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
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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. (23))
–
m
Number of shell-side passes
–
n
Number of tube-side passes, tube rows, turns, –
or items of equipment
NTU
Number of transfer units (Eqs. (11), (12))
–
P
Dimensionless temperature change (Eqs. (9)
and (10))
–
R
Heat capacity rate ratio (Eqs. (13) and (14))
–
T
_
W
Dimensionless temperature (Eq. (18))
–
Heat capacity flow rate (Eq. (6))
W/K
z
Number of baffles
–
e
NTU-ratio for cocurrent pass (Eq. (32))
–
Y
Dimensionless mean temperature difference
(Eq. (8))
–
W
Temperature
K
Subscripts
1, 2
Stream 1 or 2 in the heat exchanger
a, b
Ends of the heat exchanger
C
Pure countercurrent flow
w
Wall
z
Intermediate value
8
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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
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C5
Heat Exchanger Networks
C5 Heat Exchanger Networks
Xing Luo . 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
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3. Constantinou L, Gani R (1994) New group contribution method for estimating properties of pure compounds. AIChE J 40(10):1697–1710
4. Nannoolal Y, Rarey J, Ramjugernath D (2007) Estimation of Pure Component Properties, Part 2: Estimation of Critical Property Data by Group
Contribution. Fluid Phase Equilibria 252:1–27
5. Constantinou L, Gani R, O’Connell JP (1995) Estimation of the acentric
factor and the liquid molar volume at 298K using a new group contribution
method. Fluid Phase Equilibria 103:11–22
6. Nannoolal Y, Rarey J, Ramjugernath D, Cordes W (2004) Estimation of pure
component properties. Part 1: Estimation of the normal boiling point of
non-electrolyte organic compounds via group contributions and group
interactions. Fluid Phase Equilibria 226:45–63
7. Jakob A (1995) Thermodynamische Grundlagen der Kristallisation und ihre
Anwendung in der Modellentwicklung. Dissertation Universität Oldenburg
8. Gmehling J, Kolbe B (1988) Thermodynamik. Georg Thieme Verlag,
Stuttgart
9. Hankinson RW, Thomson GH (1979) A new correlation for saturated
densities of liquids and their mixtures. AIChE J 25:653–663
10. Peng D-Y, Robinson DB (1976) A new two constant equation of state. Ind
Eng Chem Fundam 15(1):59–64
11. Soave G (1972) Equilibrium constants from a modified Redlich-Kwong
equation of state. Chem Eng Sci 27:1197–1203
12. Ahlers J, Gmehling J (2001) Development of a universal group contribution
equation of state: 1. Prediction of fluid densities for pure compounds with a
volume translated Peng-Robinson equation of state. Fluid Phase Equilibria
191:177–188
13. Bronstein IN, Semendjajew KA (2000) Taschenbuch der Mathematik. Verlag
Harri Deutsch, Leipzig
14. Wagner W (1973) New vapour pressure measurements for argon and nitrogen and a new method of establishing rational vapour pressure equations.
Cryogenics. August 470–482
15. McGarry J (1983) Correlation and prediction of vapor pressures of pure
liquids over large pressure ranges. Ind Eng Chem Proc Des Dev 22:313–322
16. Li P, Ma P-S, Yi S-Z, Zhao Z-G, Cong L-Z (1994) A new CorrespondingStates Group-Contribution method (CSGC) for estimating vapor pressures
of pure compounds. Fluid Phase Equilibria 101:101–119
17. Riedel L (1957) Die Berechnung unbekannter thermischer Daten mit Hilfe
des erweiterten Korrespondenzprinzips. Kältetechnik 9(5):127–134
18. Vetere A (1991) Predicting the vapor pressures of pure compounds by using
the Wagner equation. Fluid Phase Equilibria 62:1–10
19. Nannoolal Y, Rarey J, Ramjugernath D (2008) Estimation of Pure Component Properties, Part 3: Estimation of the Vapor Pressure of Non-Electrolyte
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Fluid Phase Equilibria 269(1–2):117–133
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Stoffe. Springer-Verlag, Berlin/Heidelberg/New York
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Gruyter, Berlin
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heat capacity, enthalpy and entropy. Fluid Phase Equilibria 6:169–179
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viscosity of organic liquids. Chem Eng J 50:9
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viscosity at temperatures above the normal boiling point. Fluid Phase
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Temperature - Chemical Constitution Relation for Organic Compunds. Ind
Eng Chem Fundam 11(1):20–25
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D2
Properties of Selected Important Pure Substances
D2.1 Properties of Water and Steam
Wolfgang Wagner 1 . 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
1.5