168

P-PROPATH: Pure Substances and Mixtures with Fixed Composition

2.17 Water (IAPS 1984 Formulation for Scientific andGeneral Use)All equations have been cited from NBS/NRC Steam Tables[1].

2.17.1 Temperature Scale
International temperature scale 1990 (ITS-1990)

2.17.2 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:

Water (IAPS 1984)
libjhgk.a
JHGK.LIB
hgk-ssHGK–SS.EXE

2.17.3 Important Constants and Others
Molecular Formula:
Relative Molecular Mass:
Gas Constant:

H2 O
18.0152
461.52 J/(kg·K)

Critical Constants:
Critical Pressure:
Critical Temperature:
Critical Speciﬁc Volume:

22.055×10 6Pa (220.55 bar)647.126 K (373.976 ◦ C)
3.1056×10 −3m3 /kg

Triple Point:
Pressure:
Temperature:

611.731 Pa (6.11731×10 −3bar)
273.16 K (0.01 ◦ C)

Reference State:
For the liquid state at the triple point, 0 J/(kg·K) and 0 J/kg are assigned to the speciﬁc entropy and thespeciﬁc internal energy of saturated liquid, respectively.

2.17.4 Formula
Equation of State:
Equations (A.1)-(A.6) in a function form of A = A(ρ, T ) in reference [1]. Here A=speciﬁc helmholtz function,
ρ=density and T =Temperature. However, j=0,1,3,5 in equation (A.3) has been corrected to j=0,3,5.
Vapor Pressure:
Equations (A.1)-(A.6) for speciﬁc Helmholtz function and equation (A.7) for the Gibbs condition for phaseequlibrium.
Properties at Vapor-Liquid Equilibrium:
Equations (A.1)-(A.6) and equation (A.7) in reference [1] for speciﬁc volume. Equations as functions of density
and temperature, which have been derived directly by partial diﬀerentiation of the speciﬁc Helmholtz function,
equations (A.1)-(A.6), for speciﬁc entropy, speciﬁc enthalpy and isobaric speciﬁc heat, respectively.
Transport Properties:
Viscosity and thermal conductivity from equations (C.1) and (C.2) in reference [1], respectively. However,Water (IAPS 1984 Formulation for Scientific and General Use)169

exp(−A((T ∗ /T ) − 1)2 − B((ρ/ρ∗ ) − 1)4 )in equation (C.2) has been corrected toexp(−A((T/T ∗ ) − 1)2 − B((ρ/ρ∗ ) − 1)4 )Further the values of a3 =0.0036744 in Table C.1 and b14 = −0.0273093 in Table C.2 have been corrected as
a3 =−0.0036744 and b14 =−0.0253093, respectively.
The Other Properties:
Static dielectric constant and surface tension from equations (C.4) and (C.5).

References[1] L.Haar, J.S.Gallagher and G.S.Kell, NBS/NRC Steam Tables, Hemisphere,N.Y., (1984).

170

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.17–1

No.
1
94

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

Water(IAPS 1984) Function

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

Range of Argument(s)273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦ C]
6.11731×10−3 ≤P≤15000 [bar]

8A
8B
82

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

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

273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦ C]
6.11731×10−3 ≤P≤15000 [bar]

8C
8D
2

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

ALAPT(T)4

ALHP(P)

5

ALHT(T)

6

ALMPD(P)7

ALMPDD(P)8

ALMPT(P,T)

9

ALMTD(T)10

ALMTDD(T)11

AMUPD(P)12

AMUPDD(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]
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]611.731≤P<22.055×106 [Pa]6.11731×10−3 ≤P<220.55 [bar]273.16≤T<647.126 [K]0.01≤T<373.976 [◦ C]
611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦ C]
611.731≤P<22.055×106 [Pa]6.11731×10−3 ≤P<220.55 [bar]611.731≤P<22.055×106 [Pa]6.11731×10−3 ≤P<220.55 [bar]611.731≤P≤100×106 [Pa]273.15≤T≤1073.15 [K]
6.11731×10−3 ≤P≤1000 [bar]0≤T≤800 [◦C]
273.16≤T<647.126 [K]0.01≤T<373.976 [◦ C]
273.16≤T<647.126 [K]0.01≤T<373.976 [◦ C]
611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]Water (IAPS 1984 Formulation for Scientific and General Use)
Table II–2.17–1

No.
13

Name of
Function
AMUPT(P,T)

14

AMUTD(T)15

AMUTDD(T)92

BPPT(P,T)

90

91

93

16

BSPT(P,T)

BTPT(P,T)

BVPT(P,T)

CPPD(P)

171

Water(IAPS 1984) Function (cont’d)

Function and Argument(s)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 Saturated ofVapor [Pa·s]
T∗: Temperature [K], [◦C]
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]Range of Argument(s)611.731≤P≤100×106 [Pa]273.15≤T≤1073.15 [K]
6.11731×10−3 ≤P≤1000 [bar]0≤T≤800 [◦ C]
273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦C]
273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦C]
273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦ C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦ C]
6.11731×10−3 ≤P≤15000 [bar]273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦ C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦ C]
6.11731×10−3 ≤P≤15000 [bar]273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦ C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦ C]
6.11731×10−3 ≤P≤15000 [bar]273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦ C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦ C]
6.11731×10−3 ≤P≤15000 [bar]611.731≤P<22.055×106 [Pa]6.11731×10−3 ≤P<220.55 [bar]172

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.17–1

No.
17Name of
Function
CPPDD(P)18

CPPT(P,T)

19

CPTD(T)

20

CPTDD(T)21

CRP(‘A’)

7A
76

CVPD(P)
CVPDD(P)77

CVPT(P,T)

Water(IAPS 1984) Function (cont’d)

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

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
A: ‘A’=‘H’: 2.086×106 [J/kg] Speciﬁc EnthalpyP∗: ‘A’=‘P’: 22.055×106 [Pa], 220.55 [bar] Pressure
S: ‘A’=‘S’: 4.409×103 [J/(kg·K)] Speciﬁc EntropyT∗: ‘A’=‘T’: 647.126 [K], 373.976 [◦ C] Temperature
V: ‘A’=‘V’: 3.1056×10−3 [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]

Range of Argument(s)611.731≤P<22.055×106 [Pa]6.11731×10−3 ≤P<220.55 [bar]273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦ C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦ C]
6.11731×10−3 ≤P≤15000 [bar]273.16≤T<647.126 [K]0.01≤T<373.976 [◦C]
273.16≤T<647.126 [K]0.01≤T<373.976 [◦C]
one of ‘H’, ‘P’, ‘S’, ‘T’ and ‘V’

611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦ C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦ C]
6.11731×10−3 ≤P≤15000 [bar]7B
78

CVTD(T)
CVTDD(T)

2A
2B
22

EPSPD(P)EPSPDD(P)EPSPT(P,T)

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

273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦C]EPSPT: Static Dielectric Constant [–]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

611.731≤P≤500×106 [Pa]273.15≤T≤823.15 [K]
6.11731×10−3 ≤P≤5000 [bar]0≤T≤550 [◦ C]

Water (IAPS 1984 Formulation for Scientific and General Use)
Table II–2.17–1

No.
2C
2D
89

Name of
Function
EPSTD(T)EPSTDD(T)FC(‘A’)9A
96

GAMPD(P)GAMPDD(P)95

GAMPT(P,T)

173

Water(IAPS 1984) Function (cont’d)

Function and Argument(s)Range of Argument(s)FC: Fundamental Constants
M: ‘A’=‘M’: 18.0152 Relative Molecular Mass
R: ‘A’=‘R’: 461.52 [J/(kg·K)] Gas Constant

one of ‘M’ and ‘R’

GAMPDD: Ratio of Speciﬁc Heats of Saturated
Vapor [–]P∗: Pressure [Pa], [bar]GAMPT: Ratio of Speciﬁc Heats [–]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦ C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦C]
6.11731×10−3 ≤P≤15000 [bar]9B
97

GAMTD(T)GAMTDD(T)23

HPD(P)

24

HPDD(P)71

HPS(P,S)

25

HPT(P,T)GAMTDD: Ratio of Speciﬁc Heats of Saturated
Vapor [J/kg]
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]

273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦ C]
611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]611.731≤P≤500×106 [Pa]SPT(P,273.15K)≤S≤
SPT(P,1273.15K) [J/(kg·K)]
500×106 ≤P≤1500×106 [Pa]SPT(P,T0 )≤S≤
SPT(P,1273.15K) [J/(kg·K)]
where
T0 =(P×10−8 –5)×15+273.15 [K]
6.11731×10−3 ≤P≤5000 [bar]SPT(P,0◦ C)≤S≤
SPT(P,1000◦ C) [J/(kg·K)]
5000≤P≤15000 [bar]SPT(P,T0 )≤S≤
SPT(P,1000◦ C) [J/(kg·K)]
where T0 =(P×10−3 –5)×15 [◦ C]
273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦ C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦C]
6.11731×10−3 ≤P≤15000 [bar]174

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.17–1

No.
26

Name of
Function
HPX(P,X)

27

HTD(T)28

HTDD(T)

29

HTX(T,X)

84

IDENTF(‘A’)

66
68
85

PLDT(T)
PMLT(T)
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(T)SIGP(P)

32

SIGT(T)

33

SPD(P)34

SPDD(P)

Water(IAPS 1984) Function (cont’d)

Function and Argument(s)Range of Argument(s)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]
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’: ‘H2O’ Molecular Formula
S: ‘A’=‘S’: ‘WATER(IAPS 1984)’
Name of Substance
V: ‘A’=‘V’: ‘10.1’ Version Number

611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]0≤X≤1.0 [–]273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦ C]
273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦ C]
273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦ C]
0≤X≤1.0 [–]one of ‘C’, ‘S’ and ‘V’

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]

611.731≤P<22.055×106 [Pa]6.11731×10−3 ≤P<220.55 [bar]611.731≤P<22.055×106 [Pa]6.11731×10−3 ≤P<220.55 [bar]611.731≤P≤100×106 [Pa]273.15≤T≤1073.15 [K]

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

6.11731×10−3 ≤P≤1000 [bar]0≤T≤800 [◦ C]
273.16≤T<647.126 [K]0.01≤T<373.976 [◦ C]
273.16≤T<647.126 [K]0.01≤T<373.976 [◦ C]

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

273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦ 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]611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦ C]
611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]Water (IAPS 1984 Formulation for Scientific and General Use)
Table II–2.17–1

No.
35

Name of
Function
SPT(P,T)36

SPX(P,X)

37

STD(T)38

STDD(T)

39

STX(T,X)

67
69
64

TLDP(P)
TMLP(P)
TPH(P,H)

175

Water(IAPS 1984) Function (cont’d)

Function and Argument(s)SPT: Speciﬁc EntropyP∗: 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 [–]TPH∗: Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]A: Speciﬁc Enthalpy [J/kg]

Range of Argument(s)273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦ C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦ C]
6.11731×10−3 ≤P≤15000 [bar]611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]0≤X≤1.0 [–]273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦C]
273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦C]
273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦C]
0≤X≤1.0 [–]611.731≤P≤500×106 [Pa]
HPT(P,273.15K)≤H≤
HPT(P,1273.15K) [J/kg]
500×106 ≤P≤1500×106 [Pa]
HPT(P,T0)≤H≤
HPT(P,1273.15K) [J/kg]
where
T0 =(P×10−8 –5)×15+273.15[K]6.11731×10−3 ≤P≤5000 [bar]HPT(P,0◦ C)≤H≤
HPT(P,1000◦ C) [J/kg]
5000≤P≤15000 [bar]HPT(P,T0)≤H≤
HPT(P,1000◦ C) [J/kg]
where T0 =(P×10−3 –5)×15 [◦ C]

6H
65

TPH2(P,H)
TPS(P,S)TPS∗: Temperature [K], [◦C]P∗: Pressure [Pa], [bar]S: Speciﬁc Entropy [J/(kg·K)]

611.731≤P≤500×106 [Pa]SPT(P,273.15K)≤S≤
SPT(P,1273.15K) [J/(kg·K)]
500×106 ≤P≤1500×106 [Pa]SPT(P,T0 )≤S≤
SPT(P,1273.15K) [J/(kg·K)]
where
T0 =(P×10−8 –5)×15+273.15 [K]
6.11731×10−3 ≤P≤5000 [bar]SPT(P,0◦ C)≤S≤
SPT(P,1000◦ C) [J/(kg·K)]
5000≤P≤15000 [bar]SPT(P,T0 )≤S≤
SPT(P,1000◦ C) [J/(kg·K)]
where T0 =(P×10−3 –5)×15 [◦ C]

176

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.17–1

No.
6S
98
70

Name of
Function
TPS2(P,S)TPSEUP(P)TPV(P,V)41

TRPL(‘A’)

100
40

TSBP(P)
TSP(P)

74
75
42

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

UPDD(P)79

UPS(P,S)

Water(IAPS 1984) Function (cont’d)

Function and Argument(s)TPV∗: Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]V: Speciﬁc Volume [m3 /kg]

TRPL∗: Properties at Triple PointP∗: ‘A’=‘P’: 611.731 [Pa], 6.11731×10−3[bar] PressureT∗: ‘A’=‘T’: 273.16 [K], 0.01 [◦ C] Temperature

Range of Argument(s)611.731≤P≤500×106 [Pa]VPT(P,273.15K)≤V≤
VPT(P,1273.15K) [m3 /kg]
500×106 ≤P≤1500×106 [Pa]VPT(P,T0 )≤V≤
VPT(P,1273.15K) [m3 /kg]
where
T0 =(P×10−8 –5)×15+273.15[K]6.11731×10−3 ≤P≤5000 [bar]VPT(P,0◦ C)≤V≤
VPT(P,1000◦ C) [m3 /kg]
5000≤P≤15000 [bar]VPT(P,T0 )≤V≤
VPT(P,1000◦ C) [m3 /kg]
where T0 =(P×10−3 –5)×15[◦ C]
one of ‘P’ and ‘T’

TSP∗: Saturation Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [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]UPS: Speciﬁc Internal Energy [J/kg]
P∗: Pressure [Pa], [bar]S: Speciﬁc Entropy [J/(kg·K)]

611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]611.731≤P≤500×106 [Pa]SPT(P,273.15K)≤S≤
SPT(P,1273.15K) [J/(kg·K)]
500×106 ≤P≤1500×106 [Pa]SPT(P,T0 )≤S≤
SPT(P,1273.15K) [J/(kg·K)]
where
T0 =(P×10−8 –5)×15+273.15 [K]
6.11731×10−3 ≤P≤5000 [bar]SPT(P,0◦ C)≤S≤
SPT(P,1000◦ C) [J/(kg·K)]
5000≤P≤15000 [bar]SPT(P,T0 )≤S≤
SPT(P,1000◦ C) [J/(kg·K)]
where T0 =(P×10−3 –5)×15 [◦ C]

Water (IAPS 1984 Formulation for Scientific and General Use)
Table II–2.17–1

No.
44

Name of
Function
UPT(P,T)45

UPX(P,X)

46

UTD(T)

47

UTDD(T)

48

UTX(T,X)

49

VPD(P)50

VPDD(P)80

VPS(P,S)

51

VPT(P,T)

177

Water(IAPS 1984) Function (cont’d)

Function and Argument(s)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]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]

Range of Argument(s)273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦ C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦C]
6.11731×10−3 ≤P≤15000 [bar]611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]0≤X≤1.0 [–]273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦ C]
273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦ C]
273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦ C]
0≤X≤1.0 [–]611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]611.731≤P≤500×106 [Pa]SPT(P,273.15K)≤S≤
SPT(P,1273.15K) [J/(kg·K)]
500×106 ≤P≤1500×106 [Pa]SPT(P,T0 )≤S≤
SPT(P,1273.15K) [J/(kg·K)]
where
T0 =(P×10−8 –5)×15+273.15 [K]
6.11731×10−3 ≤P≤5000 [bar]SPT(P,0◦ C)≤S≤
SPT(P,1000◦ C) [J/(kg·K)]
5000≤P≤15000 [bar]SPT(P,T0 )≤S≤
SPT(P,1000◦ C) [J/(kg·K)]
where T0 =(P×10−3 –5)×15 [◦ C]
273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦ C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦C]
6.11731×10−3 ≤P≤15000 [bar]178

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.17–1

No.
52

Name of
Function
VPX(P,X)

53

VTD(T)54

VTDD(T)

55

VTX(T,X)

8E
8F
83

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

Water(IAPS 1984) Function (cont’d)

Function and Argument(s)Range of Argument(s)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 [–]611.731≤P≤22.055×106 [Pa]6.11731×10−3 ≤P≤220.55 [bar]0≤X≤1.0 [–]273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦C]
273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦C]
273.16≤T≤647.126 [K]0.01≤T≤373.976 [◦C]
0≤X≤1.0 [–]WPT: Velocity of Sound [m/s]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

273.15≤T≤423.15 [K]611.731≤P≤
100×(5+(T−273.15)/15)×106 [Pa]423.15≤T≤1273.15 [K]611.731≤P≤1500×106 [Pa]0≤T≤150 [◦C]
6.11731×10−3 ≤P≤
1000×(5+T/15) [bar]150≤T≤1000 [◦ C]
6.11731×10−3 ≤P≤15000 [bar]

8G
8H
56

WTD(T)WTDD(T)
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)

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]
A: 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]

611.731≤P<22.055×106 [Pa]6.11731×10−3 ≤P<220.55 [bar]HPD(P)≤H≤HPDD(P) [J/kg]
611.731≤P<22.055×106 [Pa]6.11731×10−3 ≤P<220.55 [bar]SPD(P)≤S≤SPDD(P) [J/(kg·K)]
611.731≤P<22.055×106 [Pa]6.11731×10−3 ≤P<220.55 [bar]UPD(P)≤U≤UPDD(P) [J/kg]
611.731≤P<22.055×106 [Pa]6.11731×10−3 ≤P<220.55 [bar]VPD(P)≤V≤VPDD(P) [m3 /kg]
273.16≤T<647.126 [K]0.01≤T<373.976 [◦C]HTD(T)≤H≤HTDD(T) [J/kg]
273.16≤T<647.126 [K]0.01≤T<373.976 [◦C]
STD(T)≤S≤STDD(T) [J/(kg·K)]
273.16≤T<647.126 [K]0.01≤T<373.976 [◦C]UTD(T)≤U≤UTDD(T) [J/kg]
273.16≤T<647.126 [K]0.01≤T<373.976 [◦C]
VTD(T)≤V≤VTDD(T) [m3 /kg]