82

P-PROPATH: Pure Substances and Mixtures with Fixed Composition

2.7 n-Hydrogen
Equations for thermodynamic properties have been cited from reference [1], one for surface tension from Miller
et al.[2], and those for viscosity and thermal conductivity from reference [3].

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

2.7.2 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:

n-Hydrogen
libjh2.a
JH2.LIB
h2-ss
H2–SS.EXE

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

n-H2
2.016
4124.62 J/(kg·K)

Critical Constants:
Critical Pressure:
Critical Temperature:
Critical Speciﬁc Volume:1.315×10 6Pa (13.15 bar)
33.19 K (−239.96 ◦C)
0.0332 m3 /kg

Triple Point:
Pressure:
Temperature:

7.199×10 3 Pa (0.07199 bar)
13.96 K (−259.19 ◦C)

Reference State:
At 1.01325 bar(1 atm) and 25.01 ◦C(298.16 K), 142.196 J/(mol·K) and 8.473×10 3 J/mol are assigned to thespeciﬁc entropy and the speciﬁc enthalpy, respectively.

2.7.4 Formula
Equation of State:
Equations (4.8) and (4.14) in a function form of P = P (ρ, T ) in reference [1]. Here P =pressure, ρ=density
and T =temperature.
Vapor Pressure:
Equation (4.14) and Table 31 in reference [1].
Properties on Bubble-Point Curve:
Equation (7.2) in reference [1].
Properties at Vapor-Liquid Equilibrium:saturated liquid: Equation (8.1) and Table 31 for speciﬁc volume, equation (4.14) and Table 19 for speciﬁc
entropy and for speciﬁc enthalpy.
saturated liquid: Equations (4.14) and (4.15) and Table 19 for speciﬁc volume. Equations (5.1) and (5.3) forthe calculation of speciﬁc entropy and speciﬁc enthalpy. Equations (5.7) and (5.8) for isochoric speciﬁc heat andisobaric speciﬁc heat.

n-Hydrogen83

All of these have been cited from reference [1].
Transport Properties:
Thermal conductivity and viscosity from reference [3].
The Other Properties:
Surface tension from reference [2].

References[1] Wooly, H.W., Scott, R.B. and Brickwedde, F.C., Compilation of Thermal Properties of Hydrogen in Its
Various Isotopic and Ortho-Para Modiﬁcations, J. Res. Nat. Bur. Stand., vol.41, (1948), pp.379–475.
[2] J.W. Miller, Jr. and C.L. Yaws, Chemical Engineering, vol.83, No.23, (1976), p.127.
[3] RC–72 Committee Report, Japan Society of Mechanical Engineers, (1987), pp.527–531.

84

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.7–1

No.
1
94
8A
8B
82

Name of
Function
AIPPT(P,T)
AJTPT(P,T)
AKPD(P)AKPDD(P)AKPT(P,T)

n−Hydrogen Function

Function and Argument(s)AKPT: Isentropic Exponent [–]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

Range of Argument(s)7.199×103 ≤P≤50×106 [Pa]273.15≤T≤673.15 [K]
0.07199≤P≤500 [bar]0≤T≤400 [◦C]

8C
8D
2

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

ALAPT(T)4

ALHP(P)

5

ALHT(T)

6
7
8

ALMPD(P)ALMPDD(P)
ALMPT(P,T)

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]

7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦C]
7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦C]

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

7.199×103 ≤P≤50×106 [Pa]273.15≤T≤673.15 [K]
0.07199≤P≤500 [bar]0≤T≤400 [◦C]

9
10
11
12
13

ALMTD(T)ALMTDD(T)
AMUPD(P)AMUPDD(P)AMUPT(P,T)

AMUPT: Coeﬃcient of Viscosity [Pa·s]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

7.199×103 ≤P≤50×106 [Pa]273.15≤T≤673.15 [K]
0.07199≤P≤500 [bar]0≤T≤400 [◦C]

14
15
92
90
91
93
16
17
18

AMUTD(T)AMUTDD(T)BPPT(P,T)
BSPT(P,T)
BTPT(P,T)
BVPT(P,T)
CPPD(P)CPPDD(P)CPPT(P,T)

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

7.199×103 ≤P≤50×106 [Pa]56≤T≤673.15 [K]
0.07199≤P≤500 [bar]−217.15≤T≤400 [◦ C]

19
20
21

CPTD(T)
CPTDD(T)CRP(‘A’)

7A
76

CVPD(P)
CVPDD(P)CRP: Critical Constants
H: ‘A’=‘H’: 0.86902×106 [J/kg] Speciﬁc EnthalpyP∗: ‘A’=‘P’: 1.3152×106 [Pa], 13.152 [bar] Pressure
S: ‘A’=‘S’: 44.760×103 [J/(kg·K)] Speciﬁc EntropyT∗: ‘A’=‘T’: 33.19 [K], −239.96 [◦ C] Temperature
V: ‘A’=‘V’: 33.20×10−3 [m3 /kg] Speciﬁc Volume

one of ‘H’, ‘P’, ‘S’, ‘T’ and ‘V’n-Hydrogen

85
Table II–2.7–1

No.
77

Name of
Function
CVPT(P,T)

n−Hydrogen Function (cont’d)

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

Range of Argument(s)7.199×103 ≤P≤50×106 [Pa]56≤T≤673.15 [K]
0.07199≤P≤500 [bar]−217.15≤T≤400 [◦ C]

7B
78
2A
2B
22
2C
2D
89

CVTD(T)
CVTDD(T)EPSPD(P)EPSPDD(P)EPSPT(P,T)
EPSTD(T)EPSTDD(T)FC(‘A’)

9A
96
95
9B
97
23

GAMPD(P)GAMPDD(P)GAMPT(P,T)
GAMTD(T)GAMTDD(T)HPD(P)

24

HPDD(P)71

HPS(P,S)

25

HPT(P,T)

26

HPX(P,X)

27

HTD(T)28

HTDD(T)

29

HTX(T,X)

84

IDENTF(‘A’)

66
68
85
86

PLDT(T)
PMLT(T)
PRPD(P)PRPDD(P)FC: Fundamental Constants
M: ‘A’=‘M’: 2.016 Relative Molecular Mass
R: ‘A’=‘R’: 4124.62 [J/(kg·K)] Gas Constant

one of ‘M’ and ‘R’

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)]

7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]7.199×103 ≤P≤50×106 [Pa]SPT(P,13.96K)≤S≤
SPT(P,673.15K) [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]
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’: ‘N-H2’ Molecular Formula
S: ‘A’=‘S’: ‘N-HYDROGEN’ Name of Substance
V: ‘A’=‘V’: ‘10.1’ Version Number

0.07199≤P≤500 [bar]SPT(P,−259.19◦ C)≤S≤
SPT(P,400◦ C) [J/(kg·K)]
7.199×103 ≤P≤50×106 [Pa]13.96≤T≤673.15 [K]
0.07199≤P≤500 [bar]−259.19≤T≤400 [◦ C]
7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]0≤X≤1.0 [–]13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦C]
13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦C]
13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦C]
0≤X≤1.0 [–]one of ‘C’, ‘S’ and ‘V’86

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.7–1

No.
81

Name of
Function
PRPT(P,T)

n−Hydrogen Function (cont’d)

Function and Argument(s)PRPT: Prandtl Number [–]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

Range of Argument(s)7.199×103 ≤P≤50×106 [Pa]273.15≤T≤673.15 [K]
0.07199≤P≤500 [bar]0≤T≤400 [◦ C]

87
88
99
30

PRTD(T)
PRTDD(T)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)

39

STX(T,X)

67
69
64

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

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

13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ 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]

7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [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]
STX: Speciﬁc Entropy of Mixture [J/(kg·K)]
T∗: Temperature [K], [◦C]
X: Dryness Fraction [–]TPH∗: Temperature [K], [◦C]P∗: Pressure [Pa], [bar]H: Speciﬁc Enthalpy [J/kg]

7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]7.199×103 ≤P≤50×106 [Pa]13.96≤T≤673.15 [K]
0.07199≤P≤500 [bar]−259.19≤T≤400 [◦ C]
7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]0≤X≤1.0 [–]13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
0≤X≤1.0 [–]7.199×103 ≤P≤50×106 [Pa]
HPT(P,13.96K)≤H≤
HPT(P,673.15K) [J/kg]
0.07199≤P≤500 [bar]HPT(P,−259.19◦ C)≤H≤
HPT(P,400◦ 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)]

7.199×103 ≤P≤50×106 [Pa]SPT(P,13.96K)≤S≤
SPT(P,673.15K) [J/(kg·K)]
0.07199≤P≤500 [bar]SPT(P,−259.19◦ C)≤S≤
SPT(P,400◦ C) [J/(kg·K)]

n-Hydrogen

87
Table II–2.7–1

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)

7944

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)

80
51

VPS(P,S)
VPT(P,T)52

VPX(P,X)n−Hydrogen 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’: 7.199×103 [Pa], 0.07199 [bar]PressureT∗: ‘A’=‘T’: 13.96 [K], −259.19 [◦C] Temperature

Range of Argument(s)7.199×103 ≤P≤50×106 [Pa]VPT(P,13.96K)≤V≤
VPT(P,673.15K) [m3 /kg]
0.07199≤P≤500 [bar]VPT(P,−259.19◦ C)≤V≤
VPT(P,400◦ C) [m3 /kg]
one of ‘P’ and ‘T’

TSP∗: Saturation Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [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]7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]

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

7.199×103 ≤P≤50×106 [Pa]13.96≤T≤673.15 [K]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]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 [–]7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]0.07199≤P≤500 [bar]−259.19≤T≤400 [◦ C]
7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]0≤X≤1.0 [–]13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
0≤X≤1.0 [–]7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]7.199×103 ≤P≤50×106 [Pa]13.96≤T≤673.15 [K]
0.07199≤P≤500 [bar]−259.19≤T≤400 [◦ C]
7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]0≤X≤1.0 [–]88

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.7–1

No.
53

Name of
Function
VTD(T)54

VTDD(T)

55

VTX(T,X)

8E
8F
83

WPD(P)WPDD(P)
WPT(P,T)n−Hydrogen Function (cont’d)

Function and Argument(s)Range of Argument(s)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 [–]13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
0≤X≤1.0 [–]WPT: Velocity of Sound [m/s]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

7.199×103 ≤P≤50×106 [Pa]273.15≤T≤673.15 [K]
0.07199≤P≤500 [bar]0≤T≤400 [◦ C]

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]
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]

7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]HPD(P)≤H≤HPDD(P) [J/kg]
7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]SPD(P)≤S≤SPDD(P) [J/(kg·K)]
7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]UPD(P)≤U≤UPDD(P) [J/kg]
7.199×103 ≤P≤1.3152×106 [Pa]0.07199≤P≤13.152 [bar]VPD(P)≤V≤VPDD(P) [m3 /kg]
13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
HTD(T)≤H≤HTDD(T) [J/kg]
13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
STD(T)≤S≤STDD(T) [J/(kg·K)]
13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
UTD(T)≤U≤UTDD(T) [J/kg]
13.96≤T≤33.19 [K]−259.19≤T ≤−239.96 [◦ C]
VTD(T)≤V≤VTDD(T) [m3 /kg]