190

P-PROPATH: Pure Substances and Mixtures with Fixed Composition

2.19 Heavy Water
Equations for thermodynamic properties have been cited from Hill et al.[1] and those for transport properties
from Matsunaga and Nagashima[2] and one for surface tension from IAPS[3].

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

2.19.2 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:

Heavy Water
libjd2o.a
JD2O.LIB
d2o-ssD2O–SS.EXE

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

D2 O
20.027415.15 J/(kg·K)

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

21.66×10 6Pa (216.6 bar)
643.89 K (370.74 ◦ C)
2.7933×10 −3m3 /kg

Triple Point:
Pressure:
Temperature:

660.1 Pa (6.601×10 −3bar)
276.95 K (3.8 ◦ 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.

2.19.4 Formula
Equation of State:
Equation (1) in a function form of ψ = ψ(ρ, T ) in reference [1]. Here ψ= speciﬁc helmholtz free energy, ρ=density and T = temperature.
Vapor Pressure:
Equation (1) in reference [1] for speciﬁc helmholtz free energy and the Gibbs condition for phase equilibrium.
Properties at Vapor-Liquid Equilibrium:
Equation (1) in reference [1] for speciﬁc volume. Equations (6) and (7) in reference [1] for speciﬁc entropy
and speciﬁc enthalpy, respectively. Equation as a function of density and temperature, which has been derived
directly by partial diﬀerentiation of the speciﬁc Helmholtz free energy, equation (1) in reference [1], for isobaric
speciﬁc heat.
Transport Properties:

Heavy Water

191

Viscosity and thermal conductivity from equations (6) and (7) in reference [2], respectively.
The Other Properties:
Surface tension from equation (10) in reference [3].

References[1] P.G.Hill,R.D.MacMillan and V.Lee, Tables of Thermodynamic Properties of Heavy Water in S.I. Units,
Atomic Energy of Canada Limited, Mississauga, Ontario, (1981).
[2] N.Matsunaga and A.Nagashima, J. Phys. Chem. Ref. Data, 12-4, (1983), pp.933–966.
[3] M.Uematsu, Netsu Bussei (Japan J. Thermophys. Prop.), 2-2, (1988), pp.84-88.

192

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.19–1

No.
1
94

8A
8B
82

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

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

8C
8D
2AKTD(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)

Heavy Water Function

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

660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]

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

660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]

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]

660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]276.95≤T<643.89 [K]3.8≤T<370.74 [◦ C]
660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]
660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]

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]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦ C]

6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦ C]

660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]660.1≤P≤100×106 [Pa]276.95≤T≤823.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤550 [◦ C]
276.95≤T<643.89 [K]3.8≤T<370.74 [◦ C]
276.95≤T<643.89 [K]3.8≤T<370.74 [◦ C]
660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]Heavy Water

193
Table II–2.19–1

No.
13

Name of
Function
AMUPT(P,T)

14

AMUTD(T)15

AMUTDD(T)92

BPPT(P,T)

90

91

93

BSPT(P,T)

BTPT(P,T)

BVPT(P,T)

16

CPPD(P)

17

CPPDD(P)18

CPPT(P,T)

19

CPTD(T)

20

CPTDD(T)21

CRP(‘A’)

Heavy Water 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 of Saturated
Vapor [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]
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
H: ‘A’=‘H’: 1.9657×106 [J/kg] Speciﬁc EnthalpyP∗: ‘A’=‘P’: 21.66×106 [Pa], 216.6 [bar] Pressure
S: ‘A’=‘S’: 4.1815×103 [J/(kg·K)] Speciﬁc EntropyT∗: ‘A’=‘T’: 643.89 [K], 370.74 [◦ C] Temperature
V: ‘A’=‘V’: 2.7933×10−3 [m3 /kg] Speciﬁc Volume

Range of Argument(s)660.1≤P≤100×106 [Pa]276.95≤T≤773.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤500 [◦C]
276.95≤T<643.89 [K]3.8≤T<370.74 [◦C]
276.95≤T<643.89 [K]3.8≤T<370.74 [◦C]
660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦C]
660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦C]
660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦C]
660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦C]
660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦C]
276.95≤T<643.89 [K]3.8≤T<370.74 [◦C]
276.95≤T<643.89 [K]3.8≤T<370.74 [◦C]
one of ‘H’, ‘P’, ‘S’, ‘T’ and ‘V’194

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.19–1

No.
7A
76

Name of
Function
CVPD(P)
CVPDD(P)77

CVPT(P,T)

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)95

GAMPT(P,T)

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)28

HTDD(T)

Heavy Water Function (cont’d)

Function and Argument(s)Range of Argument(s)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]

660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]CVTDD: Isochoric Speciﬁc Heat of Saturated
Vapor [J/(kg·K)]
T∗: Temperature [K], [◦ C]

276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]

FC: Fundamental Constants
M: ‘A’=‘M’: 20.027 Relative Molecular Mass
R: ‘A’=‘R’: 415.15 [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]

660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]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)]

276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]

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]
HTDD: Speciﬁc Enthalpy of Saturated Vapor [J/kg]
T∗: Temperature [K], [◦ C]

660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦ C]

660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦ C]

660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]660.1≤P≤100×106 [Pa]SPT(P,276.95K)≤S≤
SPT(P,1073.15K) [J/(kg·K)]
6.601×10−3 ≤P≤1000 [bar]SPT(P,3.8◦ C)≤S≤
SPT(P,800◦ C) [J/(kg·K)]
660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦ C]
660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]0≤X≤1.0 [–]276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]
276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]

Heavy Water

195
Table II–2.19–1

No.
29

Name of
Function
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(T)
PST(T)72
73
31

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

32

SIGT(T)

33

SPD(P)34

SPDD(P)35

SPT(P,T)36

SPX(P,X)

37

STD(T)38

STDD(T)

Heavy Water Function (cont’d)

Function and Argument(s)Range of Argument(s)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’: ‘D2O’ Molecular Formula
S: ‘A’=‘S’: ‘HEAVY WATER’ Name of Substance
V: ‘A’=‘V’: ‘10.1’ Version Number

276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ 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]

660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]660.1≤P≤100×106 [Pa]276.95≤T≤773.15 [K]

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

6.601×10−3 ≤P≤1000 [bar]3.8≤T≤500 [◦ C]
276.95≤T<643.89 [K]3.8≤T<370.74 [◦ C]
276.95≤T<643.89 [K]3.8≤T<370.74 [◦ C]

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

276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ 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]SPT: Speciﬁc Entropy [J/(kg·K)]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]
660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]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]

660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦ C]
660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]0≤X≤1.0 [–]276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]
276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]

196

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.19–1

No.
39

Name of
Function
STX(T,X)

67
69
64

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

Heavy Water Function (cont’d)

Function and Argument(s)Range of Argument(s)STX: Speciﬁc Entropy of Mixture [J/(kg·K)]
T∗: Temperature [K], [◦ C]
X: Dryness Fraction [–]276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦C]
0≤X≤1.0 [–]TPH∗: Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]H: Speciﬁc Enthalpy [J/kg]

660.1≤P≤100×106 [Pa]
HPT(P,276.95K)≤H≤
HPT(P,1073.15K) [J/kg]
6.601×10−3 ≤P≤1000 [bar]HPT(P,3.8◦C)≤H≤
HPT(P,800◦ C) [J/kg]

6H
65

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

660.1≤P≤100×106 [Pa]SPT(P,276.95K)≤S≤
SPT(P,1073.15K) [J/(kg·K)]
6.601×10−3 ≤P≤1000 [bar]SPT(P,3.8◦ C)≤S≤
SPT(P,800◦ 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)79

UPS(P,S)

44

45

UPT(P,T)

UPX(P,X)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 Point
P∗:‘A’=‘P’: 660.1 [Pa], 6.601×10−3 [bar] Pressure
T∗:‘A’=‘T’: 276.95 [K], 3.8 [◦ C] Temperature

21.66×106 <P≤50×106 [Pa]216.6<P≤500 [bar]660.1≤P≤100×106 [Pa]VPT(P,276.95K)≤V≤
VPT(P,1073.15K) [m3 /kg]
6.601×10−3 ≤P≤1000 [bar]VPT(P,3.8◦C)≤V≤
VPT(P,800◦ C) [m3 /kg]
one of ‘P’ and ‘T’

TSP∗: Saturation Temperature [K], [◦C]P∗: Pressure [Pa], [bar]660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [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)]

660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]

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 [–]660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]660.1≤P≤100×106 [Pa]SPT(P,276.95K)≤S≤
SPT(P,1073.15K) [J/(kg·K)]
6.601×10−3 ≤P≤1000 [bar]SPT(P,3.8◦ C)≤S≤
SPT(P,800◦ C) [J/(kg·K)]
660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦C]
660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]0≤X≤1.0 [–]Heavy Water

197
Table II–2.19–1

No.
46

Name of
Function
UTD(T)

47

UTDD(T)

48

UTX(T,X)

49

VPD(P)50

VPDD(P)80

VPS(P,S)

51

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)

8G
8H
56

WTD(T)WTDD(T)
XPH(P,H)

Heavy Water Function (cont’d)

Function and Argument(s)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]
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 [–]Range of Argument(s)276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]
276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]
276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]
0≤X≤1.0 [–]660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]660.1≤P≤100×106 [Pa]SPT(P,276.95K)≤S≤
SPT(P,1073.15K) [J/(kg·K)]
6.601×10−3 ≤P≤1000 [bar]SPT(P,3.8◦ C)≤S≤
SPT(P,800◦ C) [J/(kg·K)]
660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦ C]
660.1≤P≤21.66×106 [Pa]6.601×10−3 ≤P≤216.6 [bar]0≤X≤1.0 [–]276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]
276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]
276.95≤T≤643.89 [K]3.8≤T≤370.74 [◦ C]
0≤X≤1.0 [–]WPT: Velocity of Sound [m/s]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

660.1≤P≤100×106 [Pa]276.95≤T≤1073.15 [K]

XPH: Dryness Fraction [–]P∗: Pressure [Pa], [bar]H: Speciﬁc Enthalpy of Mixture [J/kg]

660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]HPD(P)≤H≤HPDD(P) [J/kg]

6.601×10−3 ≤P≤1000 [bar]3.8≤T≤800 [◦ C]

198

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.19–1

No.
57

Name of
Function
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)

Heavy Water Function (cont’d)

Function and Argument(s)Range of Argument(s)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]

660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]SPD(P)≤S≤SPDD(P) [J/(kg·K)]
660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]UPD(P)≤U≤UPDD(P) [J/kg]
660.1≤P<21.66×106 [Pa]6.601×10−3 ≤P<216.6 [bar]VPD(P)≤V≤VPDD(P) [m3 /kg]
276.95≤T<643.89 [K]3.8≤T<370.74 [◦C]HTD(T)≤H≤HTDD(T) [J/kg]
276.95≤T<643.89 [K]3.8≤T<370.74 [◦C]
STD(T)≤S≤STDD(T) [J/(kg·K)]
276.95≤T<643.89 [K]3.8≤T<370.74 [◦C]UTD(T)≤U≤UTDD(T) [J/kg]
276.95≤T<643.89 [K]3.8≤T<370.74 [◦C]
VTD(T)≤V≤VTDD(T) [m3 /kg]