Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon,
and Oxygen From 60 to 2000 K at Pressures to 2000 MPa
Eric W. Lemmona…
Physical and Chemical Properties Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80303
Richard T Jacobsen and Steven G. Penoncello
Center for Applied Thermodynamic Studies, College of Engineering, University of Idaho, Moscow, Idaho 83844
Daniel G. Friend
Physical and Chemical Properties Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80303
Received June 28, 1999; revised manuscript received December 2, 1999
A thermodynamic property formulation for standard dry air based upon available experimental p – ␳ – T, heat capacity, speed of sound, and vapor–liquid equilibrium data is
presented. This formulation is valid for liquid, vapor, and supercritical air at temperatures
from the solidification point on the bubble-point curve 共59.75 K兲 to 2000 K at pressures
up to 2000 MPa. In the absence of reliable experimental data for air above 873 K and 70
MPa, air properties were predicted from nitrogen data in this region. These values were
included in the determination of the formulation to extend the range of validity. Experimental shock tube measurements on air give an indication of the extrapolation behavior
of the equation of state up to temperatures and pressures of 5000 K and 28 GPa. The
available measurements of thermodynamic properties of air are summarized and analyzed. Separate ancillary equations for the calculation of dew and bubble-point pressures
and densities of air are presented. In the range from the solidification point to 873 K at
pressures to 70 MPa, the estimated uncertainty of density values calculated with the
equation of state is 0.1%. The estimated uncertainty of calculated speed of sound values
is 0.2% and that for calculated heat capacities is 1%. At temperatures above 873 K and 70
MPa, the estimated uncertainty of calculated density values is 0.5% increasing to 1.0% at
2000 K and 2000 MPa. In addition to the equation of state for standard air, a mixture
model explicit in Helmholtz energy has been developed which is capable of calculating
the thermodynamic properties of mixtures containing nitrogen, argon, and oxygen. This
model is valid for temperatures from the solidification point on the bubble-point curve to
1000 K at pressures up to 100 MPa over all compositions. The Helmholtz energy of the
mixture is the sum of the ideal gas contribution, the real gas contribution, and the contribution from mixing. The contribution from mixing is given by a single generalized
equation which is applied to all mixtures used in this work. The independent variables are
the reduced density and reduced temperature. The model may be used to calculate the
thermodynamic properties of mixtures at various compositions including dew and
bubble-point properties and critical points. It incorporates the most accurate published
equation of state for each pure fluid. The mixture model may be used to calculate the
properties of mixtures generally within the experimental accuracies of the available measured properties. The estimated uncertainty of calculated properties is 0.1% in density,
0.2% in the speed of sound, and 1% in heat capacities. Calculated dew and bubble-point
pressures are generally accurate to within 1%. © 2000 American Institute of Physics.
关S0047-2689共00兲00103-3兴
Key words: air, argon, density, equation of state, mixtures, nitrogen, oxygen, pressure, thermodynamic
properties, vapor–liquid equilibrium.
a兲
Electronic mail: [email protected]
©2000 by the U.S. Secretary of Commerce on behalf of the United States.
All rights reserved. This copyright is assigned to the American Institute
of Physics.
0047-2689Õ2000Õ29„3…Õ331Õ55Õ$37.00
331
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Contents
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1. Background. . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2. Prior Thermodynamic Property Formulations
for Air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Experimental Data. . . . . . . . . . . . . . . . . . . . . . . . . .
3. Vapor–Liquid Equilibria for Air. . . . . . . . . . . . . . .
3.1. Ancillary Equations. . . . . . . . . . . . . . . . . . . . . .
3.2. Freezing Liquid Line. . . . . . . . . . . . . . . . . . . .
4. Equation of State for Air. . . . . . . . . . . . . . . . . . . . .
4.1. Effects of Dissociation. . . . . . . . . . . . . . . . . . .
4.2. Calculation of Air Properties from
Experimental Data for Nitrogen. . . . . . . . . . . .
4.3. Fitting Procedures. . . . . . . . . . . . . . . . . . . . . . .
4.4. Ideal Gas Heat Capacity. . . . . . . . . . . . . . . . . .
4.5. Ideal Gas Helmholtz Energy. . . . . . . . . . . . . .
4.6. Equation of State for Air. . . . . . . . . . . . . . . . .
4.7. Calculation of Thermodynamic Properties....
4.8. Hugoniot Curve. . . . . . . . . . . . . . . . . . . . . . . . .
5. Mixture Model for the Nitrogen–Argon–Oxygen
System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1. Mixture Model. . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Vapor–Liquid Equilibrium 共VLE兲 Properties..
5.3. Critical Locus. . . . . . . . . . . . . . . . . . . . . . . . . .
6. Comparisons of Calculated Properties to
Experimental Data. . . . . . . . . . . . . . . . . . . . . . . . . .
6.1. Comparisons of the Ancillary Equations for
Air with Experimental Data. . . . . . . . . . . . . . .
6.2. Comparisons of the Equation of State for
Air and the Mixture Model with
Experimental and Calculated Data for Air. . .
6.3. Comparisons of the Mixture Model with
Experimental Single Phase Data. . . . . . . . . . .
6.4. Comparisons of the Mixture Model with
Experimental VLE Data. . . . . . . . . . . . . . . . . .
7. Estimated Uncertainty of Calculated Properties. . .
7.1. Characteristic Curves of Air. . . . . . . . . . . . . . .
7.2. Uncertainty of the Equation of State for Air
and of the Mixture Model. . . . . . . . . . . . . . . .
8. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9. Appendix—Tables of Properties of Air. . . . . . . . .
9.1 Representative Tables of Thermodynamic
Properties of Air. . . . . . . . . . . . . . . . . . . . . . . .
1.
2.
3.
4.
5.
6.
7.
List of Tables
Summary of measured compositions of air. . . . . . .
Composition of air using nitrogen, argon,
oxygen, and carbon dioxide as constituents. . . . . .
Composition of air using nitrogen, argon, and
oxygen as constituents. . . . . . . . . . . . . . . . . . . . . . .
Summary of prior formulations for the
thermodynamic properties of air. . . . . . . . . . . . . . .
Summary and statistical analysis of saturation
data for air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary and statistical analysis of experimental
data for air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Second virial coefficients derived from the
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356
357
357
359
360
362
362
336
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337
337
338
339
experimental p – ␳ – T data of Romberg 共1971兲. . .
8. Summary and statistical analysis of data for
mixtures of nitrogen, argon, and oxygen. . . . . . . .
9. Maxcondentherm, maxcondenbar, and critical
point for air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10. Coefficients for the dew and bubble-point
pressure and density equations for air. . . . . . . . . . .
11. Averaged molar composition of standard air at
specified temperatures. . . . . . . . . . . . . . . . . . . . . . .
12. Coefficients for the ideal gas expressions. . . . . . . .
13. Coefficients and exponents for the equation of
state for air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14. Pure fluid equations of state used in the mixture
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15. Parameters of the mixture model. . . . . . . . . . . . . . .
16. Different types of VLE calculations. . . . . . . . . . . .
17. Regions of stated uncertainty of the mixture
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A1. Thermodynamic properties of air on the dew and
bubble lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A2. Thermodynamic properties of air. . . . . . . . . . . . . .
List of Figures
1. Low temperature p – ␳ – T data for air. Solid
lines represent the dew and bubble-point
curves for air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. High temperature p – ␳ – T data for air. . . . . . . . . .
3. Isochoric and isobaric heat capacities and speed
of sound data for air. Solid lines represent the
dew and bubble-point curves for air. . . . . . . . . . . .
4. Derivation of second virial coefficient data from
the p – ␳ – T data of Romberg 共1971兲. . . . . . . . . . .
5. Derivation of second virial coefficient data from
the p – ␳ – T data of Michels et al. 共1954a兲
共1954b兲. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6. Critical region phase boundaries for air. . . . . . . . .
7. Calculated Hugoniot curve for air.. . . . . . . . . . . . .
8. Critical lines for nitrogen–argon, nitrogen–
oxygen, and argon–oxygen binary mixtures. . . . . .
9. Comparisons of dew and bubble-point properties
calculated with the ancillary equations to
experimental and calculated data for air.. . . . . . . .
10. Comparisons of densities calculated with the
equation of state to experimental data for air.. . . .
11. Comparisons of pressures calculated with the
equation of state to experimental data for air
in the critical region.. . . . . . . . . . . . . . . . . . . . . . . .
12. Comparisons of isochoric heat capacities
calculated with the equation of state to
experimental data for air.. . . . . . . . . . . . . . . . . . . . .
13. Comparisons of isobaric heat capacities calculated
with the equation of state to experimental data
for air.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14. Comparisons of speeds of sound calculated with
the equation of state to experimental data for air...
15. Comparisons of second virial coefficients
calculated with the equation of state to
340
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349
350
351
360
363
366
338
338
340
340
340
342
348
351
352
353
354
354
355
356
THERMODYNAMIC PROPERTIES OF AIR
experimental data for air.. . . . . . . . . . . . . . . . . . . . .
16. Comparisons of critical region phase boundaries
calculated with the equation of state to predicted
data for air.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17. Comparisons of densities calculated with the
equation of state to calculated p – ␳ – T data
estimated from nitrogen data. . . . . . . . . . . . . . . . . .
18. Comparisons of densities calculated with the
mixture model to experimental data for the
nitrogen–argon binary mixture.. . . . . . . . . . . . . . . .
19. Comparisons of densities calculated with the
mixture model to experimental data for the
nitrogen–oxygen and argon–oxygen binary
mixtures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20. Comparisons of bubble-point pressures calculated
with the mixture model to experimental data for
the nitrogen–argon binary mixture.. . . . . . . . . . . . .
Symbol
A
a
B
Bs
C
cp
cv
f
F
g
h
k
KT
kT
M
N
n
p
R
s
T
u
v
V
w
X
x
y
Z
␣
␤
␤s
␦
␥
356
356
357
357
357
358
333
21. Comparisons of bubble-point pressures calculated
with the mixture model to experimental data for
the nitrogen–oxygen binary mixture.. . . . . . . . . . .
22. Comparisons of bubble-point pressures calculated
with the mixture model to experimental data for
the argon–oxygen binary mixture.. . . . . . . . . . . . .
23. Comparisons of bubble-point pressures calculated
with the mixture model to experimental data for
the nitrogen–argon–oxygen ternary mixture. . . . .
24. Isochoric heat capacity versus temperature
diagram for air. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25. Isobaric heat capacity versus temperature
diagram for air. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26. Speed of sound versus temperature diagram for
air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27. Pressure versus density diagram for air.. . . . . . . . .
28. Characteristic curves for air. . . . . . . . . . . . . . . . . . .
List of Symbols
Physical quantity
Helmholtz energy
Molar Helmholtz energy
Second virial coefficient
Adiabatic bulk modulus
Third virial coefficient
Isobaric heat capacity
Isochoric heat capacity
Fugacity
Mixture coefficient
Gibbs energy
Enthalpy
Isentropic expansion coefficient
Isothermal bulk modulus
Isothermal expansion coefficient
Molar mass
Coefficients of equations
Number of moles
Presssure
Universal gas constant (8.314 510⫾0.000 070)
Entropy
Temperature
Internal energy
Molar volume
Total volume
Speed of sound
Mixture composition array
Mole fraction 共liquid mole fraction for VLE
calculations兲
Vapor mole fraction for VLE calculations
Compressibility factor
Reduced Helmholtz energy
Volume expansivity
Adiabatic compressibility
Reduced density, ␦ ⫽ ␳ / ␳ c or ␦ ⫽ ␳ / ␳ j
Heat capacity ratio
358
358
359
359
359
359
359
360
Unit
J
J/mol
dm3/mol
MPa
共dm3/mol兲2
J/共mol•K兲
J/共mol•K兲
MPa
J/mol
J/mol
MPa
g/mol
mol
MPa
J/共mol•K兲
J/共mol•K兲
K
J/mol
dm3/mol
dm3
m/s
1/K
1/MPa
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
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␬
␮
␮J
␳
␶
␻
␰
␨
␸
Isothermal compressibility
Chemical potential
Joule–Thomson coefficient
Density
Reduced temperature, ␶ ⫽T c /T or ␶ ⫽T j /T
Acentric factor
Mixture coefficient for reduced density
Mixture coefficient for reduced temperature
Constant in melting line equation
Superscripts
0
E
f
idmix
r
⬘
⬙
i
j
nbp
nbpl
nbpv
o
p
r
red
s
tp
tpl
tpv
Ideal gas property
Excess-like property
Freezing property
Ideal solution property
Residual property
Liquid phase property
Vapor phase property
Subscripts
0
c
calc
exp
Reference state property
Critical point property
Calculated point property
Experimental value
1/MPa
J/mol
K/MPa
mol/dm3
dm3/mol
K
Property of a component in the mixture
Maxcondentherm property
Normal boiling point property
Normal boiling point liquid property
Normal boiling point vapor property
Initial state point for shock tube calculations
Maxcondenbar property
Reduced property
Reducing property
Solidification point property
Triple point property
Triple point liquid property
Triple point vapor property
Fixed Points for Air
Symbol
Quantity
Valueb
Tj
Maxcondentherm temperature
132.6312 K
Maxcondentherm pressure
3.78502 MPa
pj
␳j
Maxcondentherm density
10.4477 mol/dm3
Maxcondenbar temperature
132.6035 K
Tp
Maxcondenbar pressure
3.7891 MPa
pp
␳p
Maxcondenbar density
11.0948 mol/dm3
Critical
temperature
132.5306
K
Tc
Critical pressure
3.7860 MPa
pc
␳c
Critical density
11.8308 mol/dm3
Solidification point temperature
59.75 K
Ts
Solidification point pressure
0.005265 MPa
ps
␳s
Solidification point density
33.067 mol/dm3
a
T nbp
Normal boiling point temperature
78.903 K
␳ nbpl
Normal boiling point density 共liquid兲a
30.216 mol/dm3
Molar mass
28.9586⫾0.0002 g/mol
M
Reference temperature
298.15 K
T0
Reference pressure
0.101 325 MPa
p0
Reference enthalpy at T 0
8649.34 J/mol
h 00
Reference entropy at T 0 and p 0
194.0 J/共mol•K兲
s 00
a
Normal boiling point properties are calculated on the bubble-point curve at 0.101 325 MPa.
b
Uncertainties are reported at the 2␴ confidence level; those for the critical parameters are given in Table 9.
Fixed Points for Nitrogen
Symbol
Tc
pc
␳c
T tp
Quantity
Critical temperature
Critical pressure
Critical density
Triple point temperature
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
Valuea
126.192 K
3.3958 MPa
11.1839 mol/dm3
63.151 K
THERMODYNAMIC PROPERTIES OF AIR
335
p tp
Triple point pressure
0.012 523 MPa
␳ tpv
Triple point density 共vapor兲
0.024 07 mol/dm3
␳ tpl
Triple point density 共liquid兲
30.957 mol/dm3
T nbp
Normal boiling point temperature
77.355 K
␳ nbpv
Normal boiling point density 共vapor兲
0.1646 mol/dm3
␳ nbpl
Normal boiling point density 共liquid兲
28.775 mol/dm3
␻
Acentric factor
0.037
M
Molar mass
28.013 48 g/mol
T0
Reference temperature
298.15 K
Reference pressure
0.101 325 MPa
p0
Reference enthalpy at T 0
8670.0 J/mol
h 00
Reference entropy at T 0 and p 0
191.5 J/共mol•K兲
s 00
a
Span et al. 共2000兲 report the constants given here and their associated uncertainties; temperatures for nitrogen are given on ITS-90.
Fixed Points for Argon
Quantity
Valuea
Symbol
Tc
Critical temperature
150.687 K
pc
Critical pressure
4.863 MPa
␳c
Critical density
13.407 mol/dm3
T tp
Triple point temperature
83.8058 K
p tp
Triple point pressure
0.068891 MPa
␳ tpv
Triple point density 共vapor兲
0.1015 mol/dm3
␳ tpl
Triple point density 共liquid兲
35.465 mol/dm3
T nbp
Normal boiling point temperature
87.302 K
␳ nbpv
Normal boiling point density 共vapor兲
0.1445 mol/dm3
␳ nbpl
Normal boiling point density 共liquid兲
34.930 mol/dm3
␻
Acentric factor
⫺0.002
M
Molar mass
39.948 g/mol
Reference temperature
298.15 K
T0
Reference pressure
0.101 325 MPa
p0
Reference enthalpy at T 0
6197.0 J/mol
h 00
Reference entropy at T 0 and p 0
154.737 J/共mol•K兲
s 00
a
Tegeler et al. 共1999兲 report the constants given here and their associated uncertainties; temperatures for argon are given on ITS-90.
Fixed Points for Oxygen
Symbol
Quantity
Valuea
Value 共ITS-90兲
Tc
Critical temperature
154.581 K
154.595 K
pc
Critical pressure
5.043 MPa
␳c
Critical density
13.63 mol/dm3
T tp
Triple point temperature
54.361 K
54.359 K
p tp
Triple point pressure
0.000 146 3 MPa
␳ tpv
Triple point density 共vapor兲
0.000 323 7 mol/dm3
␳ tpl
Triple point density 共liquid兲
40.816 mol/dm3
T nbp
Normal boiling point temperature
90.188 K
90.196 K
␳ nbpv
Normal boiling point density 共vapor兲
0.1396 mol/dm3
␳ nbpl
Normal boiling point density 共liquid兲
35.663 mol/dm3
␻
Acentric factor
0.022
M
Molar mass
31.9988 g/mol
Reference temperature
298.15 K
T0
Reference pressure
0.101 325 MPa
p0
Reference enthalpy at T 0
8680.0 J/mol
h 00
0
Reference entropy at T 0 and p 0
205.043 J/共mol•K兲
s0
a
Schmidt and Wagner 共1985兲 report the constants given here and their associated uncertainties; temperatures for oxygen are
given on IPTS-68 consistent with the equation of state, and on ITS-90 in the last column.
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
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1. Introduction
1.1. Background
The measurement of experimental data and the development of equations for the thermophysical properties of air
and mixtures of nitrogen, argon, and oxygen has been a continuing project at the Center for Applied Thermodynamic
Studies at the University of Idaho and the National Institute
of Standards and Technology for more than 10 years. The
experimental measurements on air are summarized by
Haynes et al. 共1998兲. Equations of state for air as a
pseudopure fluid were published by Jacobsen et al. 共1990a兲,
共1992兲. In addition, an extended corresponding states model
for calculating the thermodynamic properties of nitrogen–
argon–oxygen mixtures was published by Clarke et al.
共1994兲, and a Lagrangian interpolation model for calculating
vapor–liquid equilibrium properties for this system was published by Lemmon et al. 共1992兲. A preliminary equation of
state for air valid to temperatures of 2000 K and pressures to
2000 MPa was published by Panasiti et al. 共1999兲, and a new
model for mixtures of nitrogen, argon, and oxygen was reported by Lemmon and Jacobsen 共1998兲, 共1999兲. The equations of state for air of Jacobsen et al. 共1990a兲, 共1992兲 were
reported on the International Practical Temperature Scale of
1968 共IPTS-68兲. Version 1.0 of the NIST standard reference
database for air 关Lemmon 共1998兲兴 was based on the equation
of state of Jacobsen et al. 共1992兲. The new equation of state
and mixture model presented here are based on the International Temperature Scale of 1990 共ITS-90兲.
Atmospheric air is a mixture of fluids including nitrogen,
oxygen, argon, carbon dioxide, water vapor, and other trace
elements. The standard air considered in this report is dry
and contains no carbon dioxide or trace elements. The composition of air used here was reported by Olien 共1987兲 based
on the work of Jones 共1978兲. It is consistent with that of the
U.S. Standard Atmosphere 共1976兲. Other compositions are
given by Giacomo 共1982兲 and Waxman and Davis 共1978兲.
The mole fractions of nitrogen, oxygen, argon, and carbon
dioxide in air from each of the references listed above are
given in Table 1.
In the analysis of Olien 共1987兲, the values of Waxman and
Davis 共1978兲 were excluded because they are based on a
purified, rather than natural, sample. The difference between
the U.S. standard atmosphere 共1976兲 and values from Jones
共1978兲 is that Jones used a more accurate value for the composition of argon. The differences between Giacomo 共1982兲
of BIPM 共International Bureau of Weights and Measures兲
and the U.S. standard atmosphere are greater than those for
values from Jones. Although the argon value given by Giacomo is essentially the same as that given by Jones, the
carbon dioxide value given by Giacomo is for a laboratory
setting in which human respiration generally increases carbon dioxide concentration and decreases oxygen concentration. Therefore, the compositions given by Giacomo were
not used. Rather, the compositions given by Jones, truncated
to four significant digits as indicated in Table 2, were used.
In this work, the concentration of carbon dioxide is assumed
negligible. The normalized values based upon this assumption are given in Table 3. An analysis of experimental measurements on air at different compositions than that reported
here showed that the change caused by the difference in
composition was less than the experimental error in the measurements, and hence, no effort was made to transform measurements at different air compositions to the composition
reported here.
A property formulation is the set of equations used to
calculate properties of a fluid at specified thermodynamic
states defined by an appropriate number of independent variables. The term ‘‘fundamental equation’’ is often used in the
literature to refer to empirical descriptions of one of four
fundamental relations: internal energy, enthalpy, Gibbs energy, and Helmholtz energy. The formulations for fluid properties are often explicit in Helmholtz energy with independent variables of temperature and density. Pure fluids obey
the Maxwell criterion 共equal pressures and Gibbs energies at
constant temperatures during phase changes兲 so that all thermodynamic properties including the vapor–liquid equilibrium may be calculated from the full expression for the
Helmholtz energy without additional ancillary equations. In
this work, the general term ‘‘equation of state’’ rather than
the term ‘‘fundamental equation’’ is used to refer to the empirical models developed for calculating fluid properties.
Since air is not a pure fluid, general phase equilibrium
calculations require consideration of phase compositions.
This type of model is discussed in Sec. 5 for arbitrary mixtures of nitrogen, argon, and oxygen. For standard air at a
fixed composition, two separate equations are required in
addition to the equation of state to represent the dew and
bubble-point pressures as functions of temperature. Densities
along the dew and bubble-point curves are calculated by the
solution of the equation of state and the dew or bubble-point
pressure equations given in Sec. 3 at a given temperature.
Ancillary equations for the dew and bubble-point densities
TABLE 1. Summary of measured compositions of air
N2
O2
Ar
CO2
TABLE 2. Composition of air using nitrogen, argon, oxygen, and carbon
dioxide as constituents
U.S. Std.
Atmosphere
共1976兲
Jones 共1978兲
Waxman and
Davis 共1978兲
Giacomo
共1982兲
0.780 840
0.209 476
0.009 340
0.000 314
0.999 970
0.781 02
0.209 46
0.009 16
0.000 33
0.999 97
0.781 20
0.209 20
0.009 30
0.000 32
1.000 02
0.781 01
0.209 39
0.009 17
0.000 40
0.999 97
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
Component
Mole fraction
N2
O2
Ar
CO2
0.7810
0.2095
0.0092
0.0003
1.0000
THERMODYNAMIC PROPERTIES OF AIR
TABLE 3. Composition of air using nitrogen, argon, and oxygen as
constituents
Component
TABLE 4. Summary of prior formulations for the thermodynamic properties
of air
Mole fraction
Year
Temperature
range 共K兲
1955
1955
50–3000
102–348
10
122
Din 共1962兲
1962
Baehr and Schwier 共1961兲
1961
Vasserman and Rabinovich 共1970兲 1970
90–450
60–1250
75–160a
122
450
Vasserman et al. 共1971兲
1971
75–1300b
100
Sychev et al. 共1987兲c
Jacobsen et al. 共1990a兲
1978
1990
70–1500
60–873
100
70
Jacobsen et al. 共1992兲
Panasiti et al. 共1999兲
1992
1999
60–873
60–2000
70
2000
Author
N2
O2
Ar
337
0.7812
0.2096
Hilsenrath 共1955兲
Michels et al. 共1955兲
0.0092
1.0000
are also given and can be used as estimating functions for
iterative calculations of derived thermodynamic properties.
1.2. Prior Thermodynamic Property Formulations
for Air
Several previous thermodynamic property formulations
for air are referenced in Table 4. The most recent prior widerange formulations are those of Jacobsen and co-workers 关Jacobsen et al. 共1990a兲; Jacobsen et al. 共1992兲; Panasiti et al.
共1999兲兴, the first of which is based upon liquid heat capacities predicted using extended corresponding states methods
and the second of which used preliminary measurements of
the isochoric heat capacity from the National Institute of
Standards and Technology 共NIST兲, subsequently published
by Magee 共1994兲. The third formulation was a preliminary
equation extended to temperatures and pressures of 2000 K
and 2000 MPa using predicted properties above 870 K and
70 MPa calculated by corresponding states methods from
experimental nitrogen data.
2. Experimental Data
The estimated uncertainty of reference equations of state
for pure fluids or mixtures is generally based upon comparisons to experimental data. These data are used to determine
the coefficients of the equation and to evaluate the behavior
of the equation of state over the fluid surface. Data types
used in this work include p – ␳ – T, speed of sound, isochoric
and isobaric heat capacities, and vapor–liquid equilibrium.
The equation of state reported here was developed using
least squares fitting methods described in detail in Sec. 4.3.
For reference quality equations, extensive comparisons to all
data types are required. In the tables included in this section,
columns are included which indicate the results of statistical
analyses of the comparisons of calculated values to experimental data. The details of this analysis are given in Sec. 6.
The available saturation data are summarized in Table 5
and discussed in Sec. 6.1. Data used in the fit of the ancillary
equations are shown as bolded entries in the table. The values reported by Blanke 共1977兲 were obtained by graphical
methods from his p – ␳ – T data; several of the near critical
temperature data were used in the fit of ancillary equations.
Values calculated using the Leung–Griffiths model for air as
reported by Jacobsen et al. 共1990b兲 are also summarized in
this table. Several of these values close to the critical point
were used in the fit.
High pressure
limit 共MPa兲
50
a
Liquid states only.
Vapor states only.
c
English translation of original work published in 1978.
b
Experimental p – ␳ – T data for air are illustrated in Figs. 1
and 2 and summarized in Table 6. The solid lines represent
the dew and bubble-point curves. Data used in the fit of the
equation of state are shown as bolded entries in the table. All
available experimental data were considered in preliminary
analysis, but in the final regression of the coefficients of the
equation of state, only the most accurate data and data in
regions where no other data were available were fitted. The
air p – ␳ – T data sets used in the development of the equation
of state for air and for the mixture model were those of
Blanke 共1977兲, Howley et al. 共1994兲, Kozlov 共1968兲, Michels et al. 共1954a兲, 共1954b兲, and Romberg 共1971兲. The isochoric and isobaric heat capacity data are illustrated in Fig. 3
and summarized in Table 6. The speed of sound data of
Younglove and Frederick 共1992兲, Ewing and Goodwin
共1993兲 and of Van Itterbeek and de Rop 共1955兲 are also
illustrated in Fig. 3 and summarized in Table 6. These speed
of sound data and the isochoric heat capacity data of Magee
共1994兲 were used in the fit. The critical region data of Chashkin et al. 共1966兲 are not included in this table since their
measurements were concerned with investigating the effect
of impurities on the behavior of the isochoric heat capacity
in the critical region, and the sample had a 1.2% impurity
content 关see Sychev et al. 共1987兲兴. None of the isobaric heat
capacity data summarized in Table 6 were used to develop
the equation of state or mixture model because of the age of
the data and the availability of other more accurate derived
data 共isochoric heat capacity and speed of sound兲 in similar
regions.
A summary of sources of second virial coefficients, including those of Romberg 共1971兲 and Michels et al. 共1954a兲,
共1954b兲, are given in Table 6. The values of Michels et al.
were used in the fit of the equation of state. In addition to the
values reported by Romberg, values of the second virial coefficients were redetermined graphically from his reported
p – ␳ – T data. These values are given in Table 7. At the
higher isotherms, data below 0.5 mol/dm3 were not used in
this graphical redetermination of the values of the second
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
338
TABLE 5. Summary and statistical analysis of saturation data for air
No.
of
points
Temp.
range 共K兲
Pressure
range
共MPa兲
AADa
AADb
9
18
60–129
120–133
0.01–3.2
2.10–3.8
2.506
0.049
2.766
0.207
Kuenen and Clark 共1917兲
Michels et al. „1954a…
14
3
123–133
118–132
2.54–3.8
1.96–3.7
0.663
0.069
0.839
0.212
Overall
44
60–133
0.01–3.8
0.748
1.040
11
12
67–132
122–133
0.01–3.7
2.18–3.8
0.395
0.048
1.407
0.293
Kuenen and Clark 共1917兲
Michels et al. „1954a…
18
6
123–133
118–133
2.40–3.8
1.83–3.8
0.587
0.413
0.548
0.515
Overall
47
67–133
0.01–3.8
0.382
0.680
No.
of
points
Temp.
range 共K兲
Density
range
共mol/dm3兲
AADa
AADc
9
18
11
10
48
60–129
120–133
127–133
118–132
60–133
17.71–33.0
10.45–21.6
10.70–18.1
13.67–20.5
10.45–33.0
0.144
0.786
6.042
3.003
2.332
0.152
0.745
6.039
3.034
2.324
11
12
8
12
43
67–132
122–133
130–133
118–133
67–133
0.02–8.9
3.40–10.4
6.49–10.7
2.67–9.8
0.02–10.7
0.638
1.028
6.052
1.236
1.921
0.639
1.036
6.067
1.229
1.924
Author
Bubble-point pressure
Blanke „1977…
Jacobsen et al. „1990b…
Dew-point pressure
Blanke „1977…
Jacobsen et al. „1990b…
Bubble-point density
Blanke „1977…
Jacobsen et al. „1990b…
Kuenen and Clark 共1917兲
Michels et al. „1954a…
Overall
Dew-point density
Blanke „1977…
Jacobsen et al. „1990b…
Kuenen and Clark 共1917兲
Michels et al. „1954a…
Overall
a
Comparisons of the ancillary equations with experimental data.
Comparisons of the mixture model with experimental data.
c
Comparisons of the equation of state for air with experimental data.
b
FIG. 1. Low temperature p – ␳ – T data for air. Solid lines represent the dew
and bubble-point curves for air.
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
FIG. 2. High temperature p – ␳ – T data for air.
THERMODYNAMIC PROPERTIES OF AIR
339
TABLE 6. Summary and statistical analysis of experimental data for air
Author
No.
of
points
Temp.
range 共K兲
Pressure
range
共MPa兲
Density
range
共mol/dm3兲
AADa
共air EOS兲
AADa
共mixture
model兲
p–␳–T
Amagat 共1893兲
Blanke „1977…
78
110
273–318
61–170
0.10–304.0
0.01–4.9
0.04–31.0
0.02–33.0
0.220
0.350
0.246
0.312
42
286
273–473
67–400
1.98–10.0
1.06–35.2
0.61–4.5
1.95–32.2
0.019
0.050
0.031
0.044
348
157
199
288–873
273–348
118–248
1.21–72.2
0.73–228.0
0.56–102.0
0.21–17.2
0.30–28.7
0.33–25.2
0.072
0.022
0.147
0.069
0.030
0.152
62
10
124
128–293
273
84–122
2.52–6.20
4.71–8.6
0.02–2.0
1.20–4.5
2.12–3.9
0.03–2.7
0.094
0.091
0.028
0.100
0.102
0.045
109
1525
77–199
61–873
2.62–59.8
0.01–304.0
22.82–31.4
0.02–33.0
0.078
0.097
0.080
0.097
16
3
227
246
138–165
288–623
66–299
66–623
6.72–19.6
0.10
1.71–34.6
0.10–34.6
18.08–19.0
0.02
2.04–33.0
0.02–33.0
6.571
0.579
0.373
0.779
6.063
0.580
0.493
0.856
51
6
7
47
19
46
176
273–553
271–480
333
194–523
194–523
300–2499
194–2499
2.03–22.3
0.10
0.10–29.4
0.10–29.4
4.90–19.6
0.30–1.0
0.10–29.4
0.44–8.6
0.03
0.04–9.5
0.02–14.6
1.11–14.6
0.01–0.4
0.01–14.6
0.920
0.531
0.434
1.083
1.845
3.656
1.746
0.916
0.532
0.405
1.083
1.810
3.511
1.702
Abbey and Barlow 共1948兲
Colwell and Gibson 共1941兲
Colwell et al. 共1938兲
Ewing and Goodwin „1993…
Hardy et al. 共1942兲
King and Partington 共1930兲
6
7
9
13
7
11
293
273
297–299
255
273–297
1138–1440
⬍0.1
⬍0.1
0.10
0.03–6.9
0.10
0.10
⬍0.04
⬍0.04
0.04
0.01–3.4
0.04
0.01
0.388
0.100
0.063
0.018
1.858
1.941
0.389
0.100
0.062
0.006
1.861
1.946
Quigley 共1945兲
Shilling and Partington 共1928兲
29
28
92–259
273–1572
0.10
0.10
0.05–0.1
0.01
0.313
1.405
0.306
1.407
Tucker 共1943兲
Van Itterbeek and de Rop „1955…
Younglove and Frederick „1992…
6
44
169
292–347
229–313
90–300
0.07–0.1
0.10–1.3
0.34–13.8
0.02
0.04–0.7
0.25–29.7
2.353
0.216
0.216
2.351
0.211
0.105
Overall
329
90–1572
⬍13.8
⬍29.7
0.446
0.387
Andersen 共1950兲
Friedman 共1957兲
6
5
273–473
150–273
1.008
0.819
0.732
0.558
Hilsenrath 共1955兲
Levelt Sengers et al. 共1972兲
61
54
50–1501
100–1400
3.779
0.674
2.719
0.472
Michels et al. „1954a…
Michels et al. „1954b…
Romberg 共1971兲
4
10
39
273–348
118–248
84–473
0.220
0.127
0.240
0.357
0.159
1.130
Overall
179
50–1501
1.588
1.357
Holborn and Schultze 共1915兲
Howley et al. „1994…
Kozlov „1968…
Michels et al. „1954a…
Michels et al. „1954b…
Penning 共1923兲
Rogovaya and Kaganer 共1960兲
Romberg „1971…
Vasserman et al. 共1976兲
Overall
cv
Eucken and Hauck 共1928兲
Henry 共1931兲
Magee „1994…
Overall
cp
Bridgeman 共1929兲
Eucken 共1913兲
Holborn and Jakob 共1917兲
Jakob 共1923兲
Nesselmann 共1925兲
Poferl et al. 共1959兲
Overall
w
B
AAD—Average absolute percent deviation in density for p – ␳ – T and average absolute difference in
B 共cm3/mol兲 for the second virial coefficients.
a
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
340
FIG. 3. Isochoric and isobaric heat capacities and speed of sound data for air.
Solid lines represent the dew and bubble-point curves for air.
FIG. 4. Derivation of second virial coefficient data from the p – ␳ – T data of
Romberg 共1971兲.
virial coefficients since in many apparatus, such low density
data are subject to local adsorption by the walls of the apparatus or to higher uncertainties in the measurement of extremely low pressures. No value of the second virial coefficient was determined for the 84 K isotherm. The p – ␳ – T
data used to generate the second virial coefficients are shown
in Fig. 4. The solid lines show isotherms calculated from the
equation of state presented here and the solid curve represents the dew-point curve. The y intercept 共zero density兲
represents the second virial coefficient at a given temperature, and the third virial coefficients can be taken from the
slope of each line at zero density. The values of the second
virial coefficient calculated from the equation of state are in
good agreement with those presented in Table 7 and shown
as circles in the figure. Values of the second virial coefficients and p – ␳ – T data from Michels et al. are shown in a
similar fashion in Fig. 5. The circles at zero density represent
the second virial coefficients reported by Michels.
Binary p – ␳ – T and vapor–liquid equilibrium data for
mixtures containing nitrogen, argon, and oxygen are summarized in Table 8. The composition ranges listed in these
tables show the composition of the first component listed.
All available experimental data were considered in the preliminary analysis, but the final regression of the coefficients
of the mixture model used the data sets indicated by the
bolded entries in Table 8. Data of Crain and Sonntag 共1966兲,
Palavra 共1979兲, and Kosov and Brovanov 共1979兲 were used
for the nitrogen–argon mixture, and data of Pool et al.
共1962兲 were used for the nitrogen–oxygen and argon–
oxygen mixtures. In addition to the limited data for the
nitrogen–oxygen system, the following data sets for air were
also used in the mixture modeling: Blanke 共1977兲, Howley
et al. 共1994兲, Michels et al. 共1954a兲, 共1954b兲, Romberg
共1971兲, Magee 共1994兲, Ewing and Goodwin 共1993兲, and
Younglove and Frederick 共1992兲. The largest impact from
the addition of these data sets was on the nitrogen–oxygen
parameters, however, the argon–oxygen parameters were
also influenced to some degree by the air data. These data
had little impact on the nitrogen–argon parameters, as there
were sufficient binary data for this system to model the parameters well. The VLE data used in the model development
included the nitrogen–argon data of Hiza et al. 共1999兲, the
nitrogen–oxygen data of Duncan and Staveley 共1966兲, and
the argon–oxygen data of Burn and Din 共1962兲 and of Wilson et al. 共1965兲. Comparisons with ternary VLE data indi-
TABLE 7. Second virial coefficients derived from the experimental p – ␳ – T
data of Romberg 共1971兲
Temperature 共K/ITS-90兲
88.27
94.06
97.56
103.24
109.10
113.05
117.12
122.22
Graphical redetermination of the
second virial coefficient 共dm3/mol兲
⫺0.219
⫺0.194
⫺0.179
⫺0.160
⫺0.143
⫺0.134
⫺0.125
⫺0.115
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
FIG. 5. Second virial coefficient data and p – ␳ – T data of Michels et al.
共1954a兲, 共1954b兲.
THERMODYNAMIC PROPERTIES OF AIR
341
TABLE 8. Summary and statistical analysis of data for mixtures of nitrogen, argon, and oxygen
No.
of
points
Pressure
range
共MPa兲
Density
range
共mol/dm3兲
Temp.
range 共K兲
Comp.
range
共mol兲
AADa
264
41
201
88
6
203
24
21
144
55
1047
0.19–52.5
0.01–0.2
5.93–58.8
100.–800.
0.27–1.3
0.95–24.9
0.10–0.2
7.41–145.
0.18–13.9
0.76–9.6
0.01–800.
0.08–26.6
0.01–0.2
2.46–18.8
17.5–41.1
25.7–30.2
25.8–32.9
28.3–33.9
25.8–34.7
0.07–5.7
0.55–13.1
0.01–41.1
143–273
74–90
293–353
298–423
90–113
94–106
84
119
298–323
171–293
74–423
0.20–0.80
0.31–0.80
0.16–0.81
0.26–0.75
0.50
0.32–0.70
0.18–0.89
0.52
0.16–0.84
0.19–0.74
0.16–0.89
0.209
0.193
0.363
0.320
0.409
0.021
0.502
0.160
0.054
0.097
0.191
Elshayal and Lu 共1975兲
Fastovskii and Petrovskii 共1956兲
Hiza et al. „1999…
Jin et al. 共1993兲
Lewis and Staveley 共1975兲
Miller et al. 共1973兲
Narinskii 共1966兲
Pool et al. 共1962兲
Sprow and Prausnitz 共1966兲
Thorpe 共1968兲
Wilson et al. 共1965兲
Overall
N2 – O2 — p – ␳ – T
7
56
44
13
8
14
98
12
17
68
176
513
0.39–0.7
0.12–0.4
0.08–0.8
1.48–2.8
0.07–0.2
0.84–1.5
0.13–2.3
0.07–0.2
0.08–0.2
0.13–1.1
0.10–2.6
0.07–2.8
100
79–103
85–100
123
85
112
80–120
84
84
81–115
72–134
72–134
0.14–0.90
0.05–0.90
0.10–0.89
0.05–0.97
0.23–0.81
0.11–0.85
0.02–0.96
0.06–0.88
0.06–0.91
0.10–0.91
0.05–1.00
0.02–1.00
0.468
1.182
0.379
0.555
0.840
0.326
0.484
0.420
0.460
0.830
0.805
0.708
Blagoi and Rudenko 共1958兲
Knaap et al. 共1961兲
Kuenen et al. 共1922兲
Pool et al. „1962…
Overall
19
7
153
7
186
2.93–6.0
0.09–0.2
0.09–6.0
67–79
77
135–293
84
67–293
0.11–0.80
0.29–0.91
0.25–0.50
0.25–0.74
0.11–0.91
0.415
0.097
0.877
0.088
0.771
Armstrong et al. 共1955兲
Cockett 共1957兲
Din 共1960兲
Dodge and Dunbar 共1927兲
Duncan and Staveley „1966…
Hiza et al. 共1999兲
Pool et al. 共1962兲
Thorogood and Haselden 共1963兲
Wilson et al. 共1965兲
Yorizane et al. 共1978兲
Overall
Ar–O2 — p – ␳ – T
70
62
108
49
11
65
11
13
138
20
547
0.003–0.1
0.12–0.1
0.11–1.0
0.06–3.0
0.002–0.01
0.001–0.8
0.05–0.2
0.10
0.10–2.6
0.05–0.1
0.001–3.0
65–78
81–91
79–116
77–125
63
63–100
84
88–90
78–136
80
63–136
0.03–0.94
0.07–0.81
0.10–0.89
0.05–0.91
0.10–0.80
0.07–0.88
0.10–0.90
0.002–0.08
0.05–0.99
0.11–0.85
0.002–0.99
0.870
1.287
0.788
0.903
1.524
0.689
0.310
1.320
0.540
2.489
0.865
Blagoi and Rudenko 共1958兲
Knaap et al. 共1961兲
Pool et al. „1962…
Saji and Okuda 共1965兲
Overall
36
6
15
20
77
0.05–0.1
70–89
90
84–90
85–87
70–90
0.10–0.87
0.28–0.79
0.17–0.86
0.25–0.92
0.10–0.92
0.274
0.052
0.025
0.244
0.200
27
140
55
24
16
55
24
24
35
200
58
568
0.07–0.2
0.06–1.0
0.10–0.7
0.12–0.2
0.16–0.3
0.11–1.2
0.12–0.9
0.05–0.1
0.12–0.2
0.10–2.6
0.10
0.05–2.6
87–95
85–118
90–110
89–96
95–100
90–120
92–115
84–90
90–96
87–139
89–92
84–139
0.04–0.86
0.10–0.91
0.10–0.90
0.21–0.83
0.11–0.79
0.03–0.96
0.01–0.92
0.10–0.90
0.02–1.00
0.003–0.98
⬍0.76
⬍1.00
0.710
0.232
0.313
0.774
0.805
0.237
1.149
0.168
1.393
0.403
0.857
0.493
14
60
115
41
1427
1657
0.1
0.1
0.13–2.2
0.1
0.10–2.6
0.10–2.6
81–88
90
82–120
81–92
78–136
78–136
0.13–0.68
⬍0.004
0.04–0.86
0.01–0.89
0.001–0.99
⬍0.99
0.555
0.278
0.489
1.613
0.561
0.572
Author
N2 – Ar — p – ␳ – T
Crain and Sonntag „1966…
Holst and Hamburger 共1916兲
Kosov and Brovanov „1979…
Maslennikova et al. 共1979兲
Massengill and Miller 共1973兲
Palavra „1979…
Pool et al. 共1962兲
Ricardo et al. 共1992兲
Townsend 共1956兲
Zandbergen and Beenakker 共1967兲
Overall
N2 – Ar — VLE
b
b
30.7–38.0
29.6–34.8
1.22–19.4
29.8–34.1
1.22–38.0
N2 – O2 — VLE
Ar–O2
—
b
b
b
0.05–0.1
34.8–38.2
34.7–35.2
34.7–36.3
34.9–36.1
34.7–38.2
VLE
Bourbo and Ischkin 共1936兲
Burn and Din „1962…
Clark et al. 共1954兲
Fastovskii and Petrovskii 共1955兲
Hiza et al. 共1999兲
Narinskii 共1957兲
Parikh and Zollweg 共1997兲
Pool et al. 共1962兲
Wang 共1960兲
Wilson et al. „1965…
Yorizane et al. 共1978兲
Overall
N2 – Ar–O2 — VLE
Fastovskii and Petrovskii 共1957兲
Funada et al. 共1982兲
Narinskii 共1969兲
Weishaupt 共1948兲
Wilson et al. 共1965兲
Overall
a
AAD—Average absolute deviation in density for p – ␳ – T and average absolute deviation in bubble-point pressure for VLE.
No pressure reported, bubble-point pressure assumed.
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
b
LEMMON ET AL.
342
TABLE 10. Coefficients for the dew and bubble-point pressure and density
equations for air
i
1
2
3
4
5
6
1
2
3
4
5
Ni
Bubble-point pressure,
Eq. „1…
0.226 072 4
⫺7.080 499
5.700 283
⫺12.440 17
17.819 26
⫺10.813 64
Bubble-point density,
Eq. „2…
44.3413
⫺240.073
285.139
⫺88.3366
⫺0.892 181
i
Ni
1
2
5
8
Dew-point pressure,
Eq. „1…
⫺0.156 726 6
⫺5.539 635
0.756 721 2
⫺3.514 322
1
2
3
4
Dew-point density,
Eq. „3…
⫺2.0466
⫺4.7520
⫺13.259
⫺47.652
tion of state reported here so that the dew-point pressure and
density equations will not be double-valued at any given
temperature above the critical temperature as illustrated in
Fig. 6; thus, for these temperature dependent equations, the
dew-point line is represented by the bubble-point equation
between the maxcondentherm point and the critical point.
The fixed point properties for air used in this work are given
in Table 9.
FIG. 6. Critical region phase boundaries for air.
cated that the binary mixture parameters were sufficient for
modeling the ternary mixture interactions.
3. Vapor–Liquid Equilibria for Air
The maxcondentherm 共state point of maximum temperature along the saturation line兲, maxcondenbar 共state point of
maximum pressure along the saturation line兲, and critical
point for air used in this work were reported by Jacobsen
et al. 共1990b兲. These values were determined using a modified Leung–Griffiths model to represent the high-pressure
VLE data for ternary systems of nitrogen, argon, and oxygen. The values of the properties at the maxcondentherm
(T j , p j , ␳ j 兲 were used as reducing parameters for the equa-
3.1. Ancillary Equations
The ancillary equations were developed using linear and
nonlinear regression algorithms with the experimental database discussed in Sec. 2 and calculated data discussed in Sec.
6.1. The equation for the dew and bubble-point pressures is
冉 冊 冉 冊兺
p
Tj
⫽
ln
pj
T
8
i⫽1
N i ␪ i/2,
where the N i are the coefficients given in Table 10 for either
the dew or bubble-point pressure equation and ␪ ⫽1
⫺T/T j . Values of N i are zero for the coefficients not listed
in the table. Densities along the dew and bubble lines can be
calculated from the Helmholtz energy formulation given in
Sec. 4 at any temperature and the corresponding pressure
calculated from Eq. 共1兲. Ancillary equations for the densities
TABLE 9. Maxcondentherm, maxcondenbar, and critical point for air
Maxcondenthermb
Maxcondenbar
Critical point
Pressurea
共MPa兲
Temperaturea,c 共K兲
Density
共mol/dm3兲
3.785 02Á0.004Á⌬p
3.7891⫾0.002⫾⌬p
3.7860⫾⌬p
132.6312Á0.002Á⌬T
132.6035⫾0.004⫾⌬T
132.5306⫾⌬T
10.4477Á0.05
11.0948⫾0.05
11.8308⫾0.05
⌬p⫽0.02 MPa, ⌬T⫽0.02 K; the uncertainties in the maxcondentherm and maxcondenbar pressure and temperature comprise components related to the value associated with the critical parameters and smaller components related to the uncertainty in the distance from the critical point.
b
Values used for the reducing parameters in the equation of state.
c
Temperature on ITS-90.
a
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
共1兲
THERMODYNAMIC PROPERTIES OF AIR
along the saturation lines are given here for convenience in
certain calculations such as estimation routines. The equation
for the bubble-point density is
␳
T
⫺1⫽N 1 ␪ 0.65⫹N 2 ␪ 0.85⫹N 3 ␪ 0.95⫹N 4 ␪ 1.1⫹N 5 ln ,
␳j
Tj
共2兲
and the equation for the dew-point density is
ln
冉冊
␳
⫽N 1 ␪ 0.41⫹N 2 ␪ 1.0⫹N 3 ␪ 2.8⫹N 4 ␪ 6.5,
␳j
共3兲
where the coefficients are also given in Table 10. In these
equations, T j , p j , and ␳ j are values at the maxcondentherm.
Comparisons of these equations to experimental data are
given in Sec. 6.1. These ancillary equations are valid for
temperatures from the solidification point 共59.75 K兲 to the
maxcondentherm 共132.6312 K兲. Values for the dew-point
pressure and density between the critical point and the maxcondentherm, shown in Fig. 6, are calculated by the bubblepoint equations.
3.2. Freezing Liquid Line
A freezing liquid line for air was estimated using the melting curves for pure nitrogen, argon, and oxygen due to the
lack of experimental information for the mixture. The solidification temperature T s of air along the bubble line given by
Blanke 共1973兲 is 59.75 K. The solidification pressure p s corresponding to this temperature was calculated from the
bubble-point pressure equation, Eq. 共1兲, as 0.005 265 MPa.
The freezing liquid line for air was assumed to have the same
general pressure dependence as the freezing liquid line for
pure nitrogen. This can be expressed as
p rf ⫽ ␸ p rf ,
Air
共4兲
N2
where the reduced freezing pressures are defined as
p rf ⫽
p f共Tr兲
⫺1
p tp
共5兲
for nitrogen, argon, or oxygen, and
p rf ⫽
p f共Tr兲
⫺1
ps
共6兲
for air. In these equations, p f (T r ) is the freezing liquid pressure at the reduced temperature, T r is the reduced temperature 共T/T tp or T/T s 兲, and the subscript tp indicates the triple
point for nitrogen, argon, or oxygen. The value of ␸ was
determined at a reduced temperature of 2 from
x N2 ln p rf 共 2 兲 ⫹x Ar ln p rf 共 2 兲 ⫹x O2 ln p rf 共 2 兲
N
Ar
O
2
2
⫽ln p rf 共 2 兲 ⫽ln ␸ p rf 共 2 兲 ,
Air
N
共7兲
2
where the mole fractions x are taken from the composition of
air used in this work, and the pure fluid melting pressures
were taken from Span et al. 共2000兲, Tegeler et al. 共1999兲,
and Schmidt and Wagner 共1985兲. The value ␸ calculated
343
TABLE 11. Averaged molar composition of standard air at specified temperatures
Composition
T共K兲
1500
1600
1700
1800
1900
2000
N2
Ar
O2
NO
0.7804
0.7802
0.7797
0.7790
0.7780
0.7768
0.0093
0.0093
0.0093
0.0094
0.0094
0.0094
0.2089
0.2083
0.2078
0.2071
0.2063
0.2056
0.0014
0.0022
0.0032
0.0045
0.0063
0.0082
from this equation is 2.773 234. Although values of the
freezing liquid line for air could have been calculated from a
generalization of Eq. 共7兲, Eq. 共4兲 was selected instead since
its extrapolation behavior to very high temperatures was
known. The resulting equation for the freezing liquid pressure of air is
冋冉 冊
p
T
⫺1⫽35 493.5
ps
Ts
1.789 63
册
⫺1 ,
共8兲
derived using the melting pressure equation of nitrogen
关Span et al. 共2000兲兴.
4. Equation of State for Air
4.1. Effects of Dissociation
The details included in this and the following section are
taken from Panasiti 共1996兲 with some modifications. At high
temperatures, air and its constituents dissociate, and the composition changes to include various atomic and ionic species
and new compounds including oxides of nitrogen. Hilsenrath
and Klein 共1965兲 report the extent of dissociation in the temperature range from 1500 to 15000 K. They considered the
equilibrium between atoms, molecules, and ions for the elements nitrogen, oxygen, argon, carbon, and neon. In all, 28
species were considered by Hilsenrath and Klein. For the
temperature range of current interest, the amount of nitric
oxide 共NO兲 in equilibrium at 2000 K formed from the dissociation of oxygen and nitrogen was large enough that it
might be expected to cause a noticeable change in the thermodynamic properties of the mixture. No other constituents
were considered in the current study due to their small concentrations. Table 11 lists averaged values of composition,
derived from Hilsenrath and Klein, for a mixture of nitrogen,
argon, oxygen, and nitric oxide at various temperatures. Although Hilsenrath and Klein consider a pressure dependence,
the effect on calculated properties is small, and the composition of air is assumed to be constant over all pressures at a
given temperature.
Several methods were considered to determine the effects
of dissociation on the thermodynamic properties of air.
These methods include calculations using cubic equations,
extended corresponding states predictions 关Clarke et al.
共1994兲; Lemmon 共1996兲兴, and mixture equations of state of
the form developed by Bender 共1973兲. Use of extended corJ. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
344
responding states models with accurate pure fluid information is one of the most accurate methods for obtaining mixture properties. However, the equation of state for oxygen
关Schmidt and Wagner 共1985兲兴 has limited temperature and
pressure ranges 共less than 300 K and 82 MPa兲, and the accuracy of properties calculated beyond these limits is uncertain. In addition, there is no published equation of state for
nitric oxide. Therefore, the Peng–Robinson 共1976兲 equation
of state was used with standard mixing rules to determine the
effect of dissociation of air and its constituents. The acentric
factors ␻ required in the Peng–Robinson model and the critical parameters for nitrogen, argon, and oxygen are listed in
the fixed point tables. The critical temperature of nitric oxide
is 180.15 K, the critical pressure is 6.48 MPa, and the acentric factor is 0.6. The values of the critical parameters and the
acentric factor for nitric oxide were taken from Prasad and
Viswanath 共1974兲.
Although cubic equations generally cannot be used to calculate values of density with high accuracy over a wide
range of temperature and pressure, the purpose here was to
compare the differences in density between two mixtures:
the three-component N2 –Ar–O2 model of fixed composition
for air used in this work, and a four-component
N2 –Ar–O2 –NO model which accounted for dissociation by
the addition of the NO component. Errors associated with the
calculation of density differences should be much smaller
than those calculated for the overall value of density. The
highest deviation at 2000 K and 2000 MPa is approximately
0.1%, which is less than the expected uncertainty of experimental measurements at these high temperatures and pressures. The differences in calculated heat capacities between
the two mixtures is approximately 0.8%, also within the estimated uncertainty. Based on this analysis, it was concluded
that dissociation effects are small enough at temperatures up
to 2000 K and pressures to 2000 MPa that they were not
explicitly considered in the development of the new equation
of state for air.
4.2. Calculation of Air Properties from Experimental
Data for Nitrogen
A modified extended corresponding states technique was
used to predict properties of air corresponding to states defined by measurements of nitrogen properties. Experimental
p – ␳ – T measurements for nitrogen extend to 1800 K and
2220 MPa. Air properties were calculated from high-pressure
and high-temperature nitrogen data using the assumption that
the compressibility factors are equal
Z Air共 T Air , ␳ Air兲 ⫽Z N2共 T N2 , ␳ N2兲
共9兲
at corresponding states defined by
T Air⫽ 共 1.038 128⫹0.000 054 933T N2兲 T N2
共10兲
␳ Air⫽1.043 492␳ N2 ,
共11兲
and
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
for T in kelvin. The pressure was calculated from Eq. 共9兲 for
air using nitrogen data
p Air⫽
T Air ␳ Air
p .
T N2 ␳ N2 N2
共12兲
The numerical constants in Eqs. 共10兲 and 共11兲 were obtained by fitting selected p – ␳ – T nitrogen data of Jaeschke
and Hinze 共1991兲, Klimeck et al. 共1998兲, Michels et al.
共1936兲, and Nowak et al. 共1997兲 in the range from 200 to
520 K at pressures to 67 MPa to a preliminary version of the
air equation of state. The data of Nowak et al. represent the
most reliable high temperature, high pressure data available
for nitrogen. This fitting procedure minimized deviations between air properties estimated from nitrogen data and values
calculated from the preliminary equation of state for air. The
average absolute deviations for values calculated from the
nitrogen equation of state of Span et al. 共2000兲 were 0.01%
for the data of Jaeschke and Hinze, 0.002% for the data of
Klimeck et al., 0.02% for the data of Michels et al., and
0.001% for the data of Nowak et al. In comparison, the average absolute deviations for values calculated from the air
equation of state as compared with the transformed data were
0.02% for the data of Jaeschke and Hinze and of Klimeck
et al., 0.04% for the data of Michels et al., and 0.03% for the
data of Nowak et al. Using Eqs. 共10兲–共12兲, high temperature,
high pressure p – ␳ – T nitrogen data of Robertson and Babb
共1969兲 and Saurel 共1958兲 were transformed to predict state
points for air and were used in subsequent fitting of the equation of state for air. The data of Robertson and Babb were
used in the final regression of the coefficients. The estimated
uncertainty of calculated air properties is 1.0% in density at
the highest temperatures and pressures of 2000 K and 2000
MPa.
4.3. Fitting Procedures
The equation of state was developed using selected experimental pressure–density–temperature (p – ␳ – T) data, isochoric heat capacity data, speed of sound data, and second
virial coefficients as indicated in Table 6 and discussed in
Sec. 2. The units adopted for this work are megapascals for
pressure, moles per cubic decimeter for density, kelvins for
temperature, and joules for energy. Units of the experimental
data were converted as necessary from those of the original
publications to these units. All temperatures were converted
to the International Temperature Scale of 1990 共ITS-90兲
based on temperature differences given by Preston-Thomas
共1990兲.
The functional forms of preliminary equations for the residual part of the Helmholtz energy were optimized with the
algorithm developed by Wagner 共1974兲. The fitting process
was used to select an optimal set of terms for representing
the selected data from a large bank of terms of the form
given in Eq. 共25兲 below. The exponents i k , j k , and l k were
selected in this process. The exponents j k in Eq. 共25兲 are
generally considered to be greater than or equal to zero so
that only ideal gas terms contribute as T goes to infinity, and
THERMODYNAMIC PROPERTIES OF AIR
i k and l k are integers greater than zero. Each data point used
in the least-squares determination of the coefficients of the
equation of state was assigned a weighting factor. The
weights used in the fitting process were calculated using the
error propagation formula 共sometimes called the theorem of
propagation of variance兲. The functions for weighting were
calculated by making use of a preliminary equation of state
for the partial derivatives required for estimating variances
by the error propagation formula. In several instances, the
error propagation weights were modified by the assignment
of arbitrary multiplicative factors to increase or lessen the
effect of a particular data set on the overall representation of
the surface.
The isobaric heat capacity and speed of sound data are not
linearly related to the coefficients in the Helmholtz energy
formulation and must first be linearized before being used in
the fitting process. The isobaric heat capacity is linearized by
calculating the density at the experimental pressure and temperature and reducing the isobaric heat capacities to an
equivalent isochoric heat capacity using
冉
冊
⳵␣r
⳵ 2␣ r 2
⫺␦␶
⳵␦
⳵␦⳵␶
.
c v ⫽c p ⫺R
r
⳵␣
⳵ 2␣ r
2
1⫹2 ␦
⫹␦
⳵␦
⳵␦2
1⫹ ␦
4.4. Ideal Gas Heat Capacity
R
⫽x N2
冉 冊
R
⫹x Ar
N2
冉 冊
c 0p 共 T 兲
R
⫹x O2
Ar
冉 冊
c 0p 共 T 兲
R
.
O2
共14兲
The ideal gas heat capacity for nitrogen taken from Span
et al. 共2000兲 is
c 0p
R
4
⫽
兺
i⫽1
N i T i⫺1 ⫹
N 5u 2e u
,
共 e u ⫺1 兲 2
共15兲
5
⫽ .
R 2
Ni
c0p
i
Ni
c0p
of nitrogen,
Eq. „15…
1
2
3
4
5
6
3.5
0.306 646 9⫻10⫺5
0.470 124 0⫻10⫺8
⫺0.398 798 4⫻10⫺12
1.012 941
3364.011
1
2
3
4
5
6
7
1
2
3
4
5
6
7
8
9
10
11
c0p of air,
Eq. „18…
3.490 888 032
2.395 525 583⫻10⫺6
7.172 111 248⫻10⫺9
⫺3.115 413 101⫻10⫺13
0.223 806 688
0.791 309 509
0.212 236 768
0.197 938 904
3364.011
2242.45
11 580.4
1
2
3
4
5
6
7
8
9
10
11
12
13
of oxygen,
Eq. „17…
3.500 42
0.166 961⫻10⫺7
1.067 78
1.012 58
0.944 365
2242.45
11 580.4
␣0 of air,
Eq. „24…
0.605 719 400⫻10⫺7
⫺0.210 274 769⫻10⫺4
⫺0.158 860 716⫻10⫺3
⫺13.841 928 076
17.275 266 575
⫺0.195 363 420⫻10⫺3
2.490 888 032
0.791 309 509
0.212 236 768
⫺0.197 938 904
25.363 65
16.907 41
87.312 79
N3
N 4v 2e v
共 2/3兲 N 5 w 2 e ⫺w
⫽N 1 ⫹N 2 T ⫹ 1.5 ⫹ v
⫹
,
R
T
共 e ⫺1 兲 2 关共 2/3兲 e ⫺w ⫹1 兴 2
共17兲
c 0p
2
where v ⫽N 6 /T and w⫽N 7 /T. The coefficients for Eqs.
共15兲 and 共17兲 are given in Table 12.
The ideal gas heat capacity c 0p for air, calculated by combining the ideal gas heat capacity equations for nitrogen,
argon, and oxygen, according to Eq. 共14兲, is given by the
following expression:
c 0p
4
⫽
N
N u 2e u
N v 2e v
5
6
7
N i T i⫺1 ⫹ 1.5 ⫹ u
兺
2⫹
v
T
e
⫺1
e
⫺1 兲 2
兲
共
共
i⫽1
⫹
共 2/3 兲 N 8 w 2 e ⫺w
,
共共 2/3兲 e ⫺w ⫹1 兲 2
共18兲
where u⫽N 9 /T, v ⫽N 10 /T, and w⫽N 11 /T. The coefficients of this equation are given in Table 12; note that different values for the coefficients N i are used in Eqs. 共15兲,
共17兲, and 共18兲
4.5. Ideal Gas Helmholtz Energy
The ideal gas contribution to the Helmholtz energy of air
is given by
3
where u⫽N 6 /T. The ideal gas heat capacity for argon is
c 0p
i
R
The ideal gas heat capacity for air is given by the mole
fraction average of the ideal gas heat capacities for nitrogen,
argon, and oxygen
c 0p 共 T 兲
TABLE 12. Coefficients for the ideal gas expressions
共13兲
The speed of sound is linearized by calculating the density
and the ratio of the heat capacities ␥ from a preliminary
equation of state. To improve the representation of the speed
of sound data and of the available shock tube data for air, the
final functional form was developed using nonlinear regression techniques. Using a combination of linear and nonlinear
techniques, a functional form was obtained which yielded the
best representation of the selected experimental data. Details
of the nonlinear fitting procedures are given by Lemmon and
Jacobsen 共2000兲.
c 0p 共 T 兲
345
共16兲
The ideal gas heat capacity for oxygen taken from Schmidt
and Wagner 共1985兲 is
a 0 ⫽⫺RT⫹
兺 x i共 h 0i ⫺Ts 0i ⫹RT ln x i 兲 ,
i⫽1
共19兲
where x i is the mole fraction of component i in air, and h 0i
and s 0i are the ideal gas enthalpy and entropy of component i
at the specified temperature. The ideal gas enthalpy is given
by
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
346
0
h 0i ⫽h 0i
⫹
冕
T
T0
TABLE 13. Coefficients and exponents for the equation of state for air
共20兲
c 0pi dT,
0
h 0i
where
is the enthalpy datum value at the reference temperature (T 0 ) for component i, based upon a zero reference
point for the ideal crystal at absolute zero temperature. The
ideal gas entropy is given by
0
⫹
s 0i ⫽s 0i
冕
冉 冊
T c0
pi
T0
p0
dT⫺R ln
,
T
p0
共21兲
0
s 0i
where
is the entropy datum value at the reference temperature and pressure 共T 0 and p 0 兲 for component i, also
based upon a zero reference point of the ideal crystal at absolute zero temperature. The variable p 0 is the ideal gas pressure at the fluid density and temperature. Combining Eqs.
共19兲–共21兲 results in the following expression for the ideal
gas Helmholtz energy
3
a ⫽⫺RT⫹
0
⫹
冕
T
T0
兺 xi
i⫽1
冉
RT ln
c 0pi dT⫺T
冕
T
T0
␳T
0
0
⫹h 0i
⫺Ts 0i
␳ 0T 0
c 0pi
T
冊
共22兲
dT⫹RT ln x i ,
where p 0 /p 0 has been replaced with ␳ T/ ␳ 0 T 0 . Dividing Eq.
共22兲 by RT and replacing the temperatures with T ci / ␶ and
the densities with ␦ ␳ ci results in
3
␣ 0⫽
冉
0
0
␶ s 0i
␦ ␶ 0 h 0i
␶
a0
x i ln
⫹
⫺
⫽⫺1⫹
⫺
RT
␦ 0 ␶ RT c R R
i⫽1
兺
⫹
1
R
冕
␶
c 0pi
␶0
␶
冊
d ␶ ⫹ ln x i ,
冕
␶
c 0pi
␶0
␶2
d␶
共23兲
where ␶ 0 ⫽T ci /T 0 , ␦ 0 ⫽ ␳ 0 / ␳ ci is the reduced ideal gas density at p 0 and T 0 , T 0 is the reference temperature 共298.15
K兲, and p 0 is the reference pressure 共0.101 325 MPa兲. T ci
and ␳ ci are the critical parameters of the pure fluids. Values
0
0
and s 0i
for nitrogen, argon, and oxygen are taken from
of h 0i
Cox et al. 共1989兲 and are given in the fixed point tables.
The following expression for ␣ 0 is obtained by combining
Eqs. 共18兲 and 共23兲:
5
␣ 0 ⫽ln ␦ ⫹ 兺 N i ␶ i⫺4 ⫹N 6 ␶ 1.5⫹N 7 ln ␶
i⫽1
⫹N 8 ln关 1⫺exp共 ⫺N 11␶ 兲兴 ⫹N 9 ln关 1⫺exp共 ⫺N 12␶ 兲兴
⫹N 10 ln关 2/3⫹exp共 N 13␶ 兲兴 ,
共24兲
where ␦ ⫽ ␳ / ␳ j and ␶ ⫽T j /T, as given by Eq. 共25兲 in the Sec.
4.6, and T j and ␳ j are parameters at the maxcondentherm of
air. The coefficients of this equation are given in Table 12.
4.6. Equation of State for Air
The equation of state for air was developed using experimental data for pressure–density–temperature (p – ␳ – T),
isochoric heat capacity, speed of sound, and second virial
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
k
Nk
1
2
0.118 160 747 229
0.713 116 392 079
⫺0.161 824 192 067⫻101
3
ik
jk
lk
1
1
0
0.33
0
0
1
1.01
0
4
0.714 140 178 971⫻10⫺1
2
0
0
5
⫺0.865 421 396 646⫻10⫺1
6
0.134 211 176 704
3
3
0
0.15
0
0
7
0.112 626 704 218⫻10⫺1
4
0
0
8
⫺0.420 533 228 842⫻10⫺1
4
0.2
0
9
0.349 008 431 982⫻10⫺1
4
0.35
0
10
0.164 957 183 186⫻10⫺3
1.35
1.6
0
1
11
⫺0.101 365 037 912
6
1
12
13
⫺0.173 813 690 970
⫺0.472 103 183 731⫻10⫺1
3
0.8
1
5
0.95
1
14
⫺0.122 523 554 253⫻10⫺1
15
⫺0.146 629 609 713
6
1
1.25
3.6
1
2
16
⫺0.316 055 879 821⫻10⫺1
3
6
2
17
0.233 594 806 142⫻10⫺3
18
19
0.148 287 891 978⫻10⫺1
⫺0.938 782 884 667⫻10⫺2
11
1
3.25
3.5
2
3
3
15
3
coefficients, along with calculated air properties at high temperatures and pressures as described in Sec. 4.2. Values of
p – ␳ – T on the dew and bubble-point curves calculated using
Eqs. 共1兲, 共2兲, and 共3兲 were used to define the vapor–liquid
equilibrium boundaries. To expand the range of the equation
beyond 2000 K and 2000 MPa, data published by Nellis
et al. 共1991兲, determined using a shock tube apparatus, were
included in the fitting process as discussed in Sec. 4.8 below.
The equation of state for air used in this work is explicit in
the nondimensional Helmholtz energy
␣共 ␦,␶ 兲⫽
a 共 ␳ ,T 兲
⫽ ␣ 0共 ␦ , ␶ 兲 ⫹ ␣ r共 ␦ , ␶ 兲 ,
RT
共25兲
where ␣ 0 is the ideal-gas contribution to the Helmholtz energy given in the previous section, ␣ r is the residual contribution to the Helmholtz energy, ␦ ⫽ ␳ / ␳ j is the reduced density, ␶ ⫽T j /T is the reciprocal reduced temperature, ␳ j is the
density at the maxcondentherm, and T j is the temperature at
the maxcondentherm.
The residual Helmholtz energy contribution to the equation of state is given by
10
␣ 共 ␦ , ␶ 兲⫽ 兺 N k␦ ␶ ⫹
r
ik jk
k⫽1
19
兺
k⫽11
N k ␦ i k ␶ j k exp共 ⫺ ␦ l k 兲 .
共26兲
The coefficients N k of the equation of state are given in
Table 13. The values of i k , j k , and l k were determined from
the fitting procedures described in Sec. 4.3. For the nonexponential terms in Eq. 共26兲, i k ranges from 1 to 6 and j k
ranges from 0 to 1.35. The thermodynamic properties can be
THERMODYNAMIC PROPERTIES OF AIR
calculated from the Helmholtz energy using differentiation
with respect to density and temperature as described in Sec.
4.7.
4.7. Calculation of Thermodynamic Properties
The functions used for calculating pressure, compressibility factor, internal energy, enthalpy, entropy, Gibbs energy,
isochoric heat capacity, isobaric heat capacity, and the speed
of sound from Eq. 共25兲 are given as Eqs. 共27兲–共34兲. These
functions were used in calculating the tables of thermodynamic properties of air given in the Appendix. The densities
for the dew and bubble-point states are determined by the
simultaneous solution of the dew or bubble-point pressure
equation 共1兲 and the equation of state for a given temperature. The derived properties for saturation states are calculated as functions of temperature and density using the standard thermodynamic relations given in Eqs. 共27兲–共34兲.
冉 冊
冋冉 冊 冉 冊 册
冋冉 冊 冉 冊 册 冉 冊
冋冉 冊 冉 冊 册
⳵␣r
p
⫽1⫹ ␦
Z⫽
␳ RT
⳵␦
⳵␣
⳵␶
u
⫽␶
RT
h
⫽␶
RT
⳵␣0
⳵␶
⫹
␦
⳵␣r
⫹
⳵␶
␦
⳵␣0
⳵␶
s
⫽␶
R
⳵␣
⳵␶
0
␶
r
共28兲
⳵␣r
⫹␦
⫹1
⳵␦ ␶
␦
⳵␣r
⫹
⳵␶
␦
⫺ ␣ 0⫺ ␣ r
␦
冉 冊
⳵ 2␣ 0
⳵␶2
1⫹ ␦
⫹
␦
⳵ 2␣ r
⳵␶2
⳵␣r
⳵ 2␣ r
⫺␦␶
⳵␦ ␶
⳵␦⳵␶
⫹␦
2
␶
⳵ 2␣ r
⳵␦2
w2M c p
⳵␣r
⳵ 2␣ r
1⫹2 ␦
⫹␦2
⫽
RT
cv
⳵␦ ␶
⳵␦2
冉 冏冊
1 ⳵␣r
␳ j ⳵␦
⳵2p
⳵␳ 2
⫽
T
冋 冉 冊 冉 冊 冉 冊册
冉 冊 冋 冉 冊 冉 冊册
⳵p
⳵T
⫽R ␳ 1⫹ ␦
␳
␶ ␦ ⫽0
␮ J⫽
k T ⫽⫺
␤⫽
⳵␣r
⳵ 2␣ r
⫺␦␶
⳵␦ ␶
⳵␦⳵␶
冉 冊
⳵T
⳵p
⫽
h
冉 冊 冉 冊
v ⳵p
p ⳵v
⫽
T
⫽
p
1 ⳵p
␳ ⳵T
␬⫽
冉
冉
冉
冉
冊
冊
冊
冊
1 ⳵v
1
⫽⫺
kp
v ⳵p
⳵p
⳵v
共42兲
共43兲
T
共44兲
s
共45兲
s
1 ⳵v
1
⫽⫺
kTp
v ⳵p
T
⳵p
⳵v
T
K T ⫽k T p⫽⫺ v
共39兲
T
⳵␳
⳵p
␳
共38兲
共41兲
冉 冊 冉 冊冉 冊
B s ⫽kp⫽⫺ v
共35兲
␳ ⳵p
p ⳵␳
␶
共40兲
冉 冊
1 ⳵v
v ⳵T
共33兲
␶
T ␤ ⫺1
␳cp
w 2␳ M
v ⳵p
⫽
p ⳵v s
p
␤ s⫽
共34兲
共37兲
␶
⳵␣r
⳵ 2␣ r
⳵ 3␣ r
RT
2␦
⫹4 ␦ 2
⫹␦3
2
␳
⳵␦ ␶
⳵␦ ␶
⳵␦3
共31兲
Equations for the second and third virial coefficients are
given in Eqs. 共35兲–共36兲.
B共 T 兲⫽
冉 冊
共30兲
␶
共36兲
␶ ␦ ⫽0
⳵␣r
⳵ 2␣ r
⫹␦2
⳵␦ ␶
⳵␦2
T
2
冋 冉 冊 冉 冊册
冋 冉 冊 冉 冊册
⳵␣r
1⫹2 ␦
⳵␦
冉 冏冊
⳵ 2␣ r
⳵␦2
⫽RT 1⫹2 ␦
k⫽⫺
␦
␳ 2j
冉 冊 冋 冉 冊 冉 冊册
⳵p
⳵␳
共29兲
共32兲
1
Other derived properties, given in Eqs. 共37兲–共47兲, include
the first derivative of pressure with respect to density
( ⳵ p/ ⳵␳ ) T , second derivative of pressure with respect to density ( ⳵ 2 p/ ⳵␳ 2 ) T , first derivative of pressure with respect to
temperature ( ⳵ p/ ⳵ T) ␳ , Joule–Thomson coefficient ( ␮ J ),
isentropic expansion coefficient 共k兲, isothermal expansion
coefficient (k T ), volume expansivity ( ␤ ), adiabatic compressibility ( ␤ s ), adiabatic bulk modulus (B s ), isothermal
compressibility ( ␬ ), and isothermal bulk modulus (K T ).
␶
冋冉 冊 冉 冊 册
冋 冉 冊 冉 冊册
cv
⫽⫺ ␶ 2
R
C共 T 兲⫽
␦
g
⳵␣r
⫽1⫹ ␣ 0 ⫹ ␣ r ⫹ ␦
RT
⳵␦
cp cv
⫽ ⫹
R
R
共27兲
347
共46兲
共47兲
The derivatives of the ideal gas Helmholtz energy, Eq.
共24兲, are given in Eqs. 共48兲–共49兲.
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
348
冏
5
⳵␣0
N 8 N 11
⫽
共 i⫺4 兲 N i ␶ i⫺5 ⫹1.5N 6 ␶ 0.5⫹N 7 / ␶ ⫹ N 11␶
⳵ ␶ ␦ i⫽1
e
⫺1
兺
⫹
冏
N 9 N 12
N 10N 13
⫹
N 12␶
e
⫺1 共 2/3兲e⫺N13␶ ⫹1
共48兲
5
⳵ 2␣ 0
⫽
共 i⫺4 兲共 i⫺5 兲 N i ␶ i⫺6 ⫹0.75N 6 ␶ ⫺0.5⫺N 7 / ␶ 2
⳵ 2 ␶ ␦ i⫽1
兺
⫺
2 N 11␶
e
N 8 N 11
2 N 12␶
e
N 9 N 12
共 e N 11␶ ⫺1 兲
共 e N 12␶ ⫺1 兲 2
2⫺
2 ⫺N13␶
e
共 2/3兲 N 10N 13
⫹
共49兲
关共 2/3兲 e ⫺N 13␶ ⫹1 兴 2
The derivatives of the residual Helmholtz energy, Eq. 共26兲,
are given in Eqs. 共50兲–共55兲.
冏
10
19
⳵␣r
⫽
i N ␦ i k ⫺1 ␶ j k ⫹
N k ␦ i k ⫺1 ␶ j k
⳵ ␦ ␶ k⫽1 k k
k⫽11
兺
兺
⫻exp共 ⫺ ␦ l k 兲共 i k ⫺l k ␦ l k 兲
冏
10
共50兲
19
⳵ 2␣ r
⫽
i 共 i ⫺1 兲 N k ␦ i k ⫺2 ␶ j k ⫹
N k ␦ i k ⫺2 ␶ j k
⳵ ␦ 2 ␶ k⫽1 k k
k⫽11
兺
兺
⫻exp共 ⫺ ␦ l k 兲关共 i k ⫺l k ␦ l k 兲共 i k ⫺1⫺l k ␦ l k 兲 ⫺l 2k ␦ l k 兴
共51兲
冏
FIG. 7. Calculated Hugoniot curve for air.
extrapolation behavior of an equation of state is the examination of the Hugoniot curve. The conservation relations for
fluid properties before and after the shock wave taken from
Nellis et al. and the equation of state presented here were
used to generate the Hugoniot curve for air. The Hugoniot
curve is the locus of states accessible to a fluid after a shock
wave which occur at a specified initial state. The equations
for the conservation of mass, momentum, and energy across
the shock wave are
p⫺p 0 ⫽ ␳ 0 共 w s ⫺w 0 兲共 w p ⫺w 0 兲 ,
10
⳵ 3␣ r
⫽
i 共 i ⫺1 兲共 i k ⫺2 兲 N k ␦ i k ⫺3 ␶ j k
⳵ ␦ 3 ␶ k⫽1 k k
兺
冋
v ⫽ v 0 1⫺
19
⫹
兺
k⫽11
N k ␦ i k ⫺3 ␶ j k exp共 ⫺ ␦ l k 兲 兵 i k 共 i k ⫺1 兲共 i k ⫺2 兲
⫹ ␦ l k 关 ⫺2l k ⫹6i k l k ⫺3i 2k l k ⫺3i k l 2k ⫹3l 2k ⫺l 3k 兴
⫹共 ␦ 兲
lk 2
冏
关 3i k l 2k ⫺3l 2k ⫹3l 3k 兴 ⫺l 3k 共 ␦ l k 兲 3 其
10
共52兲
19
⳵␣r
⫽
j N ␦ i k ␶ j k ⫺1 ⫹
j k N k ␦ i k ␶ j k ⫺1 exp共 ⫺ ␦ l k 兲
⳵ ␶ ␦ k⫽1 k k
k⫽11
共53兲
兺
冏
兺
10
19
⳵ 2␣ r
⫽
j 共 j ⫺1 兲 N k ␦ i k ␶ j k ⫺2 ⫹
j k 共 j k ⫺1 兲
⳵ ␶ 2 ␦ k⫽1 k k
k⫽11
兺
兺
i k j k ⫺2
⫻N k ␦ ␶
exp共 ⫺ ␦ 兲
lk
10
共54兲
19
⳵ 2␣ r
⫽
i j N ␦ i k ⫺1 ␶ j k ⫺1 ⫹
j k N k ␦ i k ⫺1 ␶ j k ⫺1
⳵ ␶ ⳵ ␦ k⫽1 k k k
k⫽11
兺
兺
⫻exp共 ⫺ ␦ 兲共 i k ⫺l k ␦ 兲
lk
lk
共55兲
4.8. Hugoniot Curve
Data measured with a shock tube apparatus 关Nellis et al.,
共1991兲兴 were included in the optimization of the equation of
state for air to improve the extrapolation behavior beyond
2000 K and 2000 MPa. One method used to demonstrate the
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
册
共 w p ⫺w 0 兲
,
共 w s ⫺w 0 兲
共56兲
共57兲
and
u⫺u 0 ⫽0.5共 p⫹ p 0 兲共 v 0 ⫺ v 兲 ,
共58兲
where p 0 is the initial pressure, ␳ 0 is the initial mass density,
u 0 is the initial molar internal energy, v 0 is the initial molar
volume, w 0 is the initial velocity of the material ahead of the
shock front, p is the final shock pressure, v is the final molar
volume, and u is the final molar internal energy. The velocity
of the shock wave is w s and the velocity of the material
downstream from the shock front is w p . Combining Eqs.
共56兲 and 共57兲 results in
冉
v ⫽ v 0 1⫺
p⫺ p 0
␳ 0 w s2
冊
.
共59兲
Rearrangement of Eq. 共58兲 results in
v⫽
⫺2 共 u⫺u 0 兲
⫹v0 .
p⫹ p 0
共60兲
To calculate a point on the Hugoniot curve for air for a
specified upstream state (p 0 ,T 0 兲 and downstream pressure
共p兲, Eqs. 共59兲 and 共60兲 are solved simultaneously by iterating
on the unknown value for the shock wave velocity w s . The
calculated molar volume from Eq. 共59兲 is used with the
known value of p to calculate the temperature and internal
energy u from the air equation of state. Figure 7 shows the
THERMODYNAMIC PROPERTIES OF AIR
TABLE 14. Pure fluid equations of state used in the mixture model
Fluid
Nitrogen
Argon
Oxygen
Author
Temperature
range 共K兲
Maximum
pressure 共MPa兲
Span et al. 共2000兲
Tegeler et al. 共1999兲
Schmidt and Wagner 共1985兲
63.151–1000
83.806–700
54.361–300
2200
1000
82
Hugoniot curve for air calculated using this process for an
initial state on the bubble line at 77.1 K as specified by Nellis
et al. The data point on the plot is the lowest measured shock
tube point from Nellis et al. The reported shock tube points
above 30 GPa were not included because, according to Nellis
et al., nitrogen spontaneously dissociates above 30 GPa.
As shown in Fig. 7, the Hugoniot curve approaches the
shock tube point of Nellis et al. 共1991兲 indicating that the
extrapolation behavior of the equation of state presented here
is reasonable. However, the extrapolation behavior of the
formulation should not be based solely on Fig. 7. To further
assess the extrapolation behavior of the formulation, other
techniques, such as determining the isothermal behavior at
extreme pressures and densities, were used. These techniques
are described in Sec. 7.1.
5. Mixture Model for the
Nitrogen–Argon–Oxygen System
5.1. Mixture Model
The model used in this work to calculate the thermodynamic properties of nitrogen–argon–oxygen mixtures is
based on the Helmholtz energy of the mixture using a corresponding states theory that was originally developed by
Lemmon 共1996兲 and Lemmon and Jacobsen 共1998兲, 共1999兲.
The Helmholtz energy of the mixture is calculated as the
sum of an ideal gas contribution, a real gas contribution, and
a contribution from mixing. The Helmholtz energy for an
ideal solution 共the first two contributions兲 is determined at
the reduced density and temperature of the mixture using
accurate pure fluid equations of state for the mixture components. The contribution from mixing, a modified excess function, is given by a single generalized empirical equation
which is applied to all mixtures considered. Reducing parameters, which are dependent on the mole fraction, are used to
modify values of density and temperature. The model may
be used to calculate thermodynamic properties of mixtures at
various compositions, including dew and bubble-point properties and critical points. It incorporates the most accurate
published equation of state for each pure fluid as given in
Table 14. Additional information concerning the model is
given by Lemmon and Tillner-Roth 共1999兲.
An excess property of a mixture is defined as the actual
mixture property at a given condition minus the value for an
ideal solution at the same condition. In most other work dealing with excess properties, the mixing condition is defined at
constant pressure and temperature. Because the independent
variables for the pure fluid Helmholtz energy equations are
349
density and temperature, properties are calculated here at the
density and temperature of the mixture. Since this model
deals with the entire fluid surface, reduced values of density
and temperature are used rather than the physical values to
ensure that properties of the constituents are calculated for
the same phase as the mixture. While this approach is arbitrary and different from the usual excess property format, it
results in an accurate representation of the phase boundaries
for pure fluids and their mixtures.
The formulation for nitrogen–argon–oxygen mixtures
given here is a modification of the generalized model developed by Lemmon 共1996兲 for a wide range of fluids including
hydrocarbons and cryogens. It preserves the general nature
of the previous work, but is more accurate at low temperatures for the calculation of nitrogen–argon–oxygen mixture
properties than the prior formulation. By restricting the application to a particular class of fluids, the model was designed to represent the unique characteristics of this system.
The model represents available measured data in all parts of
the thermodynamic surface within their estimated experimental accuracy.
An advantage of the approach used here is that the behavior of the Helmholtz energy contribution from mixing is the
same for the nitrogen–oxygen, nitrogen–argon, and argon–
oxygen binary systems. Relatively simple scaling factors are
used to determine its magnitude for each pair. This generalization makes it possible to extend the limits of the model for
the argon–oxygen mixture, for which there are few experimental single-phase data. In addition, all vapor and liquid
thermodynamic properties, including energy, entropy, heat
capacity, sound speed, and the mixture critical temperature,
pressure, and density, can be calculated using this approach.
Preliminary equations for the mixture model based on the
Helmholtz energy have incorporated equations with 7–10
terms in the excess contribution 关Lemmon and Jacobsen,
共1998兲, 共1999兲兴. Many of these terms were included to account for deficiencies in the pure fluid equations, especially
in the extrapolation behavior to high temperatures and pressures, and at temperatures below the triple points of the pure
fluids. The equation presented here uses only two terms and
is more predictive in nature, and results calculated for the
argon–oxygen system should generally be more accurate
than the preliminary models.
The Helmholtz energy for mixtures of nitrogen, argon, and
oxygen can be calculated using
a⫽a idmix⫹a E .
共61兲
The Helmholtz energy for the ideal mixture is
3
a idmix⫽
兺 x i 关 a 0i 共 ␳ ,T 兲 ⫹a ri 共 ␦ , ␶ 兲 ⫹RT ln x i 兴 ,
i⫽1
共62兲
In these equations, ␳ and T are the mixture density and temperature, a 0i is the ideal gas Helmholtz energy for component
i, and a ri (⫽ ␣ ri RT) is the pure-fluid residual Helmholtz energy of component i evaluated at a reduced density and temperature defined below. Equations for the ideal gas HelmJ. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
350
TABLE 15. Parameters of the mixture model
Nitrogen–Argon
Nitrogen–Oxygen
Argon–Oxygen
Fij
␨ i j 共K兲
␰ i j 共dm3/mol兲
1.121 527
1.
0.597 203
⫺1.237 713
⫺0.856 350
⫺2.115 126
⫺0.000 760 31
⫺0.000 418 47
0.000 412 32
holtz energy and residual Helmholtz energy for the pure
fluids are given in the references shown in Table 14.
The excess contribution to the Helmholtz energy from
mixing used in this work is
aE
⫽ ␣ E 共 ␦ , ␶ ,x兲
RT
再兺
2
⫽
冎
3
兺
x i x j F i j 关 ⫺0.001 952 45␦ 2 ␶ ⫺1.4
i⫽1 j⫽i⫹1
⫹0.008 713 34␦ 2 ␶ 1.5兴 ,
共63兲
where the coefficients and exponents were obtained from
nonlinear regression of experimental mixture data. Values of
F i j are given in Table 15. All single phase thermodynamic
properties can be calculated from the Helmholtz energy as
described in Sec. 4.7 using the relations
3
␣ ⫽ 兺 xi
0
i⫽1
冋
a 0i 共 ␳ ,T 兲
RT
⫹ln x i
册
共64兲
rameters of the mixture model. The generalized factors and
mixture parameters F i j , ␨ i j and ␰ i j are given in Table 15.
If equations for the ideal gas Helmholtz energy in the nondimensional form ␣ 0i ( ␦ , ␶ ), similar to Eq. 共24兲, are used
rather than equations in the dimensional form a 0i ( ␳ ,T) as
indicated by Eq. 共64兲, the reducing variables for ␦ and ␶ in
the ideal gas equation are
␦ ⫽ ␳ / ␳ ci
共70兲
␶ ⫽T c i /T,
共71兲
and
rather than the reducing values defined by Eqs. 共66兲 and 共67兲.
This only applies to the ideal gas part of the equation, not to
the residual Helmholtz energy. The residual and excess terms
␣ ri ( ␦ , ␶ ) and ␣ E ( ␦ , ␶ ,x) in Eq. 共65兲 must be evaluated at the
reduced state point of the mixture defined by Eqs. 共66兲 and
共67兲. This complication is avoided though the use of dimensional equations of the form given in Eq. 共22兲 or dimensionless equations of the form given in Eq. 共23兲 where the critical
properties cancel out of the equation. Equations of the form
given in Eq. 共24兲 are derived from dimensional equations,
and the critical parameters of the pure fluids are built into the
coefficients of the equations.
5.2. Vapor–Liquid Equilibrium „VLE… Properties
In a two-phase nonreacting mixture, the thermodynamic
constraints for vapor–liquid equilibrium 共VLE兲 are
and
3
␣ ⫽ 兺 x i ␣ ri 共 ␦ , ␶ 兲 ⫹ ␣ E 共 ␦ , ␶ ,x兲 ,
共65兲
r
i⫽1
where the derivatives are taken at constant composition. Calculations of two-phase properties are described in Sec. 5.2.
The reduced values of density and temperature for the mixture used in Eqs. 共63兲 and 共65兲 are
␦ ⫽ ␳ / ␳ red
共66兲
␶ ⫽T red /T,
共67兲
and
T ⬘ ⫽T ⬙ ⫽T,
共72兲
p ⬘ ⫽ p ⬙ ⫽ p,
共73兲
and
␮ i⬘ ⫽ ␮ i⬙ ,
␳ red⫽
冉兺
i⫽1
2
xi
⫹
␳ c i i⫽1
3
兺 j⫽i⫹1
兺 x ix j␰ i j
冊
T red⫽
2
共68兲
3
兺 x i T c ⫹ i⫽1
兺 j⫽i⫹1
兺 x ix j␨ i j .
i⫽1
i
共69兲
The parameters ␨ i j and ␰ i j are used to define the shapes of
the reducing temperature lines and reducing density lines.
These reducing parameters are not the same as the critical
parameters of the mixture and are determined simultaneously
in the nonlinear fit of experimental data with the other paJ. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
f i⬘ ⫽ f i⬙ .
共75兲
The chemical potential of component i in a mixture is
⫺1
and
3
共74兲
where the superscripts ⬘ and ⬙ refer to the liquid and vapor
phases, respectively, and q is the number of components in
the mixture. Equation 共74兲 is identical to equating the fugacities of the liquid and vapor phases for each component in the
mixture
where ␳ and T are the mixture density and temperature, and
␳ red and T red are the reducing values
3
i⫽1,2,...,q,
␮ i 共 ␳ ,T 兲 ⫽
冉 冊
⳵A
⳵ni
⫽ ␮ ci 共 T 兲 ⫹RTln共 f i 兲 ,
共76兲
T,V,n j
where ␮ ci (T) is a function of temperature only and the notation n j indicates that all mole numbers are held constant
except n i . The chemical potential in an ideal gas mixture is
␮ 0i ⫽
冉 冊
⳵A0
⳵ni
⫽ ␮ ci 共 T 兲 ⫹RT ln共 f 0i 兲 ,
共77兲
T,V,n j
where f 0i is the ideal gas partial pressure of constituent i,
x i p 0 ⫽x i ␳ RT. Subtracting these equations results in
THERMODYNAMIC PROPERTIES OF AIR
351
TABLE 16. Different types of VLE calculations
Calculation type
Specified quantities
BUBL p
DEW p
BUBL T
DEW T
FLASH
T
T
p
p
Calculated quantities
and the x i
and the y i
and the x i
and the y i
T and p
f i ⫽x i ␳ RT exp
冉
p
p
T
T
⳵共 n␣r兲
⳵ni
冊
and the y i
and the x i
and the y i
and the x i
x i and y i
共78兲
,
T,V,n j
where ␣ r was defined in Eq. 共65兲. The partial derivative at
constant temperature, total volume 共not molar volume兲, and
mole number of all constituents except i is generally evaluated numerically.
Five common VLE calculations are listed in Table 16. The
VLE conditions for these five calculations can be determined
iteratively. The x i represent the mole fractions in the liquid
phase, and the y i represent the mole fractions in the vapor
phase. Details of the iterative processes can be found in Van
Ness and Abbott 共1982兲 or Smith and Van Ness 共1975兲.
5.3. Critical Locus
In the development of the mixture model, equations for
the reducing parameters were given for the calculation of the
reduced density and temperature ␦ and ␶. These parameters
are equal to the critical parameters in the pure fluid limits.
For a mixture, the reducing parameters are not the same as
the critical parameters, but are empirical functions designed
to minimize the deviations between experimental data and
the mixture model.
The criteria for the critical point of a binary mixture are
冉 冊 冉 冊
⳵ 2g
⳵x2
⳵ 3g
⫽
⳵x3
p,T
⫽0,
共79兲
冉 冊
⳵ ⳵ 2g
⬇
⳵T ⳵x2
p,T
and
冉 冊
⳵ ⳵ g
⳵T ⳵x3
⳵ g
⳵x3
3
⌬
冉 冊
⳵ ⳵ 2g
⌬T⫹
⳵p ⳵x2
p,T
冉 冊
冉 冊
⳵ ⳵ g
⳵p ⳵x3
3
⬇
p,T
冉 冊
⌬p
p,T
⌬T⫹
共80兲
⌬p,
p,T
冉 冊 冉 冊 冉 冊 冉 冊
冉 冊 冉 冊 冉 冊 冉 冊
⳵ 2g
⳵x2
⳵ ⳵ 3g
⳵p ⳵x3
p,T
⳵ ⳵ g
⳵T ⳵x3
⳵ ⳵ g
⳵
p ⳵x2
p,T
3
共81兲
where ⌬T and ⌬p are the differences from the critical point
temperature and pressure in an iterative algorithm for finding
the critical point, and the left sides of these equations represent the deviations from the zero value at the critical point
indicated in Eq. 共79兲. Solving these equations for ⌬T and ⌬p
results in
⳵ 3g
⳵x3
⫺
p,T
2
⳵ ⳵ 2g
⳵p ⳵x2
p,T
⳵ ⳵ g
⳵T ⳵x2
2
⫺
p,T
p,T
3
⳵ ⳵ g
⳵
p ⳵x3
p,T
p,T
共82兲
and
⫺
3
p,T
⌬T⬇
p,T
where g is the molar Gibbs energy of the mixture. Near the
critical point, this equation can be expanded in terms of the
numerical differences
⳵ 2g
⌬
⳵x2
FIG. 8. Critical lines for nitrogen–argon, nitrogen–oxygen, and argon–
oxygen binary mixtures.
⌬p⬇
冉 冊
⳵ 2g
⳵x2
冉 冊
冉 冊
⫺
p,T
⳵ ⳵ 2g
⳵T ⳵x2
⳵ ⳵ 2g
⳵p ⳵x2
⌬T
p,T
,
共83兲
p,T
from which an estimate of the location of the critical point
can be obtained. The reducing parameters can be used as
initial estimates for the critical pressure and temperature and
the values of T and p are repeatedly incremented according
to Eqs. 共82兲 and 共83兲 until the second and third derivatives of
the Gibbs energy are both simultaneously near zero.
The critical lines for the nitrogen–argon, nitrogen–
oxygen, and argon–oxygen binary mixtures are shown in
Fig. 8 along with experimental values of the critical temperature from Jones and Rowlinson 共1963兲. The value of T c for
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
352
oxygen reported by Jones and Rowlinson is 0.3% different
from the value given by Schmidt and Wagner 共1985兲. Likewise, the value for argon is 0.2% different from that given by
Tegeler et al. 共1999兲. To account for these differences, the
experimental values of Jones and Rowlinson were corrected
for each 共i, j兲 binary pair using
T c ⫽T c,Jones⫹x i 共 T c,i ⫺T c,i,Jones兲 ⫹x j 共 T c, j ⫺T c, j,Jones兲 .
共84兲
The adjusted values are also shown in Fig. 8.
6. Comparisons of Calculated Properties
to Experimental Data
The uncertainty of the equation of state and the mixture
model was determined by statistical comparisons of property
values calculated with the equation of state or mixture model
to experimental data. These statistics are based on the percent deviation in any property X defined as
%⌬X⫽100
冉
冊
X exp⫺X calc
,
X exp
共85兲
where X exp is the measured or predicted data, and X calc is
computed from the equation of state. Using this definition,
the average absolute deviation 共AAD兲 is defined as
FIG. 9. Comparisons of dew and bubble-point properties calculated with the
ancillary equations toexperimental and calculated data for air.
n
1
兩 %⌬X i 兩 ,
AAD⫽
n i⫽1
兺
共86兲
where n is the number of data points. For the second virial
coefficient, the difference in B 共in cm3/mol兲 is used rather
than the percent difference since the percent difference can
become very large near B⫽0.
6.1. Comparisons of the Ancillary Equations for
Air with Experimental Data
Comparisons of dew and bubble-point properties calculated using Eqs. 共1兲, 共2兲, and 共3兲 to the experimental data of
Blanke 共1977兲, Michels et al. 共1954a兲, Kuenen and Clark
共1917兲 and the calculated data reported by Jacobsen et al.
共1990b兲 are shown in Fig. 9 and the average absolute deviations are given in Table 6.
For the bubble-point pressure equation, the Blanke data
below 110 K are not in agreement with values calculated
from the mixture model given in Sec. 5, with differences
approaching 15% in pressure at the lowest temperature. The
Blanke values are the only available low-temperature data
for the properties of air on the phase boundaries, however,
they were determined graphically from p – ␳ – T data. Because of the large deviations mentioned above, they were not
used to develop the ancillary equations where they conflicted
with values calculated from the mixture model. To maintain
consistency between the mixture model and the ancillary
equation reported here, the bubble-point pressures from the
mixture model were used for temperatures below 100 K in
developing the ancillary equations. At higher temperatures,
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
the data of Michels et al. and Blanke between 120 and 130 K
and the Leung-Griffiths calculations from Jacobsen et al. between 131.8 and 132.5 K were used.
For the dew-point pressure equation, values below 66 K
from the mixture model were used in the absence of experimental data. Most of the data of Blanke are represented
within 0.3%. The Leung–Griffiths calculations from Jacobsen et al. 共1990b兲 between 130.4 and 132.6 K were fitted in
the critical region. For both the dew and bubble-point pressures, the first term of Eq. 共1兲 ensures that the first derivative
of pressure with respect to temperature is infinite at the maxcondentherm, as shown in Fig. 6.
Below 118 K, the data of Blanke are the only available
saturated density data for air. For the bubble-point densities,
both the air equation of state and the mixture model of this
work agree with the density data of Blanke to within 0.1%.
The single-phase liquid surface is represented well by accurate experimental data, and the uncertainty of density values
calculated from the equation of state should be less than
0.1% even at the lowest temperatures. For the dew-point
densities, the average absolute deviation of the data of
Blanke was 0.6%. These data have not been represented well
by previous equations of state for air 关Jacobsen et al.
共1990a兲; Jacobsen et al. 共1992兲; Panasiti et al. 共1999兲兴 nor
with preliminary equations developed using second virial coefficients, and these data show deviations of up to 2% from
all of these equations. Calculated density values from the
equation of state were used in the development of the dew
and bubble-point ancillary equations for consistency.
THERMODYNAMIC PROPERTIES OF AIR
353
FIG. 10. Comparisons of densities calculated with the equation of state to experimental data for air.
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
354
LEMMON ET AL.
FIG. 12. Comparisons of isochoric heat capacities calculated with the equation of state to experimental data for air.
FIG. 11. Comparisons of pressures calculated with the equation of state to
experimental data for air in the critical region.
6.2. Comparisons of the Equation of State for Air
and the Mixture Model with Experimental
and Calculated Data for Air
Table 6 shows the statistical analysis of comparisons to
experimental data sets for p – ␳ – T, isochoric and isobaric
heat capacities, speed of sound, and second virial coefficients
for air. Comparisons to all available experimental data are
given in Figs. 10–15. The vertical lines in these figures show
the locations of the phase boundaries at the indicated temperature. Deviations between the mixture model at the composition of standard air and the air equation of state are
shown as solid lines at the indicated isotherms or isochores.
These comparisons are quite useful in determining the consistency of data sets and the uncertainty of the equation of
state, since the mixture model has very few adjustable parameters, and only a very limited set of data was used to
determine the parameters. Equations of state can be overfit
due to the large number of adjustable parameters. For the
mixture model, this is not a problem, and deviations between
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
experimental data, the equation of state, and the mixture
model are useful in showing various trends and inconsistencies.
Figure 10 shows comparisons of densities calculated with
the equation of state to experimental p – ␳ – T data. Several
inconsistencies can be seen in the data used in the fit. At 290
K, the data of Michels et al. 共1954a兲 and of Kozlov 共1968兲
differ by an average of 0.1% in density. This offset is also
seen between the data of Kozlov and the equation of state
throughout most of the data of Kozlov. The data of Howley
et al. 共1994兲 are generally consistent with the data of Michels et al., except at temperatures below 200 K. At 155 K,
these two data sets differ by 0.1%. Although used in the fit,
the scatter in the data of Blanke is within 0.2% in the liquid,
and within 0.5% in the vapor. Differences between the overlapping vapor phase data of Romberg 共1971兲 and the equation of state are less than 0.1%, as compared with 0.5% for
the data of Blanke. There are no overlapping data in the
liquid. Despite the age of the data of Amagat 共1893兲, the
equation of state 共which was not fit to these data兲 agrees on
average to within 0.3% at pressures between 200 and 300
MPa and temperatures from 270 to 300 K. The only other
data in a comparable range are the data of Michels et al. at
270 K up to 228 MPa. The equation of state agrees within
0.1% with these data. Differences between the mixture
model and the Amagat data are larger at the highest pressures, however, these pressures are well beyond the limits of
the oxygen equation of state.
THERMODYNAMIC PROPERTIES OF AIR
FIG. 13. Comparisons of isobaric heat capacities calculated with the equation of state to experimental data for air.
The deviations of data in the critical region between 130
and 140 K are shown in Fig. 11. Since density deviations
tend to be large in the critical region for any substance 共because ⳵␳ / ⳵ p at constant temperature approaches infinity at
the critical point兲, this figure shows comparisons of pressures
calculated with the equation of state to experimental p – ␳ – T
data. The scatter between different data sets is within ⫾0.3%
in pressure throughout most of the critical region, with deviations tending to be positive for the data of Blanke 共1977兲
and Michels et al. 共1954b兲, and negative or near zero for
comparisons with the data of Howley et al. 共1994兲. Deviations between the mixture model and the equation of state
tend to be less than that with the experimental data, with the
mixture model agreeing best with the data of Howley et al.
Comparisons of values calculated from the equation of
state are shown for isochoric heat capacities in Fig. 12, isobaric heat capacities in Fig. 13, and the speed of sound in
Fig. 14. The equation of state agrees very well with the c v
data of Magee 共1994兲 except at the lowest density isochore,
2 mol/dm3, where the uncertainty of the isochoric heat capacity data tend to be highest. Comparisons with the mixture
model are quite good, except for the upturns in the vapor
phase near the saturation boundaries. Deviations with the
isobaric heat capacity data in the vapor phase are generally
within 2%, however, both the uncertainty and the scatter in
these data are higher than that for the isochoric heat capacity
data. Deviations between the equation of state and the mix-
355
ture model are nearly negligible, even at 2000 K. Comparisons between the equation of state and the speed of sound
data of Ewing and Goodwin 共1993兲 and the data of Younglove and Frederick 共1992兲 are very good at temperatures
above 200 K and below 120 K. Near the saturation boundaries and in the critical regions, the deviations tend to be
somewhat higher but generally within 1%. The mixture
model follows the data of Younglove and Frederick more
closely than does the equation of state in these regions.
The differences in the second virial coefficients are shown
in Fig. 15. Differences between the data of Romberg 共1971兲
at low temperatures with the equation of state tend to be
positive, whereas differences between the graphically determined data from Romberg given here in Table 7 tend to be
more scattered, generally within ⫾1 cm3/mol 共about 0.5% at
90 K兲 except at the lowest temperature. This scatter is due to
the difficulty of determining the second virial coefficient as
the uncertainty of p – ␳ – T data increases at low pressures
and temperatures as shown in Fig. 4. The second virial coefficients calculated from the mixture model are not as accurate as those calculated from the air equation of state. Values
of the second virial coefficient for oxygen calculated from
the equation of state of Schmidt and Wagner 共1985兲 show a
minimum at 75 K, and calculated values become positive at
temperatures below 58 K. This low temperature behavior is
unrealistic and reduces the accuracy of virial coefficients calculated using the mixture model in spite of the fact that the
calculated values from Schmidt and Wagner are within the
uncertainty of available experimental data.
Figure 16 shows calculated dew and bubble-line densities
in the critical region reported by Jacobsen et al. 共1990b兲 determined using a Leung–Griffiths model for ternary systems.
As shown in Fig. 16, the equation of state developed in this
work represents the calculated data of Jacobsen et al.
共1990b兲 more accurately than the previous equation of Jacobsen et al. 共1992兲. Densities were calculated from each
equation of state at the temperature and bubble or dew-point
pressure of the equation. This pressure was calculated from
the respective ancillary equation for each equation of state.
Dew and bubble-point states at the air composition calculated from the mixture model as described in Sec. 5.2. are
also shown in the figure.
Figure 17 shows the percent deviation in density between
values calculated with the equation of state for air and the
properties of air predicted from nitrogen data by the methods
described in Sec. 4.2 and used in the development of the air
equation of state. At temperatures above 1000 K where deviations between the nitrogen equation of state and the experimental data for nitrogen exceed 2%, the equation of state
for air mimics the trends set by the equation of state for
nitrogen 关Span et al. 共2000兲兴 as shown by the calculated data
points in Fig. 17.
6.3. Comparisons of the Mixture Model with
Experimental Single Phase Data
Summary comparisons of values calculated using the mixture model to p – ␳ – T data for mixtures of nitrogen, argon,
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
356
LEMMON ET AL.
FIG. 16. Comparisons of critical region phase boundaries calculated with the
equation of state to predicted data for air.
FIG. 14. Comparisons of speeds of sound calculated with the equation of
state to experimental data for air.
and oxygen are given in Table 8; this table indicates the
temperature range and composition range for the first component listed for each data set. The bubble-point pressures,
calculated from the model, were assumed for several data
sets for the nitrogen–oxygen and argon–oxygen systems
where the pressures were not included in the published data.
Comparisons of densities calculated from the mixture model
to experimental data are shown in Fig. 18 for the nitrogen–
argon binary mixture and in Fig. 19 for the nitrogen–oxygen
and argon–oxygen binary mixtures.
The Maslennikova et al. 共1979兲 data for the nitrogen–
argon mixture extend to 800 MPa and deviations are on average within 0.3%. From this and because of the generalized
nature of the model, calculated densities should be within
1.0% up to 800 MPa for the nitrogen–oxygen and argon–
oxygen systems where no data exist. The magnitudes of the
deviations for most of the nitrogen–argon data are similar to
those for the extended corresponding states models of Clarke
et al. 共1994兲 and version 9.08 of the NIST14 database
关Friend 共1992兲兴.
Very few data exist for the nitrogen–oxygen and argon–
oxygen mixtures. For the nitrogen–oxygen mixture, air data
and the data of Pool et al. 共1962兲 were used to determine the
parameters for the mixture model. Although the temperature
range of experimental p – ␳ – T data for the argon–oxygen
system is only 70–90 K with pressures up to 0.2 MPa in the
liquid phase, the model should be valid for all temperatures
and pressures for argon–oxygen mixtures within the ranges
of experimental data for the nitrogen–oxygen and nitrogen–
argon systems due to the predictive nature of the model.
From these comparisons, we estimate that the uncertainty of
p – ␳ – T calculations in the extended range for argon–
oxygen mixtures is within 0.5%. This estimate is based additionally on comparisons to the large amount of VLE data
available over the entire two-phase range for this mixture.
6.4. Comparisons of the Mixture Model with
Experimental VLE Data
FIG. 15. Comparisons of second virial coefficients calculated with the equation of state to experimental data for air.
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
Comparisons of bubble-point pressures calculated with the
mixture model to experimental data are shown in Fig. 20 for
THERMODYNAMIC PROPERTIES OF AIR
FIG. 17. Comparisons of densities calculated with the equation of state to
calculated p – ␳ – T data estimated from nitrogen data.
357
FIG. 19. Comparisons of densities calculated with the mixture model to
experimental data for the nitrogen–oxygen and argon–oxygen binary mixtures.
the nitrogen–argon binary mixture, Fig. 21 for the nitrogen–
oxygen binary mixture, Fig. 22 for the argon–oxygen binary
mixture, and Fig. 23 for the nitrogen–argon–oxygen ternary
mixture. The average deviations in bubble-point pressure for
the VLE data of Wilson et al. 共1965兲 for the nitrogen–argon,
nitrogen–oxygen, argon–oxygen, and nitrogen–argon–
oxygen mixtures are within 0.8% and are nearly the same as
those for the model developed by Lemmon 共1996兲. However,
the deviations between the mixture model and the lower temperature nitrogen–oxygen data of Duncan and Staveley
共1966兲 and Armstrong et al. 共1955兲 are substantially lower in
the new model reported here, and the average deviations for
these data sets are about 1.6% and 0.8%, respectively, about
50% smaller than those for the model of Lemmon 共1996兲.
7. Estimated Uncertainty of Calculated
Properties
7.1. Characteristic Curves of Air
FIG. 18. Comparisons of densities calculated with the mixture model to
experimental data for the nitrogen–argon binary mixture.
Plots of constant property lines on various thermodynamic
coordinates are useful in assessing the behavior of the equation of state in regions where there are no accurate experimental results for the corresponding property. The equation
of state for air developed here was used to produce plots of
temperature against isochoric heat capacity 共Fig. 24兲, isobaric heat capacity 共Fig. 25兲, and speed of sound 共Fig. 26兲.
As mentioned in Sec. 4.8, analytical methods in addition to
calculating the Hugoniot curve are needed to determine the
extrapolation behavior of an equation of state. Figure 27
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
358
FIG. 20. Comparisons of bubble-point pressures calculated with the mixture
model to experimental data for the nitrogen–argon binary mixture.
FIG. 21. Comparisons of bubble-point pressures calculated with the mixture
model to experimental data for the nitrogen–oxygen binary mixture.
shows a pressure versus density plot along isotherms. This
plot indicates that the equation of state presented here exhibits reasonable extrapolation behavior at high pressures and
densities.
Plots of certain ‘‘ideal curves’’ are useful in assessing the
behavior of an equation of state 关Deiters and de Reuck
共1997兲, Span and Wagner 共1997兲, Span 共2000兲兴. The characteristic curves considered in this work are the Boyle curve,
given by the equation
冉 冊
⳵Z
⳵v
⫽0,
共87兲
T
the Joule–Thomson inversion curve,
冉 冊
⳵Z
⳵T
p
冉 冊
h
⫽0,
共88兲
⫽0,
共89兲
⫽0.
共90兲
or
⳵T
⳵p
and the Joule inversion curve
冉 冊
⳵Z
⳵T
v
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
FIG. 22. Comparisons of bubble-point pressures calculated with the mixture
model to experimental data for the argon-oxygen binary mixture.
THERMODYNAMIC PROPERTIES OF AIR
359
FIG. 25. Isobaric heat capacity versus temperature diagram for air.
FIG. 23. Comparisons of bubble-point pressures calculated with the mixture
model to experimental data for the nitrogen-argon-oxygen ternary mixture.
Figure 28 illustrates these characteristic curves for the equation of state for air. Although the curves in Fig. 28 do not
provide numerical information, reasonable shapes of these
curves as shown indicate qualitatively correct extrapolation
behavior of the equation of state.
7.2. Uncertainty of the Equation of State for Air
and of the Mixture Model
The uncertainties of the models presented here have been
estimated by comparing calculated results with experimental
data, as summarized in Sec. 6, and assessing the data them-
FIG. 24. Isochoric heat capacity versus temperature diagram for air.
FIG. 26. Speed of sound versus temperature diagram for air.
FIG. 27. Pressure versus density diagram for air.
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
360
TABLE 17. Regions of stated uncertainty of the mixture model
Mixture
Nitrogen–Argon
Nitrogen–Oxygen and Air
Argon–Oxygen
a
FIG. 28. Characteristic curves for air.
selves according to the quoted experimental uncertainties
and the mutual consistency of data obtained from different
sources. A general knowledge of the behavior of thermodynamic surfaces and substantial experience with other correlating equations for well-studied fluids have also been applied in the estimation of uncertainties. The uncertainties
represent expanded combined uncertainties where a normal
distribution of errors is assumed and a coverage factor of 2
has been applied 共equivalent to a confidence level of about
95%兲. This means that if a uniform distribution of state
points is considered within the range specified below, no
more than 2% of values for a given property will deviate
from the physical value by more than the specified uncertainty.
For the equation of state of standard air, the region for
which sufficient data are available to establish reliable uncertainty estimates ranges from the solidification point to 873 K
at pressures up to 70 MPa, except in the critical region from
130 to 134 K and 9 to 13 mol/dm3. The estimated uncertainty
of density values calculated using the equation of state for air
is 0.1%. The estimated uncertainty of speed of sound values
is within 0.2% based on comparisons with the data of
Younglove and Frederick 共1992兲, Van Itterbeek and de Rop
共1955兲, and Ewing and Goodwin 共1993兲. The estimated uncertainty is 1% for calculated values of heat capacity based
upon comparisons to the experimental data of Magee 共1994兲.
In the critical region defined above, the uncertainty in pressure calculations is estimated to be 0.3%. Outside the range
of the primary experimental data for air 共T⬎870 K, p
⬎70 MPa兲 and at temperatures less than 2000 K and pressures less than 2000 MPa, the estimated uncertainty in predicted densities is 1.0%. Without experimental data, the uncertainty of extrapolated properties cannot be verified.
The uncertainty of the mixture model reported here for
arbitrary compositions of nitrogen, oxygen, and argon is
within 0.1% in density, 0.2% for the speed of sound, and 1%
in heat capacity for both binary and ternary mixtures in the
same range given for the air equation of state. The uncertainty of calculated dew and bubble-point pressures is within
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
Temperature range
共K兲
Maximum pressure
共MPa兲
70–420
60–870
70–90
70–400a
800
100
0.2
100a
No data are available to verify this range, however, the uncertainty of the
equation should be at least 0.5% in density for the range stated due to the
predictive nature of the model.
1%. The mixtures and ranges for which calculated properties
have been verified by experimental data to have deviations
within these limits are listed in Table 17. In regions where
there are no binary mixture data, the uncertainty is estimated
to be of the same magnitude. However, these estimates cannot be verified until experimental data are available to support these estimates.
Because of the generalized and predictive nature of the
mixture model, calculated densities of mixtures of nitrogen,
argon, and oxygen extrapolated to temperatures up to 1000 K
and pressures to 100 MPa have an estimated uncertainty of
0.5%. Although the equation of state for oxygen by Schmidt
and Wagner 共1985兲 is valid only to temperatures of 300 K,
the original work of Lemmon 共1996兲 demonstrated that the
oxygen equation extrapolates to temperatures up to 1000 K
within 0.5% in density through comparisons with the Kozlov
共1968兲 data. As new measurements become available, they
will refine the uncertainty estimates in regions not covered
by experimental data, and will enable continued evaluation
and optimization of the mixture model.
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9. Appendix: Tables of Properties of Air
9.1. Representative Tables of Thermodynamic
Properties of Air
Properties of air along the dew and bubble-point curves
were calculated using pressures from the appropriate ancillary equation at the specified temperature. The density was
calculated using the air equation of state for the input temperature and pressure. Dew and bubble-point entries for the
isobar tables were calculated using pressure as the input to
Eq. 共1兲 to determine the corresponding temperatures. The
densities for these entries were calculated using the temperature and pressure as input variables in the equation of state.
THERMODYNAMIC PROPERTIES OF AIR
363
TABLE A1. Thermodynamic properties of air on the dew and bubble lines
Temperature
共K兲
59.75a
59.75a
60
60
61
61
62
62
63
63
64
64
65
65
66
66
67
67
68
68
69
69
70
70
71
71
72
72
73
73
74
74
75
75
76
76
77
77
78
78
79
79
80
80
81
81
82
82
83
83
84
84
85
85
86
86
87
87
88
88
89
89
90
Pressure
共MPa兲
Density
共mol/dm3兲
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
0.005 265
0.002 43
0.005 55
0.002 58
0.006 80
0.003 27
0.008 27
0.004 11
0.009 99
0.005 12
0.012 00
0.006 33
0.014 32
0.007 76
0.016 99
0.009 44
0.020 04
0.011 42
0.023 52
0.013 71
0.027 46
0.016 37
0.031 91
0.019 43
0.036 91
0.022 93
0.042 50
0.026 92
0.048 73
0.031 44
0.055 66
0.036 55
0.063 33
0.042 28
0.071 79
0.048 70
0.081 09
0.055 86
0.091 29
0.063 81
0.102 45
0.072 61
0.114 62
0.082 32
0.127 85
0.093 00
0.142 21
0.104 71
0.157 75
0.117 51
0.174 53
0.131 47
0.192 62
0.146 65
0.212 07
0.163 12
0.232 95
0.180 94
0.255 31
0.200 18
0.279 22
0.220 91
0.304 75
33.067
0.004 91
33.031
0.005 19
32.888
0.006 47
32.745
0.008 00
32.601
0.009 82
32.457
0.011 95
32.312
0.014 44
32.166
0.017 33
32.020
0.020 66
31.873
0.024 48
31.725
0.028 84
31.576
0.033 79
31.427
0.039 38
31.277
0.045 66
31.126
0.052 70
30.974
0.060 55
30.821
0.069 27
30.668
0.078 92
30.513
0.089 56
30.357
0.101 27
30.200
0.114 10
30.042
0.128 13
29.883
0.143 43
29.722
0.160 06
29.560
0.178 11
29.397
0.197 65
29.232
0.218 75
29.066
0.241 50
28.898
0.265 98
28.729
0.292 28
28.558
0.320 48
28.385
⫺4713.1
1721.6
⫺4699.3
1728.6
⫺4644.3
1756.7
⫺4589.2
1784.7
⫺4534.1
1812.5
⫺4478.9
1840.1
⫺4423.8
1867.5
⫺4368.6
1894.7
⫺4313.4
1921.7
⫺4258.2
1948.5
⫺4202.9
1974.9
⫺4147.6
2001.1
⫺4092.2
2027.0
⫺4036.7
2052.6
⫺3981.2
2077.8
⫺3925.6
2102.7
⫺3869.8
2127.2
⫺3814.0
2151.3
⫺3758.1
2175.0
⫺3702.1
2198.3
⫺3645.9
2221.2
⫺3589.6
2243.6
⫺3533.2
2265.5
⫺3476.6
2286.9
⫺3419.8
2307.8
⫺3362.9
2328.1
⫺3305.8
2347.9
⫺3248.4
2367.1
⫺3190.9
2385.8
⫺3133.1
2403.8
⫺3075.1
2421.2
⫺3016.8
70.902
182.97
71.131
182.59
72.041
181.09
72.937
179.66
73.817
178.29
74.684
176.97
75.538
175.71
76.379
174.50
77.208
173.34
78.025
172.22
78.830
171.15
79.624
170.12
80.408
169.13
81.181
168.17
81.944
167.25
82.698
166.36
83.442
165.50
84.178
164.67
84.905
163.87
85.624
163.09
86.334
162.34
87.037
161.61
87.733
160.91
88.421
160.22
89.103
159.56
89.778
158.91
90.447
158.28
91.110
157.67
91.767
157.07
92.418
156.49
93.065
155.92
93.706
34.01
20.80
33.95
20.81
33.73
20.82
33.51
20.84
33.30
20.86
33.09
20.89
32.88
20.91
32.68
20.94
32.49
20.97
32.29
21.00
32.11
21.04
31.92
21.07
31.74
21.11
31.56
21.16
31.39
21.20
31.22
21.25
31.05
21.30
30.89
21.36
30.73
21.41
30.57
21.47
30.41
21.54
30.26
21.60
30.11
21.67
29.97
21.75
29.83
21.82
29.69
21.90
29.55
21.98
29.42
22.07
29.29
22.16
29.16
22.25
29.03
22.34
28.91
55.06
29.22
55.06
29.23
55.06
29.26
55.06
29.30
55.07
29.35
55.08
29.40
55.10
29.46
55.12
29.52
55.15
29.59
55.18
29.66
55.22
29.75
55.27
29.84
55.32
29.93
55.38
30.04
55.44
30.15
55.51
30.28
55.59
30.41
55.68
30.55
55.78
30.70
55.88
30.86
56.00
31.04
56.12
31.22
56.26
31.41
56.40
31.62
56.56
31.84
56.72
32.07
56.90
32.32
57.09
32.58
57.30
32.85
57.52
33.14
57.76
33.45
58.01
1030.3
154.8
1028.3
155.1
1020.3
156.4
1012.2
157.6
1004.0
158.8
995.8
160.0
987.5
161.2
979.1
162.3
970.7
163.4
962.2
164.5
953.7
165.6
945.1
166.7
936.4
167.7
927.7
168.7
918.9
169.7
910.0
170.6
901.1
171.6
892.1
172.5
883.0
173.4
873.9
174.2
864.7
175.1
855.4
175.8
846.1
176.6
836.7
177.4
827.2
178.1
817.6
178.8
808.0
179.4
798.2
180.0
788.4
180.6
778.6
181.2
768.6
181.7
758.5
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
364
TABLE A1. Thermodynamic properties of air on the dew and bubble lines—Continued
Temperature
共K兲
90
91
91
92
92
93
93
94
94
95
95
96
96
97
97
98
98
99
99
100
100
101
101
102
102
103
103
104
104
105
105
106
106
107
107
108
108
109
109
110
110
111
111
112
112
113
113
114
114
115
115
116
116
117
117
118
118
119
119
120
120
121
121
Pressure
共MPa兲
Density
共mol/dm3兲
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
0.243 20
0.331 96
0.267 12
0.360 91
0.292 73
0.391 66
0.320 11
0.424 29
0.349 34
0.458 86
0.380 47
0.495 43
0.413 59
0.534 08
0.448 78
0.574 86
0.486 09
0.617 86
0.525 62
0.663 13
0.567 42
0.710 74
0.611 59
0.760 77
0.658 20
0.813 29
0.707 32
0.868 36
0.759 03
0.926 06
0.813 41
0.986 45
0.870 55
1.049 61
0.930 52
1.115 61
0.993 40
1.184 53
1.059 28
1.256 42
1.128 24
1.331 38
1.200 36
1.409 47
1.275 74
1.490 77
1.354 45
1.575 34
1.436 60
1.663 27
1.522 26
1.754 62
1.611 54
1.849 47
1.704 52
1.947 89
1.801 32
2.049 95
1.902 02
2.155 73
2.006 74
2.265 29
2.115 60
0.350 68
28.210
0.382 98
28.033
0.417 47
27.854
0.454 26
27.673
0.493 45
27.489
0.535 17
27.304
0.579 53
27.115
0.626 67
26.924
0.676 71
26.730
0.729 80
26.533
0.786 09
26.333
0.845 75
26.130
0.908 95
25.923
0.975 87
25.713
1.0467
25.499
1.1217
25.281
1.2011
25.058
1.2852
24.831
1.3742
24.598
1.4684
24.361
1.5682
24.118
1.6740
23.868
1.7862
23.613
1.9053
23.350
2.0318
23.080
2.1664
22.801
2.3097
22.514
2.4625
22.217
2.6259
21.908
2.8009
21.588
2.9889
21.253
3.1913
2437.9
⫺2958.2
2454.0
⫺2899.4
2469.3
⫺2840.2
2484.0
⫺2780.8
2497.9
⫺2720.9
2511.0
⫺2660.8
2523.3
⫺2600.2
2534.8
⫺2539.2
2545.4
⫺2477.8
2555.2
⫺2416.0
2564.0
⫺2353.6
2571.9
⫺2290.8
2578.8
⫺2227.4
2584.6
⫺2163.4
2589.4
⫺2098.9
2593.0
⫺2033.7
2595.5
⫺1967.8
2596.7
⫺1901.2
2596.6
⫺1833.8
2595.1
⫺1765.6
2592.2
⫺1696.5
2587.7
⫺1626.4
2581.7
⫺1555.4
2573.8
⫺1483.2
2564.2
⫺1409.9
2552.5
⫺1335.2
2538.7
⫺1259.2
2522.7
⫺1181.6
2504.0
⫺1102.4
2482.7
⫺1021.2
2458.3
⫺937.90
2430.6
155.36
94.342
154.82
94.974
154.29
95.602
153.77
96.225
153.26
96.845
152.75
97.461
152.26
98.074
151.78
98.684
151.30
99.291
150.83
99.896
150.36
100.50
149.90
101.10
149.44
101.70
148.99
102.29
148.54
102.89
148.10
103.49
147.65
104.08
147.21
104.68
146.77
105.27
146.33
105.87
145.89
106.47
145.45
107.06
145.00
107.67
144.55
108.27
144.10
108.88
143.64
109.49
143.18
110.11
142.70
110.73
142.22
111.36
141.73
112.00
141.22
112.65
140.70
22.44
28.79
22.54
28.68
22.64
28.56
22.74
28.45
22.85
28.35
22.96
28.24
23.08
28.14
23.20
28.04
23.32
27.95
23.44
27.86
23.57
27.77
23.70
27.68
23.83
27.60
23.97
27.53
24.11
27.45
24.26
27.38
24.41
27.32
24.56
27.26
24.72
27.20
24.89
27.15
25.06
27.10
25.23
27.06
25.42
27.03
25.61
27.00
25.81
26.98
26.01
26.97
26.23
26.96
26.46
26.97
26.70
26.98
26.96
27.01
27.23
27.05
27.51
33.77
58.28
34.11
58.57
34.47
58.87
34.85
59.20
35.26
59.55
35.68
59.93
36.13
60.33
36.61
60.76
37.12
61.22
37.65
61.71
38.23
62.23
38.83
62.80
39.48
63.40
40.18
64.05
40.92
64.75
41.71
65.51
42.57
66.32
43.49
67.21
44.49
68.16
45.57
69.20
46.75
70.34
48.04
71.58
49.45
72.95
51.01
74.46
52.73
76.13
54.64
78.00
56.79
80.09
59.21
82.46
61.96
85.16
65.10
88.28
68.74
91.92
72.99
182.2
748.4
182.6
738.2
183.1
727.9
183.5
717.5
183.8
707.0
184.2
696.5
184.5
685.8
184.7
675.0
184.9
664.2
185.1
653.3
185.3
642.2
185.4
631.1
185.5
619.8
185.6
608.5
185.6
597.1
185.5
585.5
185.5
573.9
185.4
562.1
185.2
550.2
185.1
538.2
184.9
526.1
184.6
513.9
184.3
501.5
184.0
489.0
183.6
476.3
183.2
463.5
182.7
450.5
182.2
437.3
181.7
423.9
181.1
410.2
180.4
396.3
179.8
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
THERMODYNAMIC PROPERTIES OF AIR
365
TABLE A1. Thermodynamic properties of air on the dew and bubble lines—Continued
Temperature
共K兲
122
122
123
123
124
124
125
125
126
126
127
127
128
128
129
129
130
130
131
131
132
132
132.6312b
a
Pressure
共MPa兲
Density
共mol/dm3兲
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
2.378 71
2.228 71
2.496 04
2.346 20
2.617 34
2.468 23
2.742 67
2.594 95
2.872 07
2.726 56
3.005 54
2.863 31
3.143 06
3.005 51
3.284 48
3.153 61
3.429 47
3.308 35
3.576 98
3.471 16
3.722 84
3.646 25
3.785 02
20.903
3.4103
20.534
3.6481
20.144
3.9078
19.727
4.1934
19.278
4.5101
18.788
4.8653
18.242
5.2697
17.616
5.7405
16.863
6.3074
15.869
7.0343
14.198
8.1273
10.4477
⫺852.17
2399.1
⫺763.63
2363.3
⫺671.82
2322.6
⫺576.07
2276.3
⫺475.47
2223.2
⫺368.72
2161.9
⫺253.75
2090.3
⫺127.06
2004.9
18.109
1899.9
198.35
1763.0
478.83
1553.9
1111.3
113.31
140.16
113.98
139.59
114.68
139.00
115.40
138.38
116.15
137.71
116.93
137.00
117.78
136.22
118.70
135.34
119.76
134.33
121.07
133.10
123.13
131.33
127.87
27.11
27.82
27.19
28.16
27.30
28.52
27.44
28.91
27.62
29.34
27.85
29.83
28.17
30.37
28.61
30.99
29.24
31.73
30.27
32.62
32.34
33.81
35.26
96.23
78.02
101.4
84.05
107.8
91.43
115.9
100.6
126.5
112.4
140.9
128.0
161.9
149.6
195.2
181.3
256.2
232.6
401.5
329.9
1015.
598.0
2196.
382.0
179.1
367.4
178.3
352.3
177.5
336.7
176.7
320.4
175.8
303.2
174.9
285.0
174.0
265.4
173.0
243.7
171.9
219.1
170.8
189.1
169.4
168.0
Solidification point.
Maxcondentherm.
b
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
366
TABLE A2. Thermodynamic properties of air
Temperature
共K兲
59.77
60
62
64
66
68
70
72
74
76
78
78.90
81.72
82
84
86
88
90
92
94
96
98
100
102
104
106
108
110
112
114
116
118
120
122
124
126
128
130
132
134
136
138
140
142
144
146
148
150
155
160
165
170
175
180
185
190
195
200
210
220
230
240
Density
共mol/dm3兲
Internal
energy
共J/mol兲
Enthalpy
共J/mol兲
33.069
33.036
32.750
32.462
32.171
31.878
31.581
31.281
30.978
30.670
30.358
30.215
0.155 27
0.154 67
0.150 53
0.146 63
0.142 95
0.139 47
0.136 17
0.133 03
0.130 05
0.127 21
0.124 49
0.121 90
0.119 42
0.117 04
0.114 76
0.112 57
0.110 47
0.108 44
0.106 49
0.104 62
0.102 81
0.101 06
0.099 377
0.097 748
0.096 174
0.094 650
0.093 175
0.091 747
0.090 363
0.089 021
0.087 718
0.086 455
0.085 227
0.084 035
0.082 877
0.081 750
0.079 065
0.076 553
0.074 198
0.071 985
0.069 902
0.067 937
0.066 081
0.064 324
0.062 659
0.061 079
0.058 147
0.055 486
0.053 059
0.050 836
⫺4713.1
⫺4700.3
⫺4590.2
⫺4480.1
⫺4369.9
⫺4259.7
⫺4149.3
⫺4038.7
⫺3927.9
⫺3816.7
⫺3705.2
⫺3654.7
1628.3
1634.6
1679.4
1723.8
1767.9
1811.7
1855.4
1898.8
1942.1
1985.2
2028.2
2071.0
2113.8
2156.4
2199.0
2241.5
2284.0
2326.3
2368.6
2410.9
2453.1
2495.3
2537.4
2579.5
2621.5
2663.5
2705.5
2747.5
2789.4
2831.3
2873.2
2915.1
2956.9
2998.7
3040.5
3082.3
3186.8
3291.1
3395.4
3499.6
3603.8
3707.9
3812.0
3916.0
4020.0
4124.0
4331.9
4539.8
4747.6
4955.4
0.101 325 MPa isobar
⫺4710.0
70.905
⫺4697.2
71.119
⫺4587.1
72.924
⫺4477.0
74.672
⫺4366.8
76.367
⫺4256.5
78.013
⫺4146.1
79.614
⫺4035.5
81.172
⫺3924.6
82.691
⫺3813.4
84.173
⫺3701.9
85.622
⫺3651.4
86.266
2280.9
160.41
2289.8
160.52
2352.5
161.28
2414.8
162.01
2476.7
162.72
2538.2
163.41
2599.5
164.09
2660.4
164.74
2721.2
165.38
2781.7
166.00
2842.1
166.61
2902.2
167.21
2962.3
167.79
3022.2
168.36
3082.0
168.92
3141.6
169.47
3201.2
170.01
3260.7
170.53
3320.1
171.05
3379.4
171.56
3438.7
172.05
3497.8
172.54
3557.0
173.02
3616.0
173.50
3675.1
173.96
3734.0
174.42
3793.0
174.87
3851.9
175.31
3910.7
175.75
3969.5
176.18
4028.3
176.60
4087.1
177.02
4145.8
177.43
4204.5
177.83
4263.1
178.23
4321.8
178.62
4468.3
179.59
4614.7
180.51
4761.0
181.41
4907.2
182.29
5053.3
183.13
5199.3
183.96
5345.3
184.76
5491.2
185.54
5637.1
186.29
5782.9
187.03
6074.5
188.45
6365.9
189.81
6657.3
191.11
6948.6
192.35
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
34.01
33.96
33.52
33.09
32.69
32.30
31.92
31.56
31.22
30.89
30.57
30.43
21.73
21.71
21.58
21.48
21.40
21.33
21.27
21.22
21.17
21.13
21.09
21.06
21.03
21.01
20.98
20.96
20.94
20.93
20.91
20.90
20.89
20.87
20.86
20.85
20.84
20.84
20.83
20.82
20.82
20.81
20.81
20.80
20.80
20.79
20.79
20.78
20.78
20.77
20.76
20.76
20.75
20.75
20.75
20.75
20.75
20.74
20.74
20.74
20.74
20.75
55.05
55.05
55.05
55.07
55.11
55.17
55.25
55.37
55.51
55.68
55.88
55.99
31.56
31.52
31.26
31.04
30.85
30.69
30.55
30.42
30.32
30.22
30.13
30.05
29.98
29.92
29.86
29.81
29.76
29.72
29.68
29.64
29.61
29.58
29.55
29.52
29.50
29.48
29.45
29.43
29.42
29.40
29.38
29.37
29.35
29.34
29.33
29.32
29.29
29.27
29.25
29.23
29.22
29.20
29.19
29.18
29.17
29.16
29.15
29.14
29.13
29.13
1030.6
1028.8
1012.6
996.3
979.6
962.7
945.5
928.1
910.4
892.3
874.0
865.6
177.2
177.5
180.0
182.4
184.8
187.1
189.4
191.7
193.9
196.1
198.2
200.3
202.4
204.5
206.5
208.6
210.5
212.5
214.5
216.4
218.3
220.2
222.1
223.9
225.8
227.6
229.4
231.2
232.9
234.7
236.4
238.2
239.9
241.6
243.3
244.9
249.1
253.1
257.1
261.1
264.9
268.7
272.5
276.2
279.8
283.4
290.5
297.4
304.1
310.7
THERMODYNAMIC PROPERTIES OF AIR
367
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
59.78
60
62
64
66
68
70
72
74
76
78
80
82
84
85.39
87.99
88
90
92
94
96
98
100
102
104
106
Density
共mol/dm3兲
Internal
energy
共J/mol兲
0.048 793
0.046 908
0.045 164
0.043 546
0.042 040
0.040 634
0.039 320
0.038 089
0.036 932
0.035 844
0.034 818
0.033 850
0.032 933
0.032 066
0.031 243
0.030 461
0.027 074
0.024 365
0.022 149
0.020 303
0.018 742
0.017 403
0.016 243
0.015 228
0.013 536
0.012 183
0.011 075
0.010 153
0.009 372
0.008 703
0.008 122
0.007 615
0.007 167
0.006 769
0.006 413
0.006 092
5163.2
5371.1
5578.9
5786.8
5994.8
6203.0
6411.2
6619.5
6828.1
7036.8
7245.7
7454.9
7664.3
7874.0
8084.0
8294.3
9351.8
10 421.0
11 503.0
12 602.0
13 717.0
14 849.0
15 999.0
17 166.0
19 549.0
21 994.0
24 494.0
27 042.0
29 633.0
32 261.0
34 922.0
37 612.0
40 329.0
43 069.0
45 830.0
48 610.0
33.072
33.041
32.756
32.468
32.177
31.884
31.588
31.288
30.985
30.678
30.366
30.050
29.728
29.400
29.168
0.292 03
0.291 99
0.284 13
0.276 75
0.269 81
0.263 27
0.257 08
0.251 21
0.245 64
0.240 33
0.235 27
⫺4712.9
⫺4701.0
⫺4591.0
⫺4481.0
⫺4370.9
⫺4260.7
⫺4150.3
⫺4039.8
⫺3929.1
⫺3818.0
⫺3706.5
⫺3594.7
⫺3482.3
⫺3369.2
⫺3290.4
1718.8
1719.0
1765.8
1812.1
1857.9
1903.2
1948.2
1993.0
2037.4
2081.6
2125.6
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
7239.9
193.53
7531.1
194.68
7822.4
195.78
8113.7
196.84
8405.1
197.86
8696.5
198.85
8988.1
199.80
9279.8
200.73
9571.6
201.63
9863.6
202.50
10 156.0
203.34
10 448.0
204.17
10 741.0
204.97
11 034.0
205.75
11 327.0
206.51
11 621.0
207.26
13 094.0
210.73
14 579.0
213.86
16 078.0
216.71
17 592.0
219.35
19 123.0
221.80
20 671.0
224.09
22 237.0
226.25
23 820.0
228.30
27 035.0
232.08
30 311.0
235.53
33 642.0
238.71
37 022.0
241.65
40 444.0
244.39
43 904.0
246.95
47 397.0
249.36
50 919.0
251.63
54 466.0
253.79
58 038.0
255.83
61 630.0
257.77
65 242.0
259.62
0.2 MPa isobar
⫺4706.8
70.908
⫺4695.0
71.106
⫺4584.9
72.911
⫺4474.8
74.659
⫺4364.6
76.353
⫺4254.4
77.999
⫺4144.0
79.599
⫺4033.4
81.157
⫺3922.6
82.675
⫺3811.5
84.157
⫺3700.0
85.605
⫺3588.0
87.022
⫺3475.5
88.411
⫺3362.4
89.773
⫺3283.6
90.705
2403.6
156.49
2403.9
156.50
2469.7
157.24
2534.8
157.95
2599.1
158.64
2662.9
159.32
2726.2
159.97
2789.1
160.60
2851.6
161.22
2913.8
161.83
2975.7
162.42
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
20.75
20.76
20.76
20.77
20.78
20.80
20.81
20.83
20.85
20.87
20.89
20.92
20.94
20.97
21.01
21.04
21.25
21.50
21.80
22.13
22.47
22.82
23.17
23.51
24.15
24.73
25.25
25.70
26.10
26.45
26.76
27.04
27.29
27.51
27.71
27.90
29.13
29.13
29.13
29.13
29.14
29.15
29.16
29.18
29.19
29.21
29.23
29.26
29.28
29.31
29.34
29.38
29.58
29.83
30.13
30.45
30.79
31.14
31.48
31.82
32.47
33.05
33.57
34.02
34.42
34.77
35.08
35.35
35.60
35.82
36.03
36.21
317.1
323.4
329.6
335.6
341.5
347.4
353.1
358.7
364.2
369.7
375.0
380.3
385.4
390.5
395.5
400.5
424.2
446.4
467.3
487.1
505.9
523.9
541.2
557.8
589.6
619.6
648.1
675.5
701.7
727.0
751.5
775.2
798.2
820.5
842.3
863.5
34.01
33.96
33.52
33.10
32.69
32.30
31.93
31.57
31.22
30.89
30.57
30.27
29.97
29.69
29.50
22.25
22.24
22.05
21.90
21.77
21.66
21.57
21.49
21.42
21.36
21.30
55.05
55.04
55.04
55.06
55.10
55.16
55.24
55.35
55.49
55.65
55.86
56.10
56.38
56.71
56.98
33.14
33.14
32.70
32.33
32.03
31.77
31.54
31.34
31.17
31.01
30.87
1031.0
1029.3
1013.2
996.8
980.2
963.3
946.1
928.7
911.0
893.0
874.7
856.1
837.2
817.8
804.2
181.2
181.2
183.8
186.3
188.7
191.1
193.5
195.8
198.0
200.3
202.4
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
368
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
108
110
112
114
116
118
120
122
124
126
128
130
132
134
136
138
140
142
144
146
148
150
155
160
165
170
175
180
185
190
195
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
Density
共mol/dm3兲
Internal
energy
共J/mol兲
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
0.230 44
0.225 83
0.221 41
0.217 17
0.213 11
0.209 20
0.205 45
0.201 83
0.198 35
0.194 99
0.191 75
0.188 63
0.185 61
0.182 68
0.179 86
0.177 12
0.174 47
0.171 90
0.169 40
0.166 98
0.164 63
0.162 35
0.156 93
0.151 86
0.147 12
0.142 67
0.138 49
0.134 55
0.130 83
0.127 32
0.124 00
0.120 84
0.115 00
0.109 70
0.104 87
0.100 46
0.096 399
0.092 660
0.089 203
0.085 996
0.083 012
0.080 230
0.077 629
0.075 193
0.072 905
0.070 753
0.068 725
0.066 810
0.064 999
0.063 285
0.061 658
0.060 114
0.053 424
0.048 077
0.043 704
0.040 061
0.036 980
0.034 338
0.032 049
0.030 047
0.026 709
0.024 039
0.021 855
2169.4
2213.0
2256.5
2299.9
2343.1
2386.2
2429.2
2472.2
2515.0
2557.8
2600.4
2643.0
2685.6
2728.1
2770.5
2812.9
2855.3
2897.6
2939.8
2982.1
3024.3
3066.4
3171.7
3276.8
3381.8
3486.6
3591.4
3696.0
3800.6
3905.1
4009.5
4113.9
4322.5
4531.0
4739.3
4947.6
5155.9
5364.1
5572.3
5780.6
5988.9
6197.2
6405.7
6614.3
6823.0
7032.0
7241.1
7450.4
7660.0
7869.9
8080.0
8290.5
9348.5
10 418.0
11 501.0
12 600.0
13 715.0
14 847.0
15 997.0
17 164.0
19 548.0
21 993.0
24 493.0
3037.3
3098.7
3159.8
3220.8
3281.6
3342.2
3402.7
3463.1
3523.3
3583.4
3643.4
3703.3
3763.2
3822.9
3882.5
3942.1
4001.6
4061.1
4120.5
4179.8
4239.1
4298.3
4446.2
4593.8
4741.2
4888.5
5035.5
5182.4
5329.2
5475.9
5622.5
5768.9
6061.7
6354.2
6646.4
6938.6
7230.6
7522.5
7814.4
8106.3
8398.1
8690.1
8982.0
9274.1
9566.3
9858.7
10 151.0
10 444.0
10 737.0
11 030.0
11 324.0
11 618.0
13 092.0
14 578.0
16 077.0
17 592.0
19 123.0
20 672.0
22 238.0
23 821.0
27 036.0
30 313.0
33 644.0
162.99
163.55
164.11
164.65
165.17
165.69
166.20
166.70
167.19
167.67
168.14
168.61
169.06
169.51
169.95
170.39
170.82
171.24
171.65
172.06
172.47
172.86
173.83
174.77
175.68
176.56
177.41
178.24
179.04
179.82
180.59
181.33
182.76
184.12
185.42
186.66
187.85
189.00
190.10
191.16
192.18
193.17
194.13
195.06
195.96
196.83
197.68
198.50
199.31
200.09
200.85
201.59
205.07
208.20
211.06
213.69
216.14
218.44
220.60
222.64
226.43
229.88
233.05
21.26
21.21
21.17
21.14
21.11
21.08
21.06
21.03
21.01
20.99
20.97
20.96
20.94
20.93
20.92
20.90
20.89
20.88
20.87
20.87
20.86
20.85
20.83
20.82
20.81
20.80
20.79
20.78
20.78
20.77
20.77
20.77
20.76
20.76
20.76
20.76
20.76
20.77
20.77
20.78
20.79
20.80
20.82
20.83
20.85
20.87
20.90
20.92
20.95
20.98
21.01
21.04
21.25
21.51
21.80
22.13
22.47
22.82
23.17
23.51
24.15
24.73
25.25
30.75
30.64
30.53
30.44
30.36
30.28
30.21
30.14
30.08
30.03
29.98
29.93
29.89
29.85
29.81
29.77
29.74
29.71
29.68
29.65
29.63
29.60
29.55
29.50
29.46
29.43
29.40
29.37
29.35
29.32
29.31
29.29
29.26
29.24
29.22
29.21
29.20
29.19
29.19
29.19
29.19
29.20
29.20
29.21
29.23
29.24
29.26
29.29
29.31
29.34
29.37
29.40
29.59
29.84
30.14
30.46
30.80
31.14
31.49
31.83
32.47
33.05
33.57
204.6
206.7
208.8
210.9
212.9
214.9
216.9
218.8
220.8
222.7
224.6
226.5
228.3
230.1
232.0
233.8
235.5
237.3
239.1
240.8
242.5
244.2
248.4
252.6
256.6
260.6
264.5
268.4
272.2
275.9
279.6
283.2
290.4
297.3
304.0
310.7
317.1
323.4
329.6
335.7
341.6
347.5
353.2
358.8
364.4
369.8
375.2
380.4
385.6
390.7
395.7
400.7
424.4
446.6
467.5
487.3
506.1
524.1
541.4
558.1
589.8
619.8
648.3
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
THERMODYNAMIC PROPERTIES OF AIR
369
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
1200
1300
1400
1500
1600
1700
1800
1900
2000
59.84
60
62
64
66
68
70
72
74
76
78
80
82
84
86
88
90
92
94
96
96.12
98.36
100
102
104
106
108
110
112
114
116
118
120
122
124
126
128
130
132
134
136
138
140
142
144
146
148
150
155
160
165
170
175
Density
共mol/dm3兲
Internal
energy
共J/mol兲
0.020 034
0.018 494
0.017 173
0.016 029
0.015 027
0.014 144
0.013 358
0.012 656
0.012 023
27 041.0
29 632.0
32 261.0
34 922.0
37 612.0
40 329.0
43 069.0
45 830.0
48 610.0
33.080
33.057
32.772
32.485
32.195
31.903
31.608
31.309
31.007
30.701
30.391
30.076
29.755
29.429
29.096
28.756
28.408
28.051
27.683
27.304
27.281
0.695 38
0.678 71
0.659 81
0.642 25
0.625 86
0.610 51
0.596 06
0.582 43
0.569 54
0.557 31
0.545 69
0.534 63
0.524 08
0.514 00
0.504 35
0.495 11
0.486 25
0.477 73
0.469 55
0.461 67
0.454 08
0.446 76
0.439 69
0.432 87
0.426 28
0.419 89
0.413 72
0.399 10
0.385 55
0.372 95
0.361 19
0.350 19
⫺4712.3
⫺4703.4
⫺4593.5
⫺4483.6
⫺4373.6
⫺4263.6
⫺4153.5
⫺4043.1
⫺3932.6
⫺3821.7
⫺3710.5
⫺3598.9
⫺3486.8
⫺3374.0
⫺3260.7
⫺3146.5
⫺3031.4
⫺2915.2
⫺2797.8
⫺2679.0
⫺2671.8
1830.0
1872.9
1924.1
1974.2
2023.5
2072.0
2120.0
2167.4
2214.4
2260.9
2307.1
2352.9
2398.5
2443.8
2488.9
2533.8
2578.4
2622.9
2667.2
2711.3
2755.3
2799.2
2843.0
2886.6
2930.2
2973.6
3017.0
3125.0
3232.6
3339.8
3446.6
3553.2
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
37 024.0
235.99
40 447.0
238.73
43 906.0
241.30
47 399.0
243.71
50 921.0
245.98
54 469.0
248.13
58 040.0
250.17
61 633.0
252.12
65 245.0
253.97
0.5 MPa isobar
⫺4697.1
70.919
⫺4688.2
71.067
⫺4578.2
72.871
⫺4468.2
74.618
⫺4358.1
76.311
⫺4247.9
77.956
⫺4137.6
79.554
⫺4027.2
81.111
⫺3916.4
82.627
⫺3805.4
84.108
⫺3694.1
85.554
⫺3582.3
86.969
⫺3469.9
88.356
⫺3357.1
89.716
⫺3243.5
91.052
⫺3129.1
92.367
⫺3013.8
93.663
⫺2897.4
94.942
⫺2779.8
96.207
⫺2660.7
97.460
⫺2653.4
97.535
2549.0
151.13
2609.6
151.74
2681.9
152.45
2752.7
153.14
2822.4
153.80
2891.0
154.45
2958.8
155.07
3025.9
155.67
3092.3
156.26
3158.1
156.83
3223.4
157.39
3288.2
157.93
3352.6
158.47
3416.6
158.99
3480.3
159.50
3543.6
160.00
3606.7
160.48
3669.5
160.96
3732.0
161.43
3794.4
161.90
3856.5
162.35
3918.4
162.80
3980.1
163.23
4041.7
163.66
4103.1
164.09
4164.4
164.50
4225.5
164.91
4377.8
165.91
4529.4
166.88
4680.4
167.80
4830.9
168.70
4981.0
169.57
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
25.70
26.10
26.45
26.76
27.04
27.29
27.51
27.71
27.90
34.02
34.42
34.77
35.08
35.35
35.60
35.82
36.03
36.21
675.7
701.9
727.2
751.7
775.4
798.3
820.7
842.5
863.7
34.01
33.98
33.54
33.11
32.71
32.32
31.94
31.59
31.24
30.91
30.59
30.28
29.99
29.70
29.43
29.17
28.92
28.68
28.46
28.24
28.23
23.36
23.07
22.79
22.56
22.37
22.21
22.07
21.95
21.85
21.76
21.68
21.61
21.54
21.48
21.43
21.38
21.34
21.30
21.26
21.23
21.20
21.17
21.14
21.12
21.10
21.08
21.06
21.02
20.98
20.95
20.93
20.90
55.02
55.02
55.01
55.02
55.06
55.11
55.19
55.30
55.43
55.59
55.79
56.02
56.29
56.61
56.98
57.41
57.91
58.49
59.15
59.92
59.98
37.31
36.53
35.75
35.11
34.57
34.10
33.70
33.35
33.04
32.77
32.52
32.30
32.10
31.92
31.75
31.60
31.46
31.34
31.22
31.11
31.01
30.91
30.83
30.75
30.67
30.60
30.53
30.39
30.26
30.15
30.05
29.97
1032.1
1030.8
1014.7
998.4
981.9
965.1
948.0
930.7
913.1
895.2
877.0
858.5
839.7
820.5
801.0
781.0
760.6
739.8
718.4
696.5
695.2
185.0
187.4
190.3
193.0
195.7
198.2
200.7
203.2
205.5
207.9
210.1
212.4
214.6
216.7
218.8
220.9
223.0
225.0
227.0
229.0
230.9
232.8
234.7
236.6
238.4
240.3
242.1
246.5
250.9
255.1
259.3
263.4
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
370
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
180
185
190
195
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
59.93
60
62
64
66
68
70
72
74
76
78
80
82
84
86
88
90
Density
共mol/dm3兲
Internal
energy
共J/mol兲
0.339 87
0.330 17
0.321 04
0.312 41
0.304 25
0.289 19
0.275 59
0.263 25
0.251 99
0.241 67
0.232 18
0.223 42
0.215 31
0.207 77
0.200 75
0.194 20
0.188 06
0.182 31
0.176 89
0.171 80
0.166 99
0.162 45
0.158 15
0.154 07
0.150 20
0.133 45
0.120 07
0.109 14
0.100 04
0.092 347
0.085 752
0.080 038
0.075 038
0.066 707
0.060 042
0.054 589
0.050 045
0.046 199
0.042 902
0.040 045
0.037 544
0.035 338
0.033 377
0.031 621
0.030 042
3659.5
3765.6
3871.5
3977.3
4082.9
4293.7
4504.0
4714.1
4923.9
5133.4
5342.9
5552.2
5761.4
5970.6
6179.8
6389.1
6598.4
6807.8
7017.3
7227.0
7436.9
7647.0
7857.3
8067.9
8278.8
9338.5
10 409.0
11 494.0
12 593.0
13 709.0
14 842.0
15 993.0
17 160.0
19 545.0
21 990.0
24 491.0
27 039.0
29 631.0
32 259.0
34 921.0
37 611.0
40 328.0
43 068.0
45 829.0
48 610.0
33.094
33.083
32.800
32.514
32.225
31.934
31.641
31.344
31.044
30.740
30.431
30.119
29.801
29.478
29.148
28.812
28.467
⫺4711.2
⫺4707.2
⫺4597.6
⫺4487.9
⫺4378.2
⫺4268.5
⫺4158.6
⫺4048.6
⫺3938.4
⫺3827.9
⫺3717.0
⫺3605.8
⫺3494.2
⫺3381.9
⫺3269.1
⫺3155.5
⫺3041.1
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
Enthalpy
共J/mol兲
5130.6
5280.0
5429.0
5577.7
5726.2
6022.6
6318.3
6613.4
6908.1
7202.4
7496.4
7790.1
8083.7
8377.1
8670.5
8963.8
9257.1
9550.4
9843.9
10 137.0
10 431.0
10 725.0
11 019.0
11 313.0
11 608.0
13 085.0
14 573.0
16 075.0
17 591.0
19 123.0
20 673.0
22 240.0
23 823.0
27 040.0
30 318.0
33 650.0
37 030.0
40 453.0
43 914.0
47 407.0
50 929.0
54 477.0
58 049.0
61 641.0
65 254.0
1.0 MPa isobar
⫺4681.0
⫺4677.0
⫺4567.1
⫺4457.2
⫺4347.2
⫺4237.2
⫺4127.0
⫺4016.7
⫺3906.1
⫺3795.3
⫺3684.2
⫺3572.6
⫺3460.6
⫺3348.0
⫺3234.8
⫺3120.8
⫺3005.9
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
170.42
171.24
172.03
172.80
173.55
175.00
176.38
177.69
178.94
180.14
181.30
182.41
183.47
184.50
185.50
186.46
187.39
188.29
189.17
190.02
190.85
191.65
192.44
193.20
193.95
197.43
200.56
203.42
206.06
208.52
210.81
212.97
215.02
218.81
222.26
225.43
228.37
231.11
233.68
236.09
238.36
240.51
242.55
244.50
246.35
20.89
20.87
20.86
20.85
20.84
20.82
20.81
20.80
20.80
20.80
20.80
20.80
20.81
20.81
20.82
20.84
20.85
20.87
20.89
20.91
20.93
20.96
20.99
21.02
21.06
21.26
21.51
21.81
22.13
22.47
22.82
23.17
23.51
24.15
24.74
25.25
25.71
26.10
26.46
26.76
27.04
27.29
27.51
27.71
27.90
29.90
29.83
29.78
29.72
29.68
29.60
29.54
29.49
29.45
29.41
29.39
29.37
29.35
29.34
29.33
29.33
29.33
29.34
29.35
29.36
29.37
29.39
29.41
29.44
29.47
29.65
29.89
30.17
30.48
30.82
31.16
31.51
31.84
32.48
33.06
33.57
34.03
34.42
34.77
35.08
35.36
35.60
35.83
36.03
36.21
267.4
271.3
275.1
278.9
282.6
289.9
297.0
303.9
310.6
317.1
323.5
329.8
335.9
341.9
347.8
353.6
359.3
364.8
370.3
375.7
381.0
386.2
391.3
396.3
401.3
425.1
447.3
468.2
488.0
506.8
524.8
542.1
558.7
590.5
620.4
648.9
676.2
702.5
727.8
752.2
775.9
798.8
821.2
842.9
864.1
34.02
34.00
33.56
33.14
32.73
32.34
31.97
31.61
31.27
30.93
30.62
30.31
30.01
29.73
29.46
29.20
28.95
54.97
54.97
54.96
54.97
55.00
55.05
55.12
55.21
55.33
55.49
55.67
55.89
56.15
56.45
56.80
57.20
57.67
1033.8
1033.3
1017.3
1001.1
984.7
968.0
951.1
933.9
916.5
898.8
880.8
862.5
843.8
824.9
805.6
786.0
765.9
70.936
71.002
72.804
74.549
76.241
77.884
79.480
81.034
82.549
84.026
85.470
86.882
88.265
89.622
90.954
92.264
93.555
THERMODYNAMIC PROPERTIES OF AIR
371
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
92
94
96
98
100
102
104
106
106.22
108.10
110
112
114
116
118
120
122
124
126
128
130
132
134
136
138
140
142
144
146
148
150
155
160
165
170
175
180
185
190
195
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
450
500
Density
共mol/dm3兲
Internal
energy
共J/mol兲
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
28.115
27.752
27.379
26.993
26.593
26.177
25.742
25.284
25.232
1.3836
1.3382
1.2951
1.2559
1.2200
1.1870
1.1563
1.1276
1.1009
1.0757
1.0519
1.0295
1.0082
0.988 04
0.968 81
0.950 48
0.932 97
0.916 22
0.900 18
0.884 78
0.869 99
0.855 77
0.822 47
0.792 01
0.763 99
0.738 11
0.714 11
0.691 76
0.670 90
0.651 36
0.633 01
0.615 74
0.584 06
0.555 66
0.530 03
0.506 76
0.485 53
0.466 07
0.448 16
0.431 62
0.416 30
0.402 05
0.388 76
0.376 35
0.364 72
0.353 80
0.343 53
0.333 85
0.324 71
0.316 06
0.307 87
0.300 09
0.266 51
0.239 74
⫺2925.6
⫺2809.1
⫺2691.2
⫺2571.8
⫺2450.7
⫺2327.5
⫺2201.8
⫺2073.2
⫺2059.0
1873.7
1931.9
1990.8
2047.6
2102.9
2156.7
2209.5
2261.3
2312.2
2362.5
2412.1
2461.1
2509.7
2557.8
2605.5
2652.8
2699.8
2746.4
2792.8
2838.9
2884.8
2930.5
3043.8
3156.0
3267.4
3377.9
3487.9
3597.2
3706.1
3814.6
3922.6
4030.4
4245.0
4458.7
4671.7
4884.0
5095.9
5307.4
5518.5
5729.5
5940.2
6150.8
6361.4
6571.9
6782.4
6992.9
7203.6
7414.4
7625.3
7836.4
8047.7
8259.3
9322.0
10 395.0
⫺2890.1
⫺2773.1
⫺2654.7
⫺2534.8
⫺2413.1
⫺2289.3
⫺2162.9
⫺2033.7
⫺2019.3
2596.5
2679.2
2763.0
2843.9
2922.5
2999.2
3074.3
3148.1
3220.6
3292.1
3362.7
3432.5
3501.5
3569.9
3637.7
3704.9
3771.6
3837.9
3903.7
3969.2
4034.3
4099.0
4259.6
4418.6
4576.3
4732.8
4888.2
5042.8
5196.6
5349.8
5502.4
5654.4
5957.2
6258.4
6558.4
6857.4
7155.5
7453.0
7749.9
8046.3
8342.3
8638.1
8933.6
9229.0
9524.2
9819.4
10 115.0
10 410.0
10 705.0
11 000.0
11 296.0
11 592.0
13 074.0
14 566.0
94.828
96.086
97.332
98.568
99.798
101.02
102.25
103.48
103.62
146.73
147.49
148.24
148.96
149.64
150.30
150.93
151.54
152.13
152.70
153.25
153.79
154.32
154.84
155.34
155.83
156.31
156.78
157.24
157.69
158.13
158.57
159.62
160.63
161.60
162.53
163.44
164.31
165.15
165.97
166.76
167.53
169.01
170.41
171.74
173.01
174.23
175.40
176.52
177.60
178.64
179.64
180.61
181.54
182.45
183.33
184.19
185.02
185.83
186.62
187.39
188.13
191.63
194.77
28.71
28.48
28.26
28.06
27.87
27.69
27.53
27.38
27.37
24.74
24.21
23.78
23.43
23.15
22.91
22.71
22.54
22.39
22.26
22.15
22.05
21.95
21.87
21.80
21.73
21.66
21.61
21.55
21.51
21.46
21.42
21.33
21.26
21.20
21.14
21.10
21.06
21.03
21.00
20.98
20.95
20.92
20.90
20.88
20.86
20.85
20.85
20.85
20.85
20.85
20.86
20.87
20.88
20.90
20.91
20.93
20.96
20.98
21.01
21.04
21.07
21.27
21.53
58.21
58.83
59.55
60.38
61.36
62.50
63.85
65.48
65.68
44.60
42.69
41.11
39.85
38.81
37.94
37.20
36.56
36.00
35.52
35.08
34.69
34.34
34.03
33.74
33.48
33.24
33.02
32.82
32.64
32.46
32.30
31.95
31.66
31.41
31.19
31.00
30.84
30.70
30.57
30.46
30.36
30.19
30.06
29.95
29.85
29.78
29.72
29.66
29.62
29.59
29.56
29.54
29.53
29.52
29.52
29.52
29.52
29.53
29.54
29.56
29.58
29.73
29.95
745.4
724.4
702.9
680.9
658.2
634.9
610.8
585.8
583.0
185.2
188.7
192.1
195.3
198.3
201.2
204.0
206.8
209.4
211.9
214.4
216.8
219.2
221.5
223.8
226.0
228.2
230.3
232.4
234.5
236.5
238.5
243.4
248.1
252.7
257.1
261.5
265.7
269.8
273.9
277.9
281.7
289.3
296.6
303.7
310.6
317.3
323.8
330.2
336.4
342.5
348.4
354.3
360.0
365.6
371.1
376.6
381.9
387.1
392.3
397.3
402.3
426.2
448.5
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
372
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
550
600
650
700
750
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
60.11
62
64
66
68
70
72
74
76
78
80
82
84
86
88
90
92
94
96
98
100
102
104
106
108
110
112
114
116
118
118.52
119.94
120
122
124
126
128
130
132
134
136
138
140
142
Density
共mol/dm3兲
Internal
energy
共J/mol兲
0.217 90
0.199 72
0.184 35
0.171 19
0.159 79
0.149 81
0.133 19
0.119 90
0.109 02
0.099 953
0.092 279
0.085 701
0.079 999
0.075 008
0.070 604
0.066 689
0.063 185
0.060 031
11 481.0
12 582.0
13 699.0
14 834.0
15 985.0
17 153.0
19 539.0
21 986.0
24 487.0
27 036.0
29 628.0
32 257.0
34 919.0
37 610.0
40 327.0
43 067.0
45 829.0
48 609.0
33.121
32.854
32.570
32.285
31.997
31.706
31.412
31.116
30.815
30.511
30.203
29.891
29.573
29.249
28.919
28.583
28.238
27.885
27.522
27.149
26.763
26.364
25.948
25.514
25.058
24.577
24.065
23.513
22.913
22.245
22.059
2.9766
2.9709
2.8114
2.6809
2.5702
2.4740
2.3888
2.3124
2.2432
2.1799
2.1217
2.0678
2.0176
⫺4709.1
⫺4605.7
⫺4496.5
⫺4387.3
⫺4278.1
⫺4168.8
⫺4059.3
⫺3949.7
⫺3839.9
⫺3729.9
⫺3619.4
⫺3508.6
⫺3397.4
⫺3285.5
⫺3173.1
⫺3059.9
⫺2945.9
⫺2830.9
⫺2714.7
⫺2597.3
⫺2478.4
⫺2357.8
⫺2235.2
⫺2110.2
⫺1982.5
⫺1851.4
⫺1716.2
⫺1576.0
⫺1429.3
⫺1273.6
⫺1231.7
1788.0
1791.1
1880.8
1961.3
2035.7
2105.5
2171.9
2235.5
2296.8
2356.4
2414.3
2470.9
2526.4
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
16 070.0
197.64
17 589.0
200.28
19 124.0
202.74
20 675.0
205.04
22 243.0
207.20
23 828.0
209.25
27 047.0
213.04
30 326.0
216.49
33 659.0
219.67
37 041.0
222.61
40 465.0
225.35
43 925.0
227.91
47 419.0
230.32
50 942.0
232.60
54 490.0
234.75
58 062.0
236.79
61 655.0
238.73
65 268.0
240.59
2.0 MPa isobar
⫺4648.7
70.970
⫺4544.8
72.673
⫺4435.1
74.414
⫺4325.3
76.103
⫺4215.6
77.741
⫺4105.7
79.334
⫺3995.7
80.884
⫺3885.5
82.393
⫺3775.0
83.866
⫺3664.3
85.304
⫺3553.2
86.710
⫺3441.7
88.087
⫺3329.7
89.436
⫺3217.2
90.760
⫺3103.9
92.062
⫺2989.9
93.343
⫺2875.0
94.606
⫺2759.1
95.852
⫺2642.1
97.084
⫺2523.6
98.305
⫺2403.7
99.517
⫺2281.9
100.72
⫺2158.1
101.92
⫺2031.8
103.13
⫺1902.7
104.33
⫺1770.0
105.55
⫺1633.1
106.78
⫺1491.0
108.04
⫺1342.0
109.34
⫺1183.7
110.69
⫺1141.0
111.05
2459.9
141.25
2464.3
141.29
2592.2
142.35
2707.4
143.28
2813.8
144.13
2913.9
144.92
3009.1
145.66
3100.4
146.36
3188.4
147.02
3273.8
147.65
3357.0
148.26
3438.2
148.84
3517.7
149.41
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
21.82
22.14
22.48
22.83
23.18
23.52
24.16
24.74
25.26
25.71
26.11
26.46
26.77
27.04
27.29
27.51
27.71
27.90
30.22
30.53
30.86
31.19
31.53
31.87
32.50
33.07
33.58
34.03
34.43
34.78
35.09
35.36
35.61
35.83
36.03
36.22
469.4
489.2
508.0
526.0
543.2
559.9
591.5
621.5
650.0
677.2
703.4
728.7
753.1
776.7
799.7
822.0
843.7
864.9
34.02
33.61
33.18
32.78
32.39
32.02
31.66
31.32
30.99
30.67
30.36
30.07
29.78
29.51
29.25
29.00
28.76
28.53
28.31
28.10
27.90
27.72
27.55
27.40
27.26
27.14
27.04
26.97
26.94
26.96
26.97
27.21
27.17
26.12
25.36
24.78
24.33
23.96
23.66
23.40
23.18
22.99
22.83
22.68
54.88
54.86
54.86
54.88
54.91
54.97
55.05
55.15
55.29
55.45
55.64
55.87
56.13
56.44
56.80
57.21
57.69
58.23
58.86
59.57
60.41
61.37
62.49
63.82
65.40
67.31
69.66
72.64
76.56
82.02
83.81
68.49
68.18
60.34
55.18
51.49
48.71
46.54
44.78
43.33
42.11
41.07
40.16
39.38
1037.4
1022.4
1006.5
990.3
973.8
957.2
940.3
923.1
905.7
888.1
870.2
852.0
833.5
814.7
795.6
776.1
756.2
736.0
715.3
694.1
672.5
650.2
627.4
603.9
579.6
554.3
528.0
500.4
470.9
439.1
430.4
180.5
180.7
186.1
190.8
195.1
199.0
202.6
206.1
209.3
212.4
215.4
218.3
221.0
THERMODYNAMIC PROPERTIES OF AIR
373
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
144
146
148
150
155
160
165
170
175
180
185
190
195
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
60.64
62
64
66
68
70
72
74
Density
共mol/dm3兲
Internal
energy
共J/mol兲
1.9707
1.9267
1.8853
1.8462
1.7572
1.6785
1.6082
1.5448
1.4872
1.4345
1.3861
1.3413
1.2997
1.2610
1.1909
1.1291
1.0739
1.0243
0.979 42
0.938 59
0.901 25
0.866 94
0.835 28
0.805 97
0.778 73
0.753 36
0.729 65
0.707 45
0.686 60
0.666 99
0.648 50
0.631 04
0.614 51
0.598 86
0.531 41
0.477 83
0.434 20
0.397 94
0.367 32
0.34 112
0.31 842
0.298 57
0.265 50
0.239 05
0.217 40
0.199 36
0.184 08
0.170 99
0.159 63
0.149 69
0.140 92
0.133 12
0.126 14
0.119 85
2580.9
2634.4
2687.2
2739.2
2866.7
2991.0
3112.7
3232.4
3350.4
3466.9
3582.3
3696.5
3809.9
3922.4
4145.5
4366.5
4585.7
4803.5
5020.2
5236.0
5451.0
5665.4
5879.3
6092.8
6306.0
6519.0
6731.7
6944.4
7156.9
7369.5
7582.1
7794.8
8007.6
8220.6
9289.2
10 367.0
11 457.0
12 561.0
13 680.0
14 816.0
15 970.0
17 139.0
19 528.0
21 976.0
24 479.0
27 030.0
29 623.0
32 253.0
34 915.0
37 607.0
40 324.0
43 065.0
45 827.0
48 608.0
33.200
33.012
32.736
32.458
32.178
31.895
31.611
31.324
⫺4702.6
⫺4629.1
⫺4521.2
⫺4413.4
⫺4305.7
⫺4198.0
⫺4090.2
⫺3982.4
Enthalpy
共J/mol兲
3595.7
3672.5
3748.0
3822.5
4004.9
4182.5
4356.3
4527.1
4695.2
4861.1
5025.2
5187.6
5348.6
5508.4
5824.9
6137.9
6448.1
6756.1
7062.2
7366.9
7670.2
7972.4
8273.8
8574.3
8874.3
9173.7
9472.7
9771.4
10 070.0
10 368.0
10 666.0
10 964.0
11 262.0
11 560.0
13 053.0
14 552.0
16 063.0
17 586.0
19 125.0
20 680.0
22 251.0
23 838.0
27 061.0
30 343.0
33 679.0
37 062.0
40 487.0
43 949.0
47 444.0
50 967.0
54 517.0
58 089.0
61 683.0
65 296.0
5.0 MPa isobar
⫺4552.0
⫺4477.6
⫺4368.5
⫺4259.4
⫺4150.3
⫺4041.2
⫺3932.0
⫺3822.8
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
149.95
150.48
151.00
151.50
152.69
153.82
154.89
155.91
156.88
157.82
158.72
159.58
160.42
161.23
162.77
164.23
165.61
166.92
168.17
169.36
170.51
171.61
172.67
173.68
174.67
175.62
176.54
177.43
178.30
179.14
179.95
180.75
181.52
182.28
185.79
188.95
191.83
194.48
196.94
199.25
201.42
203.47
207.26
210.72
213.90
216.84
219.58
222.15
224.56
226.83
228.98
231.03
232.97
234.82
22.55
22.43
22.32
22.22
22.02
21.85
21.71
21.60
21.50
21.42
21.35
21.29
21.24
21.19
21.12
21.07
21.02
20.99
20.97
20.95
20.94
20.93
20.93
20.93
20.93
20.94
20.95
20.97
20.98
21.00
21.03
21.05
21.08
21.11
21.30
21.55
21.84
22.16
22.50
22.84
23.19
23.53
24.17
24.75
25.26
25.72
26.11
26.46
26.77
27.05
27.29
27.52
27.72
27.90
38.68
38.06
37.51
37.01
35.96
35.12
34.44
33.87
33.39
32.99
32.64
32.34
32.08
31.84
31.46
31.15
30.90
30.70
30.53
30.39
30.28
30.18
30.09
30.03
29.97
29.92
29.88
29.85
29.83
29.82
29.81
29.80
29.80
29.81
29.91
30.09
30.33
30.62
30.93
31.26
31.58
31.91
32.53
33.10
33.61
34.05
34.44
34.79
35.10
35.37
35.61
35.83
36.04
36.22
223.7
226.3
228.8
231.3
237.2
242.7
248.1
253.1
258.0
262.8
267.3
271.8
276.1
280.3
288.4
296.2
303.6
310.8
317.8
324.6
331.2
337.6
343.8
349.9
355.9
361.7
367.4
373.0
378.5
383.9
389.2
394.4
399.5
404.5
428.5
450.8
471.8
491.5
510.3
528.3
545.5
562.1
593.7
623.6
652.0
679.2
705.3
730.5
754.8
778.4
801.3
823.6
845.3
866.4
34.04
33.75
33.33
32.93
32.54
32.17
31.82
31.48
54.61
54.58
54.55
54.54
54.55
54.57
54.61
54.67
1047.7
1037.3
1021.9
1006.3
990.5
974.6
958.5
942.2
71.073
72.287
74.019
75.698
77.326
78.907
80.445
81.942
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
374
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
76
78
80
82
84
86
88
90
92
94
96
98
100
102
104
106
108
110
112
114
116
118
120
122
124
126
128
130
132
134
136
138
140
142
144
146
148
150
155
160
165
170
175
180
185
190
195
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
Density
共mol/dm3兲
Internal
energy
共J/mol兲
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
31.034
30.742
30.446
30.146
29.843
29.535
29.223
28.906
28.582
28.253
27.917
27.574
27.222
26.861
26.490
26.108
25.713
25.304
24.879
24.436
23.972
23.483
22.966
22.415
21.822
21.176
20.462
19.654
18.706
17.533
15.954
13.686
11.096
9.2688
8.1721
7.4446
6.9126
6.4975
5.7485
5.2273
4.8317
4.5153
4.2532
4.0305
3.8376
3.6681
3.5173
3.3819
3.1473
2.9500
2.7806
2.6330
2.5028
2.3868
2.2825
2.1880
2.1020
2.0232
1.9507
1.8837
1.8216
1.7637
1.7097
⫺3874.5
⫺3766.4
⫺3658.2
⫺3549.7
⫺3441.0
⫺3331.9
⫺3222.4
⫺3112.4
⫺3002.0
⫺2890.9
⫺2779.1
⫺2666.5
⫺2553.1
⫺2438.6
⫺2322.9
⫺2206.0
⫺2087.5
⫺1967.4
⫺1845.3
⫺1720.9
⫺1594.0
⫺1464.0
⫺1330.4
⫺1192.4
⫺1049.1
⫺899.10
⫺740.19
⫺569.09
⫺380.05
⫺162.02
108.31
470.13
892.71
1229.6
1462.3
1636.9
1778.7
1900.3
2152.4
2362.0
2547.3
2716.8
2875.2
3025.5
3169.5
3308.6
3443.6
3575.4
3831.0
4078.5
4319.9
4556.6
4789.7
5019.7
5247.4
5473.0
5697.0
5919.6
6141.1
6361.6
6581.2
6800.3
7018.8
⫺3713.4
⫺3603.8
⫺3493.9
⫺3383.8
⫺3273.4
⫺3162.6
⫺3051.3
⫺2939.5
⫺2827.0
⫺2713.9
⫺2600.0
⫺2485.2
⫺2369.4
⫺2252.4
⫺2134.2
⫺2014.5
⫺1893.1
⫺1769.8
⫺1644.3
⫺1516.3
⫺1385.4
⫺1251.1
⫺1112.7
⫺969.37
⫺820.02
⫺662.99
⫺495.84
⫺314.69
⫺112.75
123.16
421.72
835.47
1343.3
1769.0
2074.2
2308.5
2502.1
2669.9
3022.2
3318.5
3582.1
3824.1
4050.8
4266.1
4472.4
4671.7
4865.2
5053.8
5419.6
5773.4
6118.1
6455.6
6787.4
7114.6
7438.0
7758.2
8075.7
8390.9
8704.2
9015.9
9326.2
9635.2
9943.3
83.401
84.824
86.214
87.574
88.904
90.208
91.488
92.744
93.980
95.196
96.395
97.579
98.748
99.906
101.05
102.19
103.33
104.46
105.59
106.72
107.86
109.01
110.17
111.36
112.57
113.83
115.14
116.55
118.09
119.86
122.07
125.09
128.75
131.77
133.90
135.52
136.83
137.96
140.27
142.15
143.78
145.22
146.54
147.75
148.88
149.94
150.95
151.90
153.69
155.34
156.87
158.30
159.66
160.94
162.16
163.33
164.44
165.51
166.54
167.53
168.48
169.40
170.30
31.15
30.83
30.52
30.23
29.94
29.67
29.41
29.15
28.91
28.68
28.45
28.24
28.03
27.84
27.66
27.48
27.32
27.17
27.03
26.90
26.79
26.70
26.62
26.57
26.55
26.57
26.63
26.78
27.04
27.53
28.44
29.89
30.37
29.21
27.96
26.99
26.24
25.66
24.63
23.95
23.46
23.08
22.78
22.54
22.35
22.18
22.04
21.92
21.72
21.58
21.46
21.37
21.31
21.25
21.21
21.17
21.15
21.13
21.12
21.11
21.11
21.12
21.12
54.75
54.85
54.98
55.13
55.31
55.52
55.77
56.06
56.38
56.75
57.17
57.64
58.18
58.79
59.48
60.26
61.15
62.17
63.34
64.69
66.26
68.12
70.34
73.05
76.44
80.80
86.66
95.03
107.94
130.20
173.22
241.20
246.60
178.44
131.40
105.29
89.47
78.99
63.74
55.49
50.29
46.71
44.09
42.09
40.51
39.24
38.19
37.31
35.92
34.88
34.08
33.45
32.94
32.52
32.17
31.88
31.63
31.42
31.24
31.09
30.96
30.85
30.76
925.7
909.0
892.1
875.0
857.7
840.2
822.4
804.4
786.2
767.7
748.9
729.9
710.6
690.9
671.0
650.7
630.0
609.0
587.6
565.7
543.3
520.4
496.8
472.5
447.2
420.8
393.0
363.1
330.4
294.1
253.7
216.2
199.5
199.2
202.8
206.9
211.0
214.9
223.8
231.8
239.1
245.9
252.2
258.2
263.9
269.3
274.5
279.4
288.8
297.7
306.0
314.0
321.5
328.8
335.9
342.7
349.2
355.6
361.8
367.9
373.8
379.6
385.2
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
THERMODYNAMIC PROPERTIES OF AIR
375
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
360
370
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
61.52
62
64
66
68
70
72
74
76
78
80
82
84
86
88
90
92
94
96
98
100
102
104
106
108
110
112
114
116
118
120
122
124
126
128
130
132
Density
共mol/dm3兲
Internal
energy
共J/mol兲
1.6591
1.6117
1.5671
1.5250
1.4852
1.3152
1.1814
1.0731
0.983 39
0.907 81
0.843 21
0.787 32
0.738 47
0.657 11
0.592 03
0.538 74
0.494 31
0.456 67
0.424 38
0.396 36
0.371 82
0.350 15
0.330 88
0.313 61
0.298 06
7236.8
7454.5
7672.0
7889.3
8106.4
9192.6
10 284.0
11 384.0
12 497.0
13 624.0
14 766.0
15 924.0
17 099.0
19 494.0
21 949.0
24 456.0
27 011.0
29 607.0
32 239.0
34 904.0
37 598.0
40 317.0
43 059.0
45 823.0
48 605.0
33.329
33.264
32.998
32.731
32.462
32.192
31.921
31.648
31.373
31.096
30.817
30.536
30.253
29.966
29.677
29.384
29.088
28.788
28.484
28.176
27.863
27.546
27.222
26.893
26.558
26.215
25.866
25.509
25.143
24.768
24.383
23.988
23.582
23.164
22.732
22.287
21.826
⫺4691.3
⫺4665.6
⫺4559.7
⫺4454.0
⫺4348.4
⫺4243.0
⫺4137.6
⫺4032.4
⫺3927.1
⫺3821.9
⫺3716.7
⫺3611.5
⫺3506.1
⫺3400.7
⫺3295.2
⫺3189.5
⫺3083.5
⫺2977.4
⫺2870.9
⫺2764.1
⫺2656.9
⫺2549.4
⫺2441.3
⫺2332.7
⫺2223.5
⫺2113.6
⫺2003.1
⫺1891.7
⫺1779.5
⫺1666.3
⫺1552.1
⫺1436.8
⫺1320.2
⫺1202.4
⫺1083.1
⫺962.17
⫺839.59
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
10 250.0
171.16
10 557.0
172.00
10 863.0
172.82
11 168.0
173.61
11 473.0
174.38
12 994.0
177.97
14 516.0
181.17
16 044.0
184.08
17 581.0
186.76
19 131.0
189.24
20 696.0
191.56
22 275.0
193.74
23 869.0
195.80
27 103.0
199.61
30 394.0
203.07
33 737.0
206.26
37 126.0
209.21
40 556.0
211.95
44 021.0
214.52
47 519.0
216.93
51 045.0
219.21
54 596.0
221.36
58 171.0
223.40
61 766.0
225.35
65 380.0
227.20
10.0 MPa isobar
⫺4391.2
71.245
⫺4364.9
71.671
⫺4256.7
73.390
⫺4148.5
75.054
⫺4040.4
76.668
⫺3932.4
78.233
⫺3824.4
79.755
⫺3716.4
81.234
⫺3608.4
82.674
⫺3500.3
84.077
⫺3392.2
85.446
⫺3284.0
86.782
⫺3175.6
88.088
⫺3067.0
89.366
⫺2958.2
90.616
⫺2849.1
91.842
⫺2739.7
93.044
⫺2630.0
94.224
⫺2519.8
95.384
⫺2409.2
96.524
⫺2298.1
97.647
⫺2186.3
98.753
⫺2073.9
99.844
⫺1960.8
100.92
⫺1846.9
101.99
⫺1732.2
103.04
⫺1616.5
104.08
⫺1499.7
105.11
⫺1381.8
106.14
⫺1262.6
107.16
⫺1142.0
108.17
⫺1019.9
109.18
⫺896.19
110.19
⫺770.65
111.19
⫺643.14
112.20
⫺513.47
113.20
⫺381.42
114.21
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
21.13
21.15
21.17
21.19
21.22
21.39
21.62
21.90
22.21
22.54
22.89
23.23
23.56
24.20
24.77
25.29
25.74
26.13
26.48
26.79
27.06
27.30
27.53
27.73
27.91
30.68
30.61
30.56
30.51
30.47
30.41
30.48
30.64
30.87
31.14
31.43
31.74
32.04
32.63
33.18
33.67
34.10
34.48
34.82
35.12
35.39
35.63
35.85
36.05
36.23
390.7
396.1
401.4
406.6
411.7
435.9
458.3
479.2
498.9
517.6
535.4
552.5
569.0
600.3
629.9
658.1
685.1
711.0
736.0
760.1
783.6
806.3
828.4
850.0
871.0
34.08
33.98
33.57
33.17
32.79
32.43
32.07
31.74
31.41
31.09
30.79
30.50
30.21
29.94
29.68
29.42
29.18
28.94
28.71
28.49
28.28
28.08
27.89
27.70
27.52
27.35
27.19
27.03
26.89
26.75
26.62
26.50
26.39
26.28
26.19
26.10
26.03
54.19
54.18
54.12
54.07
54.03
54.00
53.99
53.99
54.01
54.04
54.09
54.15
54.24
54.34
54.47
54.61
54.78
54.97
55.19
55.44
55.72
56.02
56.36
56.74
57.16
57.61
58.12
58.67
59.27
59.93
60.65
61.44
62.30
63.25
64.28
65.41
66.66
1064.0
1060.5
1046.0
1031.3
1016.5
1001.6
986.5
971.4
956.1
940.7
925.2
909.6
893.8
877.9
861.9
845.8
829.6
813.2
796.8
780.2
763.5
746.7
729.7
712.7
695.5
678.3
661.0
643.6
626.2
608.7
591.1
573.6
556.0
538.4
520.9
503.5
486.1
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
376
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
Density
共mol/dm3兲
Internal
energy
共J/mol兲
134
136
138
140
142
144
146
148
150
155
160
165
170
175
180
185
190
195
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
21.349
20.855
20.342
19.810
19.257
18.684
18.090
17.478
16.851
15.253
13.709
12.331
11.170
10.218
9.4390
8.7946
8.2534
7.7920
7.3931
6.7353
6.2116
5.7819
5.4208
5.1116
4.8429
4.6064
4.3961
4.2075
4.0370
3.8819
3.7400
3.6096
3.4891
3.3774
3.2735
3.1765
3.0857
3.0004
2.9202
2.5803
2.3157
2.1029
1.9274
1.7800
1.6542
1.5454
1.4504
1.2922
1.1655
1.0618
0.975 11
0.901 65
0.838 54
0.783 74
0.735 69
0.693 21
0.655 39
0.621 49
0.590 94
⫺715.17
⫺588.77
⫺460.24
⫺329.46
⫺196.33
⫺60.807
77.041
217.00
358.66
715.54
1064.0
1388.9
1682.4
1944.8
2180.7
2395.5
2593.7
2778.9
2953.7
3279.3
3581.7
3867.3
4140.6
4404.4
4660.8
4911.3
5157.0
5398.7
5637.1
5872.8
6106.2
6337.7
6567.4
6795.8
7023.0
7249.1
7474.4
7699.0
7923.0
9037.7
10 151.0
11 268.0
12 395.0
13 533.0
14 685.0
15 852.0
17 033.0
19 441.0
21 904.0
24 419.0
26 980.0
29 581.0
32 218.0
34 886.0
37 583.0
40 305.0
43 050.0
45 815.0
48 600.0
33.574
33.480
33.230
⫺4666.7
⫺4627.8
⫺4525.5
63.24
64
66
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
Enthalpy
共J/mol兲
⫺246.76
⫺109.26
31.349
175.34
322.96
474.42
629.83
789.15
952.10
1371.2
1793.4
2199.9
2577.7
2923.4
3240.1
3532.6
3805.4
4062.3
4306.3
4764.1
5191.5
5596.8
5985.3
6360.7
6725.7
7082.2
7431.7
7775.4
8114.2
8448.9
8780.0
9108.1
9433.5
9756.7
10 078.0
10 397.0
10 715.0
11 032.0
11 347.0
12 913.0
14 469.0
16 023.0
17 583.0
19 151.0
20 730.0
22 322.0
23 928.0
27 179.0
30 484.0
33 837.0
37 235.0
40 672.0
44 143.0
47 646.0
51 176.0
54 731.0
58 308.0
61 906.0
65 522.0
20.0 MPa isobar
⫺4071.0
⫺4030.5
⫺3923.7
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
115.22
116.24
117.27
118.30
119.35
120.41
121.48
122.56
123.66
126.41
129.09
131.59
133.84
135.85
137.63
139.24
140.69
142.03
143.26
145.50
147.49
149.29
150.94
152.47
153.91
155.25
156.52
157.73
158.88
159.97
161.03
162.04
163.01
163.94
164.85
165.72
166.57
167.39
168.19
171.88
175.16
178.12
180.84
183.35
185.69
187.88
189.96
193.79
197.27
200.46
203.42
206.17
208.74
211.16
213.44
215.59
217.64
219.58
221.44
25.96
25.90
25.86
25.82
25.79
25.77
25.76
25.75
25.73
25.65
25.45
25.11
24.70
24.30
23.94
23.62
23.35
23.11
22.90
22.56
22.30
22.10
21.93
21.80
21.70
21.61
21.54
21.49
21.44
21.41
21.38
21.36
21.35
21.34
21.34
21.34
21.35
21.37
21.38
21.52
21.73
22.00
22.30
22.62
22.95
23.29
23.62
24.24
24.81
25.32
25.77
26.16
26.50
26.81
27.08
27.32
27.54
27.74
27.93
68.02
69.51
71.13
72.88
74.76
76.71
78.69
80.60
82.31
84.77
83.46
78.69
72.33
66.09
60.75
56.38
52.86
50.01
47.67
44.10
41.53
39.62
38.14
36.98
36.04
35.28
34.64
34.11
33.66
33.28
32.95
32.67
32.42
32.21
32.03
31.87
31.73
31.61
31.50
31.18
31.08
31.12
31.27
31.47
31.71
31.97
32.24
32.79
33.30
33.76
34.18
34.55
34.88
35.17
35.43
35.66
35.88
36.07
36.25
468.8
451.7
434.8
418.1
401.9
386.1
371.0
356.7
343.4
316.0
297.6
287.3
282.7
281.8
283.1
285.6
288.8
292.4
296.3
304.3
312.4
320.3
328.0
335.4
342.7
349.7
356.5
363.1
369.5
375.7
381.8
387.7
393.5
399.1
404.6
410.0
415.3
420.5
425.6
449.6
471.8
492.5
511.9
530.3
547.8
564.6
580.8
611.6
640.7
668.5
695.0
720.6
745.2
769.1
792.2
814.7
836.5
857.9
878.6
34.18
34.03
33.64
53.48
53.44
53.33
1094.3
1089.3
1076.1
71.587
72.224
73.867
THERMODYNAMIC PROPERTIES OF AIR
377
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
68
70
72
74
76
78
80
82
84
86
88
90
92
94
96
98
100
102
104
106
108
110
112
114
116
118
120
122
124
126
128
130
132
134
136
138
140
142
144
146
148
150
155
160
165
170
175
180
185
190
195
200
210
220
230
240
250
260
270
280
290
300
310
Density
共mol/dm3兲
Internal
energy
共J/mol兲
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
32.981
32.730
32.480
32.228
31.976
31.724
31.470
31.216
30.961
30.705
30.447
30.189
29.929
29.667
29.405
29.140
28.874
28.606
28.337
28.065
27.791
27.516
27.238
26.958
26.675
26.390
26.103
25.813
25.520
25.225
24.928
24.628
24.325
24.020
23.712
23.402
23.090
22.776
22.460
22.142
21.822
21.501
20.693
19.884
19.077
18.280
17.500
16.745
16.021
15.332
14.683
14.074
12.978
12.034
11.221
10.519
9.9093
9.3749
8.9032
8.4837
8.1078
7.7690
7.4616
⫺4423.5
⫺4321.8
⫺4220.3
⫺4119.0
⫺4017.9
⫺3917.1
⫺3816.5
⫺3716.0
⫺3615.7
⫺3515.6
⫺3415.6
⫺3315.7
⫺3215.9
⫺3116.3
⫺3016.7
⫺2917.2
⫺2817.7
⫺2718.3
⫺2619.0
⫺2519.6
⫺2420.3
⫺2320.9
⫺2221.6
⫺2122.2
⫺2022.8
⫺1923.4
⫺1823.9
⫺1724.4
⫺1624.8
⫺1525.2
⫺1425.5
⫺1325.8
⫺1226.0
⫺1126.3
⫺1026.4
⫺926.63
⫺826.82
⫺727.03
⫺627.28
⫺527.60
⫺428.01
⫺328.54
⫺80.620
165.72
409.75
650.59
887.32
1119.0
1344.9
1564.4
1777.1
1982.9
2374.1
2740.3
3084.8
3410.9
3721.9
4020.3
4308.2
4587.4
4859.3
5125.0
5385.5
⫺3817.1
⫺3710.7
⫺3604.5
⫺3498.4
⫺3392.5
⫺3286.7
⫺3180.9
⫺3075.3
⫺2969.7
⫺2864.2
⫺2758.7
⫺2653.2
⫺2547.7
⫺2442.1
⫺2336.5
⫺2230.9
⫺2125.1
⫺2019.2
⫺1913.2
⫺1807.0
⫺1700.6
⫺1594.1
⫺1487.3
⫺1380.3
⫺1273.0
⫺1165.5
⫺1057.7
⫺949.55
⫺841.10
⫺732.32
⫺623.18
⫺513.69
⫺403.84
⫺293.61
⫺183.00
⫺72.016
39.349
151.09
263.20
375.68
488.50
601.66
885.87
1171.6
1458.1
1744.7
2030.2
2313.4
2593.3
2868.9
3139.3
3403.9
3915.2
4402.3
4867.1
5312.2
5740.2
6153.6
6554.6
6944.9
7326.1
7699.4
8065.9
75.457
76.999
78.496
79.949
81.361
82.736
84.074
85.378
86.650
87.892
89.105
90.290
91.450
92.585
93.696
94.786
95.854
96.903
97.932
98.943
99.937
100.91
101.88
102.82
103.76
104.68
105.58
106.48
107.36
108.23
109.09
109.94
110.77
111.60
112.42
113.23
114.03
114.83
115.61
116.39
117.15
117.91
119.78
121.59
123.35
125.07
126.72
128.32
129.85
131.32
132.72
134.06
136.56
138.83
140.89
142.79
144.53
146.16
147.67
149.09
150.43
151.69
152.89
33.27
32.91
32.57
32.23
31.91
31.60
31.30
31.02
30.74
30.47
30.20
29.95
29.71
29.47
29.24
29.02
28.81
28.60
28.40
28.21
28.02
27.84
27.67
27.50
27.34
27.18
27.03
26.88
26.74
26.61
26.48
26.35
26.23
26.11
26.00
25.89
25.79
25.69
25.59
25.50
25.41
25.32
25.12
24.92
24.74
24.56
24.39
24.22
24.06
23.89
23.74
23.58
23.30
23.04
22.81
22.62
22.45
22.31
22.19
22.09
22.00
21.93
21.86
53.24
53.15
53.07
53.00
52.94
52.88
52.84
52.80
52.77
52.76
52.75
52.75
52.76
52.79
52.82
52.86
52.91
52.98
53.05
53.13
53.23
53.33
53.44
53.57
53.70
53.84
53.99
54.14
54.31
54.48
54.65
54.84
55.02
55.21
55.40
55.59
55.78
55.96
56.15
56.33
56.50
56.66
57.01
57.25
57.34
57.24
56.91
56.35
55.58
54.62
53.52
52.34
49.90
47.56
45.45
43.61
42.03
40.69
39.54
38.55
37.71
36.97
36.34
1062.8
1049.4
1036.0
1022.6
1009.1
995.6
982.1
968.6
955.0
941.4
927.8
914.2
900.5
886.9
873.2
859.6
846.0
832.4
818.8
805.2
791.7
778.2
764.8
751.5
738.2
725.0
711.9
699.0
686.1
673.4
660.9
648.5
636.3
624.3
612.5
601.0
589.6
578.5
567.7
557.2
546.9
536.9
513.3
491.8
472.4
455.3
440.5
428.0
417.6
409.1
402.4
397.2
390.6
387.6
387.3
388.7
391.3
394.7
398.6
402.8
407.3
412.0
416.7
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
378
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
320
330
340
350
360
370
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
68.21
70
72
74
76
78
80
82
84
86
88
90
92
94
96
98
100
102
104
106
108
110
112
114
116
118
120
122
124
126
128
130
132
Density
共mol/dm3兲
Internal
energy
共J/mol兲
7.1814
6.9246
6.6882
6.4698
6.2673
6.0788
5.9028
5.7380
5.5834
4.9320
4.4288
4.0260
3.6950
3.4173
3.1804
2.9756
2.7966
2.4982
2.2588
2.0621
1.8975
1.7576
1.6372
1.5323
1.4402
1.3586
1.2858
1.2205
1.1615
5641.5
5893.6
6142.3
6388.2
6631.6
6872.8
7112.2
7349.9
7586.1
8752.1
9904.1
11 053.0
12 204.0
13 364.0
14 533.0
15 715.0
16 910.0
19 339.0
21 820.0
24 349.0
26 921.0
29 532.0
32 177.0
34 852.0
37 555.0
40 282.0
43 032.0
45 802.0
48 590.0
34.238
34.049
33.837
33.626
33.416
33.206
32.997
32.789
32.581
32.374
32.167
31.961
31.756
31.551
31.346
31.142
30.939
30.736
30.534
30.332
30.130
29.929
29.729
29.529
29.329
29.130
28.932
28.733
28.536
28.339
28.142
27.946
27.750
⫺4581.8
⫺4497.3
⫺4403.1
⫺4309.3
⫺4216.0
⫺4123.0
⫺4030.4
⫺3938.2
⫺3846.4
⫺3754.9
⫺3663.9
⫺3573.2
⫺3482.9
⫺3392.9
⫺3303.3
⫺3214.0
⫺3125.1
⫺3036.5
⫺2948.3
⫺2860.4
⫺2772.9
⫺2685.6
⫺2598.8
⫺2512.2
⫺2426.0
⫺2340.0
⫺2254.4
⫺2169.2
⫺2084.2
⫺1999.6
⫺1915.3
⫺1831.3
⫺1747.6
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
8426.5
154.04
8781.8
155.13
9132.7
156.18
9479.5
157.19
9822.8
158.15
10 163.0
159.08
10 500.0
159.98
10 835.0
160.85
11 168.0
161.70
12 807.0
165.56
14 420.0
168.96
16 020.0
172.01
17 617.0
174.79
19 216.0
177.35
20 822.0
179.73
22 436.0
181.96
24 061.0
184.05
27 345.0
187.92
30 674.0
191.43
34 047.0
194.64
37 461.0
197.61
40 911.0
200.37
44 393.0
202.95
47 904.0
205.38
51 442.0
207.66
55 003.0
209.82
58 586.0
211.87
62 189.0
213.81
65 809.0
215.67
50.0 MPa isobar
⫺3121.4
72.575
⫺3028.8
73.915
⫺2925.4
75.371
⫺2822.4
76.783
⫺2719.7
78.153
⫺2617.2
79.483
⫺2515.1
80.776
⫺2413.3
82.033
⫺2311.7
83.257
⫺2210.5
84.448
⫺2109.5
85.609
⫺2008.8
86.740
⫺1908.3
87.844
⫺1808.1
88.922
⫺1708.2
89.974
⫺1608.5
91.002
⫺1509.0
92.007
⫺1409.8
92.989
⫺1310.8
93.950
⫺1212.0
94.891
⫺1113.4
95.813
⫺1015.0
96.715
⫺916.88
97.599
⫺818.93
98.466
⫺721.17
99.316
⫺623.60
100.15
⫺526.23
100.97
⫺429.04
101.77
⫺332.03
102.56
⫺235.21
103.34
⫺138.56
104.10
⫺42.096
104.84
54.197
105.58
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
21.81
21.77
21.74
21.71
21.69
21.68
21.67
21.67
21.68
21.76
21.94
22.17
22.45
22.76
23.08
23.40
23.72
24.33
24.89
25.39
25.83
26.21
26.55
26.85
27.12
27.36
27.58
27.78
27.96
35.79
35.30
34.87
34.50
34.17
33.87
33.61
33.38
33.18
32.46
32.09
31.95
31.95
32.04
32.20
32.39
32.61
33.07
33.52
33.94
34.32
34.67
34.97
35.25
35.50
35.72
35.93
36.12
36.29
421.5
426.3
431.1
435.9
440.6
445.3
450.0
454.6
459.2
481.1
501.8
521.2
539.5
557.0
573.7
589.8
605.2
634.8
662.8
689.6
715.2
740.0
764.0
787.2
809.7
831.6
853.0
873.8
894.2
34.51
34.20
33.87
33.55
33.24
32.94
32.65
32.37
32.10
31.84
31.59
31.34
31.10
30.87
30.65
30.43
30.22
30.01
29.81
29.62
29.43
29.25
29.07
28.90
28.73
28.57
28.41
28.26
28.11
27.96
27.82
27.68
27.55
51.91
51.77
51.60
51.45
51.29
51.14
50.99
50.84
50.70
50.56
50.42
50.29
50.16
50.04
49.91
49.79
49.68
49.56
49.45
49.34
49.23
49.13
49.03
48.93
48.83
48.74
48.64
48.55
48.46
48.37
48.28
48.19
48.10
1172.7
1163.3
1152.9
1142.5
1132.1
1121.8
1111.6
1101.4
1091.2
1081.1
1071.1
1061.2
1051.3
1041.5
1031.7
1022.0
1012.4
1002.9
993.4
984.1
974.8
965.6
956.4
947.4
938.5
929.6
920.9
912.3
903.7
895.3
887.0
878.8
870.7
THERMODYNAMIC PROPERTIES OF AIR
379
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
134
136
138
140
142
144
146
148
150
155
160
165
170
175
180
185
190
195
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
75.92
76
78
Density
共mol/dm3兲
Internal
energy
共J/mol兲
27.555
27.361
27.167
26.974
26.781
26.589
26.398
26.207
26.017
25.545
25.079
24.618
24.163
23.714
23.272
22.837
22.410
21.990
21.579
20.783
20.022
19.299
18.613
17.963
17.350
16.773
16.228
15.716
15.234
14.780
14.353
13.950
13.569
13.210
12.870
12.549
12.244
11.955
11.680
10.489
9.5353
8.7536
8.0999
7.5440
7.0646
6.6465
6.2780
5.6573
5.1533
4.7351
4.3818
4.0790
3.8164
3.5862
3.3828
3.2015
3.0389
2.8923
2.7593
⫺1664.2
⫺1581.2
⫺1498.4
⫺1416.0
⫺1333.9
⫺1252.1
⫺1170.7
⫺1089.6
⫺1008.7
⫺808.12
⫺609.54
⫺413.01
⫺218.56
⫺26.212
164.03
352.15
538.13
721.98
903.69
1260.7
1609.4
1949.7
2282.1
2606.8
2924.2
3234.7
3538.8
3836.8
4129.2
4416.5
4699.1
4977.3
5251.6
5522.3
5789.7
6054.1
6315.8
6575.1
6832.1
8090.6
9319.0
10 531.0
11 737.0
12 943.0
14 153.0
15 370.0
16 595.0
19 076.0
21 599.0
24 163.0
26 764.0
29 400.0
32 066.0
34 760.0
37 479.0
40 221.0
42 983.0
45 764.0
48 562.0
35.183
35.176
35.002
⫺4416.8
⫺4413.2
⫺4326.8
Enthalpy
共J/mol兲
150.32
246.26
342.03
437.64
533.07
628.33
723.42
818.33
913.08
1149.2
1384.2
1618.0
1850.8
2082.3
2312.6
2541.6
2769.3
2995.7
3220.7
3666.6
4106.6
4540.6
4968.5
5390.3
5806.0
6215.8
6619.8
7018.2
7411.3
7799.4
8182.8
8561.7
8936.4
9307.3
9674.6
10 039.0
10 399.0
10 758.0
11 113.0
12 858.0
14 563.0
16 243.0
17 910.0
19 571.0
21 230.0
22 892.0
24 559.0
27 915.0
31 302.0
34 722.0
38 175.0
41 658.0
45 168.0
48 703.0
52 260.0
55 839.0
59 436.0
63 051.0
66 683.0
100.0 MPa isobar
⫺1574.5
⫺1570.4
⫺1469.9
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
106.30
107.01
107.71
108.40
109.08
109.74
110.40
111.04
111.68
113.23
114.72
116.16
117.55
118.89
120.19
121.44
122.66
123.83
124.97
127.15
129.20
131.13
132.95
134.67
136.30
137.85
139.32
140.71
142.05
143.32
144.54
145.70
146.82
147.90
148.93
149.93
150.89
151.82
152.72
156.83
160.42
163.63
166.53
169.19
171.65
173.94
176.09
180.04
183.61
186.87
189.88
192.66
195.27
197.70
200.00
202.17
204.23
206.18
208.04
27.42
27.29
27.17
27.05
26.94
26.82
26.71
26.60
26.50
26.25
26.01
25.79
25.59
25.39
25.21
25.04
24.88
24.72
24.58
24.31
24.07
23.86
23.66
23.49
23.33
23.19
23.06
22.95
22.85
22.76
22.68
22.61
22.55
22.50
22.45
22.42
22.39
22.36
22.35
22.34
22.44
22.62
22.85
23.11
23.40
23.69
23.99
24.57
25.09
25.57
25.99
26.36
26.69
26.98
27.23
27.47
27.68
27.87
28.04
48.02
47.93
47.84
47.76
47.67
47.59
47.50
47.42
47.33
47.11
46.89
46.66
46.42
46.18
45.93
45.68
45.41
45.14
44.87
44.29
43.70
43.10
42.49
41.88
41.27
40.68
40.12
39.57
39.06
38.57
38.11
37.68
37.28
36.91
36.56
36.24
35.94
35.67
35.42
34.44
33.81
33.44
33.25
33.19
33.21
33.29
33.40
33.71
34.04
34.37
34.68
34.97
35.23
35.47
35.68
35.88
36.07
36.23
36.39
862.7
854.8
847.1
839.4
831.9
824.6
817.3
810.2
803.2
786.3
770.2
754.9
740.5
726.9
714.1
702.1
690.9
680.4
670.6
653.1
638.1
625.4
614.7
605.8
598.5
592.7
588.0
584.4
581.7
579.7
578.4
577.7
577.4
577.6
578.1
578.9
580.0
581.4
582.9
592.4
604.1
616.6
629.5
642.5
655.5
668.3
681.0
705.9
730.0
753.6
776.5
798.8
820.6
841.8
862.5
882.8
902.6
922.0
941.1
34.95
34.94
34.65
50.34
50.34
50.15
1281.8
1281.5
1273.7
74.060
74.114
75.419
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
380
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
80
82
84
86
88
90
92
94
96
98
100
102
104
106
108
110
112
114
116
118
120
122
124
126
128
130
132
134
136
138
140
142
144
146
148
150
155
160
165
170
175
180
185
190
195
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
Density
共mol/dm3兲
Internal
energy
共J/mol兲
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
34.829
34.658
34.487
34.318
34.150
33.982
33.816
33.651
33.486
33.323
33.161
33.000
32.839
32.680
32.522
32.365
32.208
32.053
31.898
31.745
31.592
31.440
31.289
31.139
30.990
30.842
30.695
30.548
30.403
30.258
30.114
29.971
29.829
29.688
29.547
29.408
29.062
28.722
28.387
28.057
27.732
27.412
27.097
26.787
26.482
26.182
25.596
25.029
24.481
23.951
23.440
22.946
22.469
22.009
21.566
21.138
20.725
20.327
19.942
19.572
19.214
18.869
18.536
⫺4240.9
⫺4155.4
⫺4070.3
⫺3985.6
⫺3901.3
⫺3817.4
⫺3733.9
⫺3650.8
⫺3568.2
⫺3485.8
⫺3403.9
⫺3322.4
⫺3241.2
⫺3160.4
⫺3080.0
⫺2999.9
⫺2920.2
⫺2840.9
⫺2761.9
⫺2683.2
⫺2604.9
⫺2527.0
⫺2449.3
⫺2372.0
⫺2295.1
⫺2218.4
⫺2142.1
⫺2066.1
⫺1990.4
⫺1915.0
⫺1840.0
⫺1765.2
⫺1690.7
⫺1616.6
⫺1542.7
⫺1469.1
⫺1286.5
⫺1105.6
⫺926.45
⫺748.99
⫺573.18
⫺398.99
⫺226.38
⫺55.313
114.25
282.34
614.24
940.66
1261.9
1578.1
1889.6
2196.6
2499.3
2798.0
3092.9
3384.3
3672.2
3956.9
4238.6
4517.5
4793.8
5067.6
5339.1
⫺1369.8
⫺1270.0
⫺1170.7
⫺1071.6
⫺972.99
⫺874.69
⫺776.74
⫺679.13
⫺581.87
⫺484.94
⫺388.34
⫺292.06
⫺196.11
⫺100.48
⫺5.1555
89.857
184.56
278.97
373.08
466.90
560.44
653.68
746.65
839.34
931.76
1023.9
1115.8
1207.4
1298.8
1389.9
1480.7
1571.4
1661.7
1751.8
1841.7
1931.3
2154.4
2376.1
2596.3
2815.2
3032.8
3249.0
3464.1
3677.9
3890.4
4101.8
4521.2
4936.1
5346.7
5753.2
6155.8
6554.6
6949.8
7341.5
7729.9
8115.1
8497.3
8876.6
9253.0
9626.9
9998.2
10 367.0
10 734.0
76.686
77.918
79.115
80.280
81.414
82.518
83.595
84.644
85.668
86.668
87.644
88.597
89.528
90.439
91.330
92.202
93.055
93.891
94.709
95.511
96.297
97.067
97.823
98.565
99.293
100.01
100.71
101.40
102.07
102.74
103.39
104.04
104.67
105.29
105.90
106.50
107.96
109.37
110.73
112.03
113.30
114.51
115.69
116.83
117.94
119.01
121.05
122.98
124.81
126.54
128.18
129.75
131.24
132.66
134.03
135.33
136.59
137.79
138.95
140.06
141.14
142.18
143.19
34.37
34.10
33.83
33.58
33.33
33.09
32.85
32.63
32.40
32.19
31.98
31.78
31.58
31.39
31.20
31.02
30.84
30.66
30.50
30.33
30.17
30.01
29.86
29.71
29.57
29.43
29.29
29.15
29.02
28.90
28.77
28.65
28.53
28.41
28.30
28.19
27.92
27.67
27.43
27.20
26.99
26.78
26.59
26.41
26.23
26.07
25.76
25.48
25.23
24.99
24.78
24.59
24.42
24.26
24.11
23.98
23.86
23.75
23.65
23.57
23.49
23.42
23.35
49.96
49.78
49.60
49.42
49.24
49.06
48.89
48.72
48.55
48.38
48.22
48.06
47.90
47.74
47.58
47.43
47.28
47.13
46.98
46.84
46.69
46.55
46.41
46.28
46.14
46.01
45.88
45.75
45.62
45.49
45.36
45.24
45.12
45.00
44.88
44.76
44.47
44.19
43.91
43.65
43.38
43.13
42.88
42.64
42.40
42.16
41.71
41.27
40.86
40.45
40.07
39.70
39.34
39.00
38.68
38.37
38.07
37.78
37.51
37.26
37.01
36.78
36.56
1265.9
1258.3
1250.6
1243.1
1235.6
1228.3
1220.9
1213.7
1206.5
1199.4
1192.4
1185.4
1178.5
1171.7
1165.0
1158.3
1151.7
1145.2
1138.7
1132.3
1126.0
1119.8
1113.6
1107.5
1101.5
1095.5
1089.7
1083.9
1078.1
072.5
1066.9
1061.4
1055.9
1050.6
1045.3
1040.1
1027.3
1015.0
1003.2
991.7
980.8
970.2
960.0
950.3
941.0
932.0
915.2
899.9
885.9
873.2
861.6
851.2
841.7
833.1
825.4
818.5
812.2
806.7
801.7
797.3
793.3
789.9
786.8
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
THERMODYNAMIC PROPERTIES OF AIR
381
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
89.73
90
92
94
96
98
100
102
104
106
108
110
112
114
116
118
120
122
124
126
128
130
132
134
136
138
140
142
144
146
148
150
155
160
165
170
175
180
185
Density
共mol/dm3兲
Internal
energy
共J/mol兲
18.214
17.904
17.604
16.245
15.089
14.095
13.231
12.473
11.803
11.206
10.671
9.7481
8.9805
8.3307
7.7726
7.2877
6.8619
6.4847
6.1481
5.8456
5.5723
5.3239
5.0972
5608.4
5875.7
6141.2
7445.0
8720.1
9977.4
11 225.0
12 470.0
13 716.0
14 966.0
16 222.0
18 757.0
21 326.0
23 929.0
26 565.0
29 230.0
31 923.0
34 641.0
37 381.0
40 142.0
42 921.0
45 717.0
48 530.0
36.712
36.693
36.561
36.430
36.299
36.170
36.042
35.914
35.788
35.662
35.538
35.414
35.291
35.170
35.049
34.929
34.810
34.691
34.574
34.457
34.342
34.227
34.113
33.999
33.887
33.775
33.664
33.554
33.445
33.336
33.228
33.121
32.856
32.596
32.340
32.088
31.841
31.597
31.357
⫺4043.0
⫺4032.4
⫺3954.8
⫺3877.6
⫺3800.8
⫺3724.3
⫺3648.1
⫺3572.3
⫺3496.8
⫺3421.6
⫺3346.7
⫺3272.1
⫺3197.9
⫺3124.0
⫺3050.3
⫺2977.0
⫺2904.0
⫺2831.3
⫺2758.8
⫺2686.6
⫺2614.8
⫺2543.2
⫺2471.8
⫺2400.8
⫺2330.0
⫺2259.5
⫺2189.2
⫺2119.2
⫺2049.5
⫺1980.0
⫺1910.8
⫺1841.8
⫺1670.3
⫺1500.4
⫺1331.8
⫺1164.7
⫺998.86
⫺834.33
⫺671.06
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
11 099.0
144.16
11 461.0
145.10
11 822.0
146.01
13 601.0
150.20
15 347.0
153.88
17 072.0
157.17
18 784.0
160.15
20 487.0
162.88
22 188.0
165.40
23 889.0
167.75
25 593.0
169.95
29 015.0
173.98
32 461.0
177.61
35 933.0
180.92
39 430.0
183.96
42 952.0
186.78
46 497.0
189.40
50 062.0
191.86
53 647.0
194.18
57 249.0
196.36
60 867.0
198.43
64 501.0
200.39
68 148.0
202.26
200.0 MPa isobar
1404.9
76.473
1418.2
76.622
1515.5
77.691
1612.4
78.733
1708.9
79.749
1805.2
80.741
1901.0
81.710
1996.6
82.655
2091.7
83.580
2186.6
84.483
2281.1
85.366
2375.3
86.231
2469.2
87.076
2562.8
87.904
2656.0
88.715
2748.9
89.510
2841.6
90.288
2933.9
91.051
3025.9
91.799
3117.6
92.533
3209.1
93.253
3300.2
93.960
3391.1
94.653
3481.7
95.334
3572.0
96.003
3662.0
96.661
3751.8
97.306
3841.3
97.941
3930.5
98.565
4019.5
99.179
4108.2
99.782
4196.7
100.38
4416.7
101.82
4635.3
103.21
4852.4
104.54
5068.1
105.83
5282.4
107.07
5495.4
108.27
5707.1
109.43
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
23.30
23.25
23.21
23.10
23.12
23.22
23.39
23.61
23.86
24.11
24.38
24.90
25.39
25.83
26.23
26.58
26.89
27.16
27.40
27.62
27.82
28.01
28.17
36.36
36.16
35.98
35.22
34.69
34.34
34.13
34.03
34.01
34.05
34.12
34.33
34.59
34.85
35.10
35.34
35.55
35.75
35.94
36.10
36.26
36.41
36.55
784.1
781.8
779.8
773.7
772.4
774.3
778.2
783.7
790.1
797.4
805.1
821.8
839.3
857.4
875.6
893.9
912.2
930.3
948.2
965.9
983.4
1000.6
1017.7
35.48
35.45
35.22
35.00
34.78
34.56
34.36
34.15
33.96
33.76
33.58
33.39
33.21
33.04
32.87
32.70
32.54
32.38
32.22
32.07
31.92
31.77
31.63
31.49
31.35
31.22
31.09
30.96
30.84
30.71
30.59
30.47
30.19
29.92
29.66
29.42
29.18
28.96
28.74
48.75
48.72
48.54
48.37
48.19
48.02
47.85
47.68
47.51
47.35
47.18
47.02
46.86
46.70
46.54
46.39
46.24
46.09
45.94
45.79
45.65
45.50
45.36
45.22
45.08
44.95
44.81
44.68
44.55
44.42
44.30
44.17
43.86
43.57
43.28
43.00
42.73
42.47
42.21
1462.1
1461.4
1456.1
1450.9
1445.8
1440.7
1435.7
1430.7
1425.8
1420.9
1416.1
1411.4
1406.6
1402.0
1397.4
1392.8
1388.3
1383.8
1379.4
1375.0
1370.7
1366.4
1362.2
1358.0
1353.9
1349.8
1345.8
1341.8
1337.8
1333.9
1330.0
1326.2
1316.8
1307.7
1298.8
1290.2
1281.9
1273.7
1265.8
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
382
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
190
195
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
123.66
124
126
128
130
132
134
136
138
140
142
144
146
148
150
155
160
165
170
Density
共mol/dm3兲
Internal
energy
共J/mol兲
31.121
30.888
30.660
30.212
29.778
29.357
28.947
28.549
28.163
27.787
27.421
27.065
26.718
26.381
26.052
25.731
25.419
25.114
24.817
24.527
24.245
23.968
23.699
22.441
21.316
20.305
19.391
18.562
17.804
17.111
16.473
15.338
14.359
13.505
12.752
12.083
11.484
10.944
10.455
10.010
9.6027
9.2283
8.8829
⫺509.01
⫺348.14
⫺188.42
127.71
439.64
747.62
1051.9
1352.6
1650.0
1944.3
2235.6
2524.1
2810.0
3093.4
3374.5
3653.4
3930.3
4205.2
4478.3
4749.7
5019.5
5287.8
5554.8
6872.0
8167.3
9449.0
10 723.0
11 995.0
13 269.0
14 545.0
15 828.0
18 412.0
21 027.0
23 671.0
26 345.0
29 045.0
31 770.0
34 517.0
37 284.0
40 069.0
42 870.0
45 688.0
48 519.0
39.920
39.905
39.820
39.736
39.652
39.569
39.486
39.404
39.322
39.241
39.161
39.081
39.002
38.923
38.845
38.651
38.461
38.274
38.089
⫺2818.8
⫺2807.3
⫺2739.8
⫺2672.5
⫺2605.5
⫺2538.6
⫺2471.9
⫺2405.3
⫺2339.0
⫺2272.9
⫺2206.9
⫺2141.1
⫺2075.5
⫺2010.1
⫺1944.8
⫺1782.4
⫺1621.1
⫺1460.8
⫺1301.6
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
5917.5
110.56
6126.8
111.64
6334.8
112.70
6747.6
114.71
7156.0
116.61
7560.4
118.41
7961.0
120.11
8358.0
121.73
8751.5
123.28
9141.9
124.75
9529.3
126.16
9913.7
127.51
10 295.0
128.80
10 675.0
130.05
11 052.0
131.24
11 426.0
132.40
11 798.0
133.51
12 169.0
134.58
12 537.0
135.62
12 904.0
136.62
13 269.0
137.60
13 632.0
138.54
13 994.0
139.46
15 784.0
143.67
17 550.0
147.39
19 299.0
150.73
21 037.0
153.75
22 770.0
156.53
24 502.0
159.10
26 234.0
161.49
27 969.0
163.72
31 452.0
167.83
34 955.0
171.52
38 481.0
174.88
42 029.0
177.97
45 598.0
180.82
49 186.0
183.48
52 791.0
185.97
56 412.0
188.30
60 048.0
190.51
63 698.0
192.60
67 360.0
194.58
71 034.0
196.46
500.0 MPa isobar
9706.4
81.122
9722.5
81.252
9816.7
82.006
9910.6
82.745
10 004.0
83.472
10 098.0
84.185
10 191.0
84.885
10 284.0
85.573
10 376.0
86.249
10 469.0
86.914
10 561.0
87.567
10 653.0
88.210
10 744.0
88.842
10 836.0
89.464
10 927.0
90.075
11 154.0
91.563
11 379.0
92.994
11 603.0
94.372
11 826.0
95.700
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
28.54
28.34
28.16
27.81
27.48
27.19
26.91
26.66
26.43
26.21
26.01
25.83
25.66
25.50
25.36
25.23
25.10
24.99
24.89
24.80
24.71
24.63
24.57
24.32
24.22
24.23
24.32
24.46
24.64
24.84
25.06
25.50
25.92
26.31
26.66
26.97
27.24
27.49
27.71
27.91
28.09
28.26
28.41
41.97
41.73
41.50
41.05
40.64
40.25
39.87
39.52
39.19
38.88
38.59
38.31
38.05
37.80
37.56
37.34
37.13
36.94
36.75
36.58
36.41
36.26
36.12
35.53
35.12
34.86
34.70
34.64
34.63
34.67
34.74
34.93
35.15
35.37
35.59
35.79
35.97
36.13
36.29
36.43
36.56
36.68
36.80
1258.1
1250.7
1243.4
1229.6
1216.5
1204.2
1192.5
1181.6
1171.3
1161.6
1152.5
1143.9
1135.8
1128.2
1121.0
1114.3
1107.9
1101.9
1096.3
1091.0
1086.1
1081.4
1077.0
1058.7
1045.4
1035.9
1029.4
1025.3
1023.1
1022.5
1023.1
1027.4
1034.5
1043.7
1054.4
1066.0
1078.4
1091.3
1104.5
1118.0
1131.6
1145.2
1158.9
36.30
36.27
36.12
35.97
35.82
35.67
35.53
35.39
35.25
35.12
34.98
34.85
34.72
34.59
34.47
34.17
33.87
33.60
33.33
47.19
47.17
47.04
46.90
46.77
46.64
46.51
46.38
46.25
46.13
46.00
45.88
45.75
45.63
45.51
45.21
44.92
44.64
44.37
1860.1
1859.6
1856.8
1853.9
1851.0
1848.2
1845.4
1842.7
1839.9
1837.2
1834.5
1831.8
1829.1
1826.5
1823.9
1817.5
1811.2
1805.0
1799.0
THERMODYNAMIC PROPERTIES OF AIR
383
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
175
180
185
190
195
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
167.86
170
175
180
185
190
195
200
210
220
230
240
250
260
270
280
Density
共mol/dm3兲
Internal
energy
共J/mol兲
37.908
37.729
37.553
37.380
37.209
37.041
36.711
36.391
36.079
35.776
35.480
35.192
34.911
34.636
34.368
34.106
33.850
33.599
33.354
33.114
32.878
32.648
32.421
32.200
31.982
31.769
30.756
29.826
28.965
28.164
27.416
26.714
26.054
25.431
24.283
23.247
22.305
21.443
20.651
19.921
19.243
18.614
18.027
17.478
16.963
16.480
⫺1143.2
⫺985.89
⫺829.45
⫺673.92
⫺519.26
⫺365.46
⫺60.311
241.69
540.72
836.94
1130.5
1421.5
1710.2
1996.6
2280.8
2563.1
2843.4
3122.0
3398.9
3674.2
3948.0
4220.5
4491.6
4761.5
5030.3
5298.0
6623.2
7932.1
9231.2
10 526.0
11 820.0
13 116.0
14 417.0
15 724.0
18 356.0
21 018.0
23 707.0
26 424.0
29 164.0
31 926.0
34 708.0
37 508.0
40 324.0
43 155.0
46 000.0
48 857.0
43.415
43.352
43.208
43.065
42.925
42.786
42.649
42.514
42.249
41.990
41.738
41.493
41.252
41.018
40.789
40.565
⫺736.70
⫺670.08
⫺514.75
⫺360.10
⫺206.12
⫺52.792
99.887
251.93
554.16
853.98
1151.5
1446.8
1740.0
2031.1
2320.3
2607.7
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
12 047.0
96.982
12 267.0
98.221
12 485.0
99.419
12 702.0
100.58
12 918.0
101.70
13 133.0
102.79
13 560.0
104.87
13 981.0
106.83
14 399.0
108.69
14 813.0
110.45
15 223.0
112.12
15 629.0
113.72
16 032.0
115.24
16 432.0
116.69
16 829.0
118.09
17 223.0
119.42
17 615.0
120.70
18 003.0
121.94
18 390.0
123.13
18 774.0
124.27
19 156.0
125.38
19 536.0
126.45
19 913.0
127.49
20 290.0
128.49
20 664.0
129.46
21 037.0
130.41
22 880.0
134.75
24 696.0
138.58
26 494.0
142.00
28 279.0
145.11
30 058.0
147.96
31 833.0
150.59
33 608.0
153.04
35 384.0
155.33
38 947.0
159.53
42 526.0
163.30
46 124.0
166.73
49 741.0
169.87
53 375.0
172.78
57 026.0
175.49
60 691.0
178.02
64 370.0
180.39
68 061.0
182.63
71 763.0
184.74
75 476.0
186.75
79 198.0
188.66
1000.0 MPa isobar
22 297.0
85.397
22 397.0
85.987
22 629.0
87.335
22 860.0
88.639
23 091.0
89.899
23 319.0
91.120
23 547.0
92.303
23 774.0
93.451
24 224.0
95.645
24 669.0
97.718
25 110.0
99.679
25 548.0
101.54
25 981.0
103.31
26 411.0
105.00
26 837.0
106.60
27 260.0
108.14
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
33.07
32.82
32.58
32.35
32.13
31.91
31.51
31.13
30.78
30.45
30.14
29.85
29.58
29.33
29.10
28.88
28.67
28.47
28.29
28.12
27.96
27.82
27.68
27.55
27.43
27.32
26.89
26.61
26.47
26.41
26.43
26.50
26.60
26.72
26.99
27.27
27.54
27.79
28.01
28.21
28.39
28.55
28.70
28.83
28.95
29.07
44.10
43.84
43.58
43.33
43.09
42.86
42.40
41.98
41.57
41.19
40.82
40.47
40.15
39.84
39.54
39.27
39.00
38.75
38.52
38.30
38.09
37.89
37.70
37.52
37.36
37.20
36.56
36.11
35.81
35.63
35.53
35.49
35.51
35.55
35.70
35.89
36.08
36.26
36.43
36.58
36.72
36.85
36.97
37.08
37.18
37.27
1793.1
1787.4
1781.7
1776.2
1770.8
1765.5
1755.2
1745.3
1735.8
1726.7
1718.0
1709.5
1701.4
1693.6
1686.1
1678.8
1671.8
1665.0
1658.5
1652.2
1646.0
1640.1
1634.4
1628.8
1623.4
1618.2
1594.3
1573.6
1555.7
1540.0
1526.5
1514.8
1504.7
1496.1
1482.8
1473.8
1468.3
1465.5
1465.0
1466.3
1469.2
1473.2
1478.2
1484.0
1490.5
1497.6
37.29
37.17
36.90
36.65
36.40
36.15
35.92
35.69
35.25
34.84
34.45
34.08
33.74
33.41
33.10
32.81
46.74
46.63
46.38
46.14
45.90
45.66
45.43
45.20
44.76
44.33
43.92
43.53
43.16
42.80
42.45
42.12
2313.2
2311.1
2306.4
2301.7
2297.0
2292.5
2288.0
2283.6
2275.0
2266.7
2258.6
2250.8
2243.3
2235.9
2228.8
2221.8
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
LEMMON ET AL.
384
TABLE A2. Thermodynamic properties of air—Continued
Density
共mol/dm3兲
Internal
energy
共J/mol兲
290
300
310
320
330
340
350
360
370
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
40.345
40.130
39.920
39.714
39.512
39.314
39.119
38.928
38.741
38.557
38.376
38.198
37.351
36.567
35.836
35.150
34.505
33.895
33.316
32.765
31.736
30.791
29.916
29.101
28.338
27.622
26.946
26.307
25.701
25.125
24.577
24.054
2893.3
3177.3
3459.6
3740.5
4019.9
4297.9
4574.7
4850.3
5124.8
5398.2
5670.7
5942.2
7288.1
8619.7
9942.8
11 262.0
12 581.0
13 902.0
15 228.0
16 559.0
19 238.0
21 944.0
24 676.0
27 431.0
30 207.0
33 003.0
35 816.0
38 644.0
41 486.0
44 341.0
47 208.0
50 085.0
236.19
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
450
500
550
600
650
700
750
800
900
1000
1100
1200
47.967
47.893
47.700
47.512
47.327
47.145
46.968
46.793
46.622
46.454
46.289
46.126
45.967
45.810
45.656
45.504
45.355
45.208
44.506
43.852
43.240
42.664
42.120
41.603
41.111
40.641
39.760
38.945
38.184
37.471
3353.0
3466.7
3764.2
4060.2
4354.8
4648.0
4939.9
5230.5
5519.8
5808.0
6094.9
6380.8
6665.7
6949.6
7232.5
7514.5
7795.7
8076.2
9468.3
10 848.0
12 220.0
13 588.0
14 956.0
16 326.0
17 700.0
19 078.0
21 849.0
24 643.0
27 458.0
30 292.0
Temperature
共K兲
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
27 679.0
109.61
28 096.0
111.03
28 510.0
112.38
28 921.0
113.69
29 329.0
114.94
29 734.0
116.15
30 138.0
117.32
30 539.0
118.45
30 937.0
119.55
31 334.0
120.60
31 729.0
121.63
32 122.0
122.62
34 061.0
127.19
35 967.0
131.21
37 848.0
134.80
39 711.0
138.04
41 562.0
141.00
43 405.0
143.73
45 243.0
146.27
47 079.0
148.64
50 748.0
152.96
54 421.0
156.83
58 103.0
160.34
61 794.0
163.55
65 495.0
166.51
69 206.0
169.26
72 927.0
171.83
76 656.0
174.24
80 395.0
176.50
84 141.0
178.65
87 896.0
180.68
91 658.0
182.60
2000.0 MPa isobar
45 048.0
90.033
45 227.0
90.783
45 693.0
92.685
46 155.0
94.499
46 614.0
96.232
47 070.0
97.890
47 522.0
99.477
47 972.0
101.00
48 418.0
102.46
48 862.0
103.87
49 302.0
105.23
49 740.0
106.54
50 175.0
107.80
50 608.0
109.02
51 038.0
110.20
51 466.0
111.34
51 892.0
112.44
52 316.0
113.52
54 406.0
118.44
56 455.0
122.76
58 473.0
126.61
60 466.0
130.07
62 440.0
133.23
64 400.0
136.14
66 349.0
138.83
68 289.0
141.33
72 151.0
145.88
75 998.0
149.94
79 835.0
153.59
83 666.0
156.93
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
32.53
32.27
32.02
31.79
31.57
31.36
31.17
30.98
30.81
30.65
30.49
30.35
29.75
29.33
29.06
28.88
28.79
28.75
28.76
28.80
28.92
29.07
29.22
29.36
29.49
29.60
29.70
29.79
29.88
29.95
30.02
30.08
41.81
41.51
41.22
40.95
40.69
40.44
40.21
39.98
39.77
39.57
39.38
39.19
38.42
37.84
37.42
37.13
36.93
36.80
36.73
36.69
36.70
36.77
36.86
36.96
37.06
37.16
37.25
37.34
37.42
37.51
37.58
37.66
2215.1
2208.5
2202.1
2195.9
2189.8
2183.9
2178.1
2172.4
2166.9
2161.5
2156.2
2151.1
2126.8
2104.7
2084.6
2066.2
2049.3
2033.9
2019.9
2007.0
1984.7
1966.3
1951.2
1939.0
1929.2
1921.4
1915.5
1911.0
1908.0
1906.1
1905.2
1905.3
38.84
38.69
38.33
37.98
37.64
37.32
37.01
36.72
36.44
36.17
35.92
35.68
35.44
35.22
35.02
34.82
34.63
34.45
33.68
33.11
32.68
32.37
32.15
32.00
31.90
31.84
31.78
31.77
31.79
31.80
46.92
46.79
46.43
46.08
45.74
45.41
45.09
44.78
44.49
44.20
43.92
43.66
43.40
43.15
42.92
42.69
42.48
42.27
41.36
40.65
40.09
39.66
39.32
39.07
38.88
38.73
38.53
38.41
38.34
38.29
2923.5
2920.7
2913.6
2906.7
2899.8
2893.2
2886.7
2880.3
2874.1
2867.9
2861.9
2856.1
2850.3
2844.6
2839.0
2833.6
2828.2
2822.9
2797.6
2774.1
2752.1
2731.6
2712.4
2694.4
2677.5
2661.8
2633.2
2608.2
2586.1
2566.7
THERMODYNAMIC PROPERTIES OF AIR
385
TABLE A2. Thermodynamic properties of air—Continued
Temperature
共K兲
1300
1400
1500
1600
1700
1800
1900
2000
Density
共mol/dm3兲
Internal
energy
共J/mol兲
Enthalpy
共J/mol兲
Entropy
J/共mol-K兲
cv
J/共mol-K兲
cp
J/共mol-K兲
Speed
of sound
共m/s兲
36.799
36.162
35.556
34.978
34.425
33.894
33.384
32.893
33 143.0
36 010.0
38 889.0
41 780.0
44 680.0
475 90.0
505 07.0
534 33.0
87 493.0
91 317.0
95 138.0
98 958.0
102 780.0
106 600.0
110 420.0
114 240.0
159.99
162.82
165.46
167.93
170.24
172.42
174.49
176.45
31.82
31.83
31.84
31.85
31.85
31.85
31.86
31.86
38.25
38.22
38.21
38.20
38.19
38.19
38.20
38.21
2549.5
2534.2
2520.6
2508.5
2497.8
2488.2
2479.6
2472.1
J. Phys. Chem. Ref. Data, Vol. 29, No. 3, 2000