrogen chloride 1063.6 1053.6 773.5 1480.4 1182.2 1575.8 876.9 1443.5 785.1 1450.1 610.4 787.4 998.0 687.2 2545.3 1779.5 825.2 952.4 3119.8 3187.2 HF 1124.3 1407.8 1467.0 Hydrogen fluoride Anorganic compounds Cl2 Chlorine 982.4 1418.3 1117.0 1517.7 810.7 1372.9 562.8 706.2 988.0 640.7 2387.8 1584.0 875.9 3015.5 839.4 1303.4 987.0 1414.0 653.2 1211.1 456.7 958.0 552.8 2061.5 739.5 2831.1 1165.8 794.2 1298.3 901.6 917.0 436.3 574.6 3874.9 2628.5 974.6 1162.5 865.0 3729.9 2397.7 982.2 799.0 3576.4 2113.1 677.5368 1139.6512 897.8727 571.9328 1212.2339 202.1021 1387.6330 1077.6858 1378.7351 276.2115 954.7062 1690.6809 1496.5803 531.7253 454.1590 1094.0233 576.9982 2159.6727 1716.6784 640.0181 232.8396 1995.2359 1672.7965 908.9019 2221.6476 1261.4775 387.1443 169.0516 67.0956 170.0410 142.0821 977.9054 448.0911 959.2381 37.9218 121.7294 307.7212 814.8977 45.2615 1242.5960 117.8757 1052.1005 1899.5222 665.5992 98.8936 135.9384 350.0132 968.0655 1031.3210 63.9457 153.0246 675.9615 310.6035 2299.1821 1668.4751 2252.1437 1584.2431 604.1720 257.0928 44.5981 698.1045 757.2956 31.5027 2233.6217 3863.9557 1813.2295 1000.6634 404.4247 576.1976 153.5039 399.5870 2479.8130 1907.8899 837.4455 1592.7803 273.3275 1545.2372 534.0575 180.0873 462.1796 697.6208 65.6236 15.3973 1091.0626 627.3536 676.7593 1296.9204 1347.9901 589.1905 449.5091 948.0463 1399.1215 870.3285 F2 Fluorine 3728.2432 1093.5278 S Sulfur 1526.3565 N2 O2 Nitrogen Oxygen 1353.2681 1113.0 495.5129 372.6904 119.8686 15.9601 841.3265 1927.9722 178.6945 217.6634 D 130.7723 962.2241 C 5203.2088 297.7907 342.4370 117.2877 B 5258.9909 895.4345 1612.0090 2097.8096 A 389.6108 1727.1 250 416.2389 1752.9 200 560.4689 1777.7 150 396.2376 1311.9 100 493.2507 1537.6 50 748.3728 1906.9 20 470.9224 1605.5 2256.2 0 777.4610 Ar Argon 2503.6 25 Equation (1) 410.6099 Kr 50 Temperature ( C) Air Xe Krypton Formula Xenon Elements Substance D3.1. Table 2. Density of saturated liquids in kg/m3 Liquids and Gases D3.1 309 SF6 Sulfur hexafluoride 899.9 C4H10S C4H4S Diethyl sulfide Thiophene 1188.8 1408.7 1571.7 1208.7 1307.4 930.7 1051.8 1451.9 1613.5 CH2F2 CHF3 CF4 CH3Cl CH2Cl2 Difluoromethane (R32) Trifluoromethane (R23) Tetrafluoromethane (R14) Methyl chloride Methylene chloride 1544.9 1646.4 835.4 992.5 CCl2F2 CCl3F C2H5F C2H5Cl Dichlorodifluoromethane (R12) Trichlorofluoromethane (R11) Ethyl fluoride (R161) Ethyl chloride 959.8 798.6 1591.1 1472.7 1271.2 1393.0 CClF3 Chlorotrifluoromethane (R13) 1361.3 1483.2 1435.3 1536.1 CHClF2 CHCl2F Chlorodifluoromethane (R22) Dichlorofluoromethane (R21) CBr4 Tetrabromomethane 2604.8 925.3 757.8 1534.3 1395.4 1116.7 1427.5 1281.2 2544.3 2663.5 CH2Br2 CHBr3 Dibromomethane Tribromomethane 1730.5 1857.1 CH3Br Bromomethane 896.1 721.4 1487.3 1328.3 922.9 1380.5 849.3 656.3 1413.4 1213.0 1304.7 1083.1 2811.7 1210.1 2417.6 2889.3 1589.8 1536.9 1435.6 1268.6 858.4 839.4 1029.1 807.4 813.8 802.6 825.6 2494.6 1676.2 1593.3 1629.5 1795.2 1492.2 1528.2 CHCl3 CCl4 1326.8 923.3 808.2 980.9 599.2 1064.7 836.7 848.5 838.9 868.1 1395.0 Chloroform 1363.9 962.6 1031.1 1054.9 678.8 1087.6 855.5 870.3 861.9 894.6 1558.5 Carbon tetrachloride 1008.6 1135.8 818.4 CH3F 755.0 1115.5 878.1 896.3 889.3 926.3 1716.1 Fluoromethane (R41) Halogenated hydrocarbons 921.0 915.7 C2H6S C2H6S Ethyl mercaptan Dimethyl sulfide 956.4 CH4S Methyl mercaptan Organic compounds containing sulfur 1851.6 1604.5 1782.4 1709.4 1925.6 1758.8 1668.5 1806.7 SO3 1216.4 1302.7 910.3 50 Cl2SO2 Sulf

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