Carbon Dioxide1412.14 Carbon Dioxide
Equations for thermodynamic properties have been cited from the IUPAC Table[1], those for transport properties from Altunin et al.[2][3], and one for surface tension from Miller et al.[4].

2.14.1 Temperature Scale
International practical temperature scale 1968 (IPTS-1968)

2.14.2 The Names of Substance, Library File and Single Shot Program
Name of Substance:
Library File for UNIX:
Library File for DOS,Windows95/NT:
Single Shot Program for UNIX:
Single Shot Program for DOS,Windows95/NT:

Carbon Dioxide
libjco2.a
JCO2.LIB
co2-ssCO2–SS.EXE

2.14.3 Important Constants and Others
Molecular Formula:
Relative Molecular Mass:
Gas Constant:CO2
44.009188.92 J/(kg·K)

Critical Constants:
Critical Pressure:
Critical Temperature:
Critical Speciﬁc Volume:7.3825×10 6Pa (73.825 bar)304.21 K (31.06 ◦C)
2.1459×10 −3m3 /kg

Triple Point:
Pressure:
Temperature:

0.5185×10 6Pa (5.185 bar)
216.58 K (−56.57◦C)

Reference State:
At the state of the perfect crystal at 0 K, 0 J/(kg·K) and 0 J/kg are assigned to the speciﬁc entropy and thespeciﬁc enthalpy, respectively.

2.14.4 Formula
Equation of State:
Equation (14) in a function form of P = P (ρ, T ) in reference [1]. Here P =pressure, ρ=density and T =temperature.

Vapor Pressure:
Equation (3) in reference [1].
Properties at Vapor-Liquid Equilibrium:
Equations (4) and (5) for speciﬁc volume, equation (16) for speciﬁc entropy, and equation (18) for speciﬁc
enthalpy, and equations (20) and (22) for isobaric speciﬁc heat, respectively. All of these have been cited fromreference [1].
Pressure and Temperature on Melting Line:
Equation (2) in reference [1].
Transport Properties:

142

P-PROPATH: Pure Substances and Mixtures with Fixed Composition

Equations (7) and (9) in reference [2] for viscosity. Equations (5) and (6) in reference [3] for thermal conductivity.
The Other Properties:
Surface tension from reference [4].

References[1] S.Angus, B.Armstrong and K.M.de Reuck, International Thermodynamic Table of the Fluid State-3 Carbon
Dioxide, IUPAC, vol.3, (1976).
[2] V.V.Altunin and M.A.Sakhabetdinov, Teploenergetika, 19–8, (1972), p.85.
[3] V.V.Altunin and M.A.Sakhabetdinov, Teploenergetika, 20–5, (1973), p.85.
[4] J.W.Miller Jr. and C.L.Yaws, Chem. Eng.,83–23, (1976), p.127.

Carbon Dioxide

143
Table II–2.14–1 Carbon Dioxide Function

No.
1
94

Name of
Function
AIPPT(P,T)
AJTPT(P,T)

Function and Argument(s)AJTPT: Joule-Thomson Coeﬃcient [K/Pa]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

Range of Argument(s)10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦ C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦ C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦ C]

8A
8B
82

AKPD(P)AKPDD(P)AKPT(P,T)

AKPT: Aidabatic Exponent [–]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦ C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦ C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦ C]

8C
8D
2

AKTD(T)
AKTDD(T)
ALAPP(P)3

ALAPT(T)4

ALHP(P)

5

ALHT(T)

6

ALMPD(P)7

ALMPDD(P)

ALAPP: Laplace Coeﬃcient [m]P∗: Pressure [Pa], [bar]
ALAPT: Laplace Coeﬃcient [m]T∗: Temperature [K], [◦ C]
ALHP: Latent Heat of Vaporization [J/kg]
P∗: Pressure [Pa], [bar]ALHT: Latent Heat of Vaporization [J/kg]
T∗: Temperature [K], [◦ C]
ALMPD: Thermal Conductivity of Saturated
Liquid [W/(m·K)]
P∗: Pressure [Pa], [bar]
ALMPDD: Thermal Conductivity of Saturated
Vapor [W/(m·K)]
T∗: Temperature [K], [◦ C]

0.5185×106 ≤P<7.3825×106 [Pa]5.185≤P<73.825 [bar]216.58≤T<304.21 [K]−56.57≤T<31.06 [◦ C]
0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]
1.286×106 ≤P<7.3825×106 [Pa]12.86≤P<73.825 [bar]0.5185×106 ≤P<7.3825×106 [Pa]5.185≤P<73.825 [bar]144

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.14–1 Carbon Dioxide Function (cont’d)

No.
8

Name of
Function
ALMPT(P,T)

9

ALMTD(T)10

ALMTDD(T)11

AMUPD(P)12

AMUPDD(P)13

AMUPT(P,T)

14

AMUTD(T)15

AMUTDD(T)Function and Argument(s)ALMPT: Thermal Conductivity [W/(m·K)]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

ALMTD: Thermal Conductivity of Saturated
Liquid [W/(m·K)]
T∗: Temperature [K], [◦C]
ALMTDD: Thermal Conductivity of Saturated
Vapor [W/(m·K)]
T∗: Temperature [K], [◦C]
AMUPD: Coeﬃcient of Viscosity of Saturated
Liquid [Pa·s]
P∗: Pressure [Pa], [bar]
AMUPDD: Coeﬃcient of Viscosity of Saturated
Vapor [Pa·s]
P∗: Pressure [Pa], [bar]
AMUPT: Coeﬃcient of Viscosity [Pa·s]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

AMUTD: Coeﬃcient of Viscosity of Saturated
Liquid [Pa·s]
T∗: Temperature [K], [◦C]
AMUTDD: Coeﬃcient of Viscosity of Saturated
Vapor [Pa·s]
T∗: Temperature [K], [◦C]

Range of Argument(s)10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤PST(240K) [Pa]TSP(P)≤T≤1100 [K]
PST(240K)<P≤60×106
240≤T≤1100 [K]
60×106 <P<100×106 [Pa]240≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦C]
5.185≤P≤PST(−33.15◦ C) [bar]TSP(P)≤T≤826.85 [◦C]
PST(−33.15◦ C)<P≤600 [bar]−33.15≤T≤826.85 [◦C]
600<P<1000 [bar]−33.15≤T≤426.85 [◦C]
240≤T<304.21 [K]−33.15≤T<31.06 [◦C]
216.58≤T<304.21 [K]−56.57≤T<31.06 [◦C]
1.286×106 ≤P≤7.3825×106 [Pa]12.86≤P≤73.825 [bar]0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤PST(240K) [Pa]TSP(P)≤T≤1100 [K]
PST(240K)<P≤60×106
240≤T≤1100 [K]
60×106 <P<100×106 [Pa]240≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦C]
5.185≤P≤PST(−33.15◦ C) [bar]TSP(P)≤T≤826.85 [◦C]
PST(−33.15◦ C)<P≤600 [bar]−33.15≤T≤826.85 [◦C]
600<P<1000 [bar]−33.15≤T≤426.85 [◦C]
240≤T≤304.21 [K]−33.15≤T≤31.06 [◦C]
216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦C]

Carbon Dioxide

145
Table II–2.14–1 Carbon Dioxide Function (cont’d)

No.
92

90

91

93

Name of
Function
BPPT(P,T)

BSPT(P,T)

BTPT(P,T)

BVPT(P,T)

16

CPPD(P)

17

CPPDD(P)Function and Argument(s)BPPT: Volumetric Coeﬃcient of Expansion[1/K]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

BSPT: Isentropic Compressibility [1/Pa]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

BTPT: Isothermal Compressibility [1/Pa]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

BVPT: Pressure Coeﬃcient [1/K]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

CPPD: Isobaric Speciﬁc Heat of Saturated
Liquid [J/(kg·K)]
P∗: Pressure [Pa], [bar]
CPPDD: Isobaric Speciﬁc Heat of Saturated
Vapor [J/(kg·K)]
P∗: Pressure [Pa], [bar]Range of Argument(s)10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦ C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦C]
10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦ C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦C]
10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦ C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦C]
10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦ C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦C]
0.5185×106 ≤P<7.3825×106 [Pa]5.185≤P<73.825 [bar]0.5185×106 ≤P<7.3825×106 [Pa]5.185≤P<73.825 [bar]146

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.14–1 Carbon Dioxide Function (cont’d)

No.
18

Name of
Function
CPPT(P,T)

19

CPTD(T)

20

CPTDD(T)21

CRP(‘A’)

7A
76

CVPD(P)
CVPDD(P)77

CVPT(P,T)

Function and Argument(s)Range of Argument(s)CPPT: Isobaric Speciﬁc Heat [J/(kg·K)]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]

CPTD: Isobaric Speciﬁc Heat of Saturated
Liquid [J/(kg·K)]
T∗: Temperature [K], [◦ C]
CPTDD: Isobaric Speciﬁc Heat of Saturated
Vapor [J/(kg·K)]
T∗: Temperature [K], [◦ C]
CRP: Critical Constants
H: ‘A’=‘H’: 636.64×103 [J/kg] Speciﬁc EnthalpyP∗: ‘A’=‘P’: 7.3825×106 [Pa], 73.825 [bar] Pressure
S: ‘A’=‘S’: 3.5579×103 [J/(kg·K)] Speciﬁc EntropyT∗: ‘A’=‘T’: 304.21 [K], 31.06 [◦C] Temperature
V: ‘A’=‘V’: 2.1459×10−3 [m3 /kg] Speciﬁc Volume
CVPDD: Isochoric Speciﬁc Heat of Saturated
Vapor [J/(kg·K)]
P∗: Pressure [Pa], [bar]CVPT: Isochoric Speciﬁc Heat [J/(kg·K)]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦ C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦ C]
216.58≤T<304.21 [K]−56.57≤T<31.06 [◦ C]
216.58≤T<304.21 [K]−56.57≤T<31.06 [◦ C]
one of ‘H’, ‘P’, ‘S’, ‘T’ and ‘V’

0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦ C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦ C]

7B
78

CVTD(T)
CVTDD(T)

2A
2B
22
2C
2D
89

EPSPD(P)EPSPDD(P)EPSPT(P,T)
EPSTD(T)EPSTDD(T)FC(‘A’)9A
96

GAMPD(P)GAMPDD(P)

CVTDD: Isochoric Speciﬁc Heat of Saturated
Vapor [J/(kg·K)]
T∗: Temperature [K], [◦ C]

216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]

FC: Fundamental Constants
M: ‘A’=‘M’: 44.009 Relative Molecular Mass
R: ‘A’=‘R’: 188.92 [J/(kg·K)] Gas Constant

one of ‘M’ and ‘R’

GAMPDD: Ratio of Speciﬁc Heats of Saturated
Vapor [–]P∗: Pressure [Pa], [bar]0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]Carbon Dioxide

147
Table II–2.14–1 Carbon Dioxide Function (cont’d)

No.
95

Name of
Function
GAMPT(P,T)

Function and Argument(s)GAMPT: Ratio of Speciﬁc Heats [–]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

Range of Argument(s)10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦ C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦ C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦ C]

9B
97

GAMTD(T)GAMTDD(T)23

HPD(P)

24

HPDD(P)71

HPS(P,S)

25

HPT(P,T)

26

HPX(P,X)

27

HTD(T)GAMTDD: Ratio of Speciﬁc Heats of Saturated
Vapor [–]T∗: Temperature [K], [◦C]
HPD: Speciﬁc Enthalpy of Saturated Liquid [J/kg]
P∗: Pressure [Pa], [bar]HPDD: Speciﬁc Enthalpy of Saturated Vapor [J/kg]
P∗: Pressure [Pa], [bar]HPS: Speciﬁc Enthalpy [J/kg]
P∗: Pressure [Pa], [bar]S: Speciﬁc Entropy [J/(kg·K)]

HPT: Speciﬁc Enthalpy [J/kg]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

HPX: Speciﬁc Enthalpy of Mixture [J/kg]
P∗: Pressure [Pa], [bar]
X: Dryness Fraction [–]HTD: Speciﬁc Enthalpy of Saturated Liquid[J/kg]T∗: Temperature [K], [◦C]

216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]
0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]10000≤P<0.5185×106 [Pa]SPT(P,220K)≤S≤
SPT(P,1100K) [J/(kg·K)]
0.5185×106 ≤P≤60×106 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,1100K) [J/(kg·K)]
60×106 <P<100×106 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,700K) [J/(kg·K)]
0.1≤P<5.185 [bar]SPT(P,−53.15◦ C)≤S≤
SPT(P,826.85◦ C) [J/(kg·K)]
5.185≤P≤600 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,826.85◦ C) [J/(kg·K)]
600<P<1000 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,426.85◦ C) [J/(kg·K)]
10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦ C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦ C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦ C]
0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]0≤X≤1.0 [–]216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]

148

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.14–1 Carbon Dioxide Function (cont’d)No.
28

Name of
Function
HTDD(T)

29

HTX(T,X)

84

IDENTF(‘A’)

66
68

PLDT(T)
PMLT(T)85

PRPD(P)86

PRPDD(P)81

PRPT(P,T)

87

PRTD(T)

88

PRTDD(T)99
30

PSBT(P)
PST(T)72
73
31

PSTD(P)
PSTDD(P)SIGP(P)

32

SIGT(T)

33

SPD(P)34

SPDD(P)

Function and Argument(s)Range of Argument(s)HTDD: Speciﬁc Enthalpy of Saturated Vapor[J/kg]T∗: Temperature [K], [◦C]
HTX: Speciﬁc Enthalpy of Mixture [J/kg]
T∗: Temperature [K], [◦C]
X: Dryness Fraction [–]IDENTF: CHARACTER TYPE FUNCTION
for Package Identiﬁcation (Length 20)
C: ‘A’=‘C’: ‘CO2’ Molecular Formula
S: ‘A’=‘S’: ‘CARBON DIOXIDE’ Name of Substance
V: ‘A’=‘V’: ‘10.1’ Version Number

216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦C]

PMLT∗: Pressure on Melting Curve [Pa], [bar]T∗: Temperature [K], [◦C]
PRPD: Prandtl Number of Saturated Liquid [–]P∗: Pressure [Pa], [bar]
PRPDD: Prandtl Number of Saturated Vapor [–]P∗: Pressure [Pa], [bar]
PRPT: Prandtl Number [–]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

216.58≤T≤237 [K]−56.57≤T≤−36.15 [◦C]
1.286×106 ≤P<7.3825×106 [Pa]12.86≤P<73.825 [bar]0.5185×106 ≤P<7.3825×106 [Pa]5.185≤P<73.825 [bar]10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤PST(240K) [Pa]TSP(P)≤T≤1100 [K]
PST(240K)<P≤60×106
240≤T≤1100 [K]
60×106 <P<100×106 [Pa]240≤T≤700 [K]

216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦C]
0≤X≤1.0 [–]one of ‘C’, ‘S’ and ‘V’

PRTD: Prandtl Number of Saturated Liquid [–]T∗: Temperature [K], [◦C]
PRTDD: Prandtl Number of Saturated Vapor [–]T∗: Temperature [K], [◦C]

0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦ C]
5.185≤P≤PST(−33.15◦ C) [bar]TSP(P)≤T≤826.85 [◦ C]
PST(−33.15◦ C)<P≤600 [bar]−33.15≤T≤826.85 [◦ C]
600<P<1000 [bar]−33.15≤T≤426.85 [◦ C]
240≤T<304.21 [K]−33.15≤T<31.06 [◦C]
216.58≤T<304.21 [K]−56.57≤T<31.06 [◦C]

PST∗: Saturation Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦C]

SIGP: Surface Tension [N/m]P∗: Pressure [Pa], [bar]
SIGT: Surface Tension [N/m]T∗: Temperature [K], [◦C]
SPD: Speciﬁc Entropy of Saturated Liquid[J/(kg·K)]
P∗: Pressure [Pa], [bar]SPDD: Speciﬁc Entropy of Saturated Vapor[J/(kg·K)]
P∗: Pressure [Pa], [bar]0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦C]
0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]Carbon Dioxide

149
Table II–2.14–1 Carbon Dioxide Function (cont’d)

No.
35

Name of
Function
SPT(P,T)36

SPX(P,X)

37

STD(T)38

STDD(T)

39

STX(T,X)

67
69

TLDP(P)
TMLP(P)64

TPH(P,H)

Function and Argument(s)SPT: Speciﬁc Entropy [J/(kg·K)]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

SPX: Speciﬁc Entropy of Mixture [J/(kg·K)]
P∗: Pressure [Pa], [bar]
X: Dryness Fraction [–]STD: Speciﬁc Entropy of Saturated Liquid[J/(kg·K)]
T∗: Temperature [K], [◦ C]
STDD: Speciﬁc Entropy of Saturated Vapor[J/(kg·K)]
T∗: Temperature [K], [◦ C]
STX: Speciﬁc Entropy of Mixture [J/(kg·K)]
T∗: Temperature [K], [◦ C]
X: Dryness Fraction [–]TMLP∗: Temperature on Melting Curve[K], [◦C]P∗: Pressure [Pa], [ bar]
TPH∗: Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]H: Speciﬁc Enthalpy [J/kg]

Range of Argument(s)10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦ C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦ C]
0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]0≤X≤1.0 [–]216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]
216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]
216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]
0≤X≤1.0 [–]0.5185×106 ≤P≤100×106 [Pa]5.185≤P≤1000 [bar]10000≤P<0.5185×106 [Pa]
HPT(P,220K)≤H≤
HPT(P,1100K) [J/kg]
0.5185×106 ≤P≤60×106 [Pa]
HPT(P,TMLP(P))≤H≤
HPT(P,1100K) [J/kg]
60×106 <P<100×106 [Pa]
HPT(P,TMLP(P))≤H≤
HPT(P,700K) [J/kg]
0.1≤P<5.185 [bar]HPT(P,−53.15◦ C)≤H≤
HPT(P,826.85◦C) [J/kg]
5.185≤P≤600 [bar]HPT(P,TMLP(P))≤H≤
HPT(P,826.85◦C) [J/kg]
600<P<1000 [bar]HPT(P,TMLP(P))≤H≤
HPT(P,426.85◦C) [J/kg]

6H

TPH2(P,H)

150

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.14–1 Carbon Dioxide Function (cont’d)

No.
65

Name of
Function
TPS(P,S)

Function and Argument(s)TPS∗: Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]S: Speciﬁc Entropy [J/(kg·K)]

Range of Argument(s)10000≤P<0.5185×106 [Pa]SPT(P,220K)≤S≤
SPT(P,1100K) [J/(kg·K)]
0.5185×106 ≤P≤60×106 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,1100K) [J/(kg·K)]
60×106 <P<100×106 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,700K) [J/(kg·K)]
0.1≤P<5.185 [bar]SPT(P,−53.15◦ C)≤S≤
SPT(P,826.85◦ C) [J/(kg·K)]
5.185≤P≤600 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,826.85◦ C) [J/(kg·K)]
600<P<1000 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,426.85◦ C) [J/(kg·K)]

6S
98

TPS2(P,S)TPSEUP(P)70

TPV(P,V)41

TRPL(‘A’)

100
40

TSBP(P)
TSP(P)

74
75
42

TSPD(P)TSPDD(P)UPD(P)43

UPDD(P)TPSEUP: Pseudo Boiling Point [K], [◦ C]
P∗: Pressure [Pa], [bar]TPV∗: Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]V: Speciﬁc Volume [m3 /kg]

TRPL∗: Properties at Triple PointP∗: ‘A’=‘P’: 0.5185×106 [Pa], 5.185 [bar]PressureT∗: ‘A’=‘T’: 216.58 [K], −56.57 [◦C]
Temperature

7.3825×106 <P≤30×106 [Pa]73.825<P≤300 [bar]10000≤P<0.5185×106 [Pa]VPT(P,220K)≤V≤
VPT(P,1100K) [m3 /kg]
0.5185×106 ≤P≤60×106 [Pa]VPT(P,TMLP(P))≤V≤
VPT(P,1100K) [m3 /kg]
60×106 <P<100×106 [Pa]VPT(P,TMLP(P))≤V≤
VPT(P,700K) [m3 /kg]
0.1≤P<5.185 [bar]VPT(P,−53.15◦C)≤V≤
VPT(P,826.85◦ C) [m3 /kg]
5.185≤P≤600 [bar]VPT(P,TMLP(P))≤V≤
VPT(P,826.85◦ C) [m3 /kg]
600<P<1000 [bar]VPT(P,TMLP(P))≤V≤
VPT(P,426.85◦ C) [m3 /kg]
one of ‘P’ and ‘T’

TSP∗: Saturation Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]UPD: Speciﬁc Internal Energy of Saturated
Liquid [J/kg]
P∗: Pressure [Pa], [bar]UPDD: Speciﬁc Internal Energy of Saturated
Vapor [J/kg]
P∗: Pressure [Pa], [bar]0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]Carbon Dioxide

151
Table II–2.14–1 Carbon Dioxide Function (cont’d)

No.
79

44

Name of
Function
UPS(P,S)

UPT(P,T)45

UPX(P,X)

46

UTD(T)

47

UTDD(T)

48

UTX(T,X)

49

VPD(P)50

VPDD(P)

Function and Argument(s)UPS: Speciﬁc Internal Energy [J/kg]
P∗: Pressure [Pa], [bar]S: Speciﬁc Entropy [J/(kg·K)]

UPT: Speciﬁc Internal Energy [J/kg]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

UPX: Speciﬁc Internal Energy of Mixture [J/kg]
P∗: Pressure [Pa], [bar]
X: Dryness Fraction [–]UTD: Speciﬁc Internal Energy of Saturated
Liquid [J/kg]
T∗: Temperature [K], [◦ C]
UTDD: Speciﬁc Internal Energy of Saturated
Vapor [J/kg]
T∗: Temperature [K], [◦ C]
UTX: Speciﬁc Internal Energy of Mixture [J/kg]
T∗: Temperature [K], [◦ C]
X: Dryness Fraction [–]VPD: Speciﬁc Volume of Saturated Liquid [m3 /kg]P∗: Pressure [Pa], [bar]VPDD: Speciﬁc Volume of Saturated Vapor [m3 /kg]P∗: Pressure [Pa], [bar]Range of Argument(s)10000≤P<0.5185×106 [Pa]SPT(P,220K)≤S≤
SPT(P,1100K) [J/(kg·K)]
0.5185×106 ≤P≤60×106 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,1100K) [J/(kg·K)]
60×106 <P<100×106 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,700K) [J/(kg·K)]
0.1≤P<5.185 [bar]SPT(P,−53.15◦ C)≤S≤
SPT(P,826.85◦ C) [J/(kg·K)]
5.185≤P≤600 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,826.85◦ C) [J/(kg·K)]
600<P<1000 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,426.85◦ C) [J/(kg·K)]
10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦ C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦ C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦ C]
0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]0≤X≤1.0 [–]216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]
216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]
216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]
0≤X≤1.0 [–]0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]152

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.14–1 Carbon Dioxide Function (cont’d)

No.
80

51

Name of
Function
VPS(P,S)

VPT(P,T)52

VPX(P,X)

53

VTD(T)54

VTDD(T)

55

VTX(T,X)

8E
8F
83

WPD(P)WPDD(P)
WPT(P,T)

Function and Argument(s)VPS: Speciﬁc Volume [m3 /kg]P∗: Pressure [Pa], [bar]S: Speciﬁc Entropy [J/(kg·K)]

VPT: Speciﬁc Volume [m3 /kg]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

VPX: Speciﬁc Volume of Mixture [m3 /kg]P∗: Pressure [Pa], [bar]
X: Dryness Fraction [–]VTD: Speciﬁc Volume of Saturated Liquid [m3 /kg]
T∗: Temperature [K], [◦ C]
VTDD: Speciﬁc Volume of Saturated Vapor [m3 /kg]
T∗: Temperature [K], [◦ C]
VTX: Speciﬁc Volume of Mixture [m3 /kg]
T∗: Temperature [K], [◦ C]
X: Dryness Fraction [–]WPT: Velocity of Sound [m/s]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

Range of Argument(s)10000≤P<0.5185×106 [Pa]SPT(P,220K)≤S≤
SPT(P,1100K) [J/(kg·K)]
0.5185×106 ≤P≤60×106 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,1100K) [J/(kg·K)]
60×106 <P<100×106 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,700K) [J/(kg·K)]
0.1≤P<5.185 [bar]SPT(P,−53.15◦ C)≤S≤
SPT(P,826.85◦ C) [J/(kg·K)]
5.185≤P≤600 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,826.85◦ C) [J/(kg·K)]
600<P<1000 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,426.85◦ C) [J/(kg·K)]
10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦ C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦ C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦ C]
0.5185×106 ≤P≤7.3825×106 [Pa]5.185≤P≤73.825 [bar]0≤X≤1.0 [–]216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]
216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]
216.58≤T≤304.21 [K]−56.57≤T≤31.06 [◦ C]
0≤X≤1.0 [–]10000≤P<0.5185×106 [Pa]220≤T≤1100 [K]
0.5185×106 ≤P≤60×106 [Pa]TMLP(P)≤T≤1100 [K]
60×106 <P<100×106 [Pa]TMLP(P)≤T≤700 [K]
0.1≤P<5.185 [bar]−53.15≤T≤826.85 [◦ C]
5.185≤P≤600 [bar]TMLP(P)≤T≤826.85 [◦ C]
600<P<1000 [bar]TMLP(P)≤T≤426.85 [◦ C]

8G
8H

WTD(T)WTDD(T)

Carbon Dioxide

153
Table II–2.14–1 Carbon Dioxide Function (cont’d)No.
56

Name of
Function
XPH(P,H)57

XPS(P,S)58

XPU(P,U)59

XPV(P,V)60

XTH(T,H)

61

XTS(T,S)62

XTU(T,U)63

XTV(T,V)

Function and Argument(s)Range of Argument(s)XPH: Dryness Fraction [–]P∗: Pressure [Pa], [bar]H: Speciﬁc Enthalpy of Mixture [J/kg]
XPS: Dryness Fraction [–]P∗: Pressure [Pa], [bar]S: Speciﬁc Entropy of Mixture [J/(kg·K)]
XPU: Dryness Fraction [–]P∗: Pressure [Pa], [bar]U: Speciﬁc Internal Energy of Mixture [J/kg]
XPV: Dryness Fraction [–]P∗: Pressure [Pa], [bar]V: Speciﬁc Volume of Mixture [m3 /kg]
XTH: Dryness Fraction [–]T∗: Temperature [K], [◦ C]
H: Speciﬁc Enthalpy of Mixture [J/kg]
XTS: Dryness Fraction [–]T∗: Temperature [K], [◦ C]
S: Speciﬁc Entropy of Mixture [J/(kg·K)]
XTU: Dryness Fraction [–]T∗: Temperature [K], [◦ C]
U: Speciﬁc Internal Energy of Mixture [J/kg]
XTV: Dryness Fraction [–]T∗: Temperature [K], [◦ C]
V: Speciﬁc Volume of Mixture [m3 /kg]

0.5185×106 ≤P<7.3825×106 [Pa]5.185≤P<73.825 [bar]HPD(P)≤H≤HPDD(P) [J/kg]
0.5185×106 ≤P<7.3825×106 [Pa]5.185≤P<73.825 [bar]SPD(P)≤S≤SPDD(P) [J/(kg·K)]
0.5185×106 ≤P<7.3825×106 [Pa]5.185≤P<73.825 [bar]UPD(P)≤U≤UPDD(P) [J/kg]
0.5185×106 ≤P<7.3825×106 [Pa]5.185≤P<73.825 [bar]VPD(P)≤V≤VPDD(P) [m3 /kg]
216.58≤T<304.21 [K]−56.57≤T<31.06 [◦ C]
HTD(T)≤H≤HTDD(T) [J/kg]
216.58≤T<304.21 [K]−56.57≤T<31.06 [◦ C]
STD(T)≤S≤STDD(T) [J/(kg·K)]
216.58≤T<304.21 [K]−56.57≤T<31.06 [◦ C]
UTD(T)≤U≤UTDD(T) [J/kg]
216.58≤T<304.21 [K]−56.57≤T<31.06 [◦ C]
VTD(T)≤V≤VTDD(T) [m3 /kg]