Helium 4(IUPAC-IPTS 1968)35

2. Individual Sustance and Formulation
2.1 Helium 4(IUPAC-IPTS 1968)
Equations for thermodynamic properties have been cited from the IUPAC Table[1], and those for transport
properties from McCarty et al.[2] and Hands et al.[3].

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

2.1.2 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:

Helium 4
libjhe4.a
JHE4.LIB
he4-ssHE4–SS.EXE

2.1.3 Important Constants and Others
Molecular Formula:
Relative Molecular Mass:
Gas Constant:He
4.00262077.2 J/(kg·K)

Critical Constants:
Critical Pressure:
Critical Temperature:
Critical Speciﬁc Volume:0.22746×10 6Pa (2.2746 bar)
5.2014 K (−267.9486 ◦C)
0.014360 m3 /kg

Triple Point:
Pressure:
Temperature:

5.040×10 3 Pa (0.05040 bar)2.1773 K (−270.9727 ◦C)

Reference State:
At 1.01325 bar(1 atm) and 25◦C(298.15 K)(ideal gas state) 126.039 J/(mol·K) and 6197 J/mol are assigned tothe speciﬁc entropy and the speciﬁc enthalpy, respectively.

2.1.4 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.
However, n50 , n51 , n60 , n61 , n62 , n70 , n71 , n72 in table I in the same reference have been corrected as n60 , n61 ,n62 , n70 , n71 , n72 , n50 , n51 , respectively.
Vapor Pressure:
Equation(7) in reference[1]. However 1.2774706525× 102 in table J in the same reference have been corrected
as 1.4127497598×10 2.
Properties at Vapor-Liquid Equilibrium:
Equations (7), (8) and (14) for speciﬁc volume, equation (7) and the equation given on page 39 for speciﬁc
entropy, and equation (7) and the equation given on page 40 for speciﬁc enthalpy, and equations (7) and (23) for
isosbaric speciﬁc heat, respectively. All of these have been cited from reference[1].
Pressure and Temperature on λ-Line:

36

P-PROPATH: Pure Substances and Mixtures with Fixed Composition

Equation (3) in reference [1]Pressure and Temperature on Melting Line:
Equations (5) and (6) in reference [1]Transport Properties:
Viscosity from reference[2] and thermal conductivity from reference[3]. Both are valid in the temperature rangeof T<173.15 ◦ C(100 K).

References[1] S.Angus and K.M.de Reuck, Helium International Thermodynamic Table of the Fluid State, IUPAC, (1977).
[2] R.D.McCarty, N.B.S. Technical Note 631, (Nov., 1972), p.9.
[3] B.A.Hands and V.D.Arp, Cryogenics, vol.21, (1981), p.697.

Helium 4(IUPAC-IPTS 1968)

37

Table II–2.1–1

No.
1
94

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

Helium 4(IUPAC−IPTS 1968) Function

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

Range of Argument(s)5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦ C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦ C]
exclude the critical region shownin Fig.II-2-2

8A
8B
82

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

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

5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦ C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦ 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)8

ALMPT(P,T)

9

ALMTD(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]
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]

5.04×103 ≤P≤0.218797×106 [Pa]0.0504≤P≤2.18797 [bar]2.1773≤T≤5.15 [K]−270.9727≤T≤−268 [◦C]
5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
46.99×103 ≤P≤0.219×106 [Pa]0.4699≤P≤2.19 [bar]46.99×103 ≤P≤0.219×106 [Pa]0.4699≤P≤2.19 [bar]5.04×103 ≤P<10.397×106 [Pa]3.5≤T≤300 [K]
10.397×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤300 [K]
0.0504≤P<103.97 [bar]−269.65≤T≤26.85 [◦ C]
103.97≤P≤700 [bar]TMLP(P)≤T≤26.85 [◦C]
exclude the critical region shownin Fig.II-2-1
3.5≤T≤5.15 [K]−269.65≤T≤−268 [◦ C]

38

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.1–1

No.
10

Name of
Function
ALMTDD(T)11

AMUPD(P)12

AMUPDD(P)13

AMUPT(P,T)

14

AMUTD(T)15

AMUTDD(T)92

BPPT(P,T)

90

91

BSPT(P,T)

BTPT(P,T)

Helium 4(IUPAC−IPTS 1968) Function (cont’d)

Function and Argument(s)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]
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]

Range of Argument(s)3.5≤T≤5.15 [K]−269.65≤T≤−268 [◦C]
46.99×103 ≤P≤0.22746×106 [Pa]0.4699≤P≤2.2746 [bar]46.99×103 ≤P≤0.22746×106 [Pa]0.4699≤P≤2.2746 [bar]5.04×103 ≤P<10.397×106 [Pa]3.5≤T≤300 [K]
10.397×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤300 [K]
0.0504≤P<103.97 [bar]−269.65≤T≤26.85 [◦C]
103.97≤P≤700 [bar]TMLP(P)≤T≤26.85 [◦ C]
3.5≤T≤5.2014 [K]−269.65≤T≤−267.9486 [◦ C]
3.5≤T≤5.2014 [K]−269.65≤T≤−267.9486 [◦ C]
5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦C]
5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦C]
5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦C]

Helium 4(IUPAC-IPTS 1968)

39

Table II–2.1–1

No.
93

Name of
Function
BVPT(P,T)

16

CPPD(P)

17

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)

Helium 4(IUPAC−IPTS 1968) Function (cont’d)

Function and Argument(s)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’: 6.7406×103 [J/kg] Speciﬁc EnthalpyP∗: ‘A’=‘P’: 0.22746×106 [Pa], 2.2746 [bar]Pressure
S: ‘A’=‘S’: 5.6988×103 [J/(kg·K)] Speciﬁc EntropyT∗: ‘A’=‘T’: 5.2014 [K], −267.9486 [◦ C]
Temperature
V: ‘A’=‘V’: 0.014360 [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)5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦ C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦ C]
5.04×103 ≤P≤0.219×106 [Pa]0.0504≤P≤2.19 [bar]5.04×103 ≤P≤0.219×106 [Pa]0.0504≤P≤2.19 [bar]5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦ C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦ C]
exclude the critical region shownin Fig.II-2-2
2.1773≤T≤5.15 [K]−270.9727≤T≤−268 [◦ C]
2.1773≤T≤5.15 [K]−270.9727≤T≤−268 [◦ C]
one of ‘H’, ‘P’, ‘S’, ‘T’ and ‘V’

5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦ C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦ C]

7B
78

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

2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]

40

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.1–1

No.
2A
2B
22
2C
2D
89

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

GAMPD(P)GAMPDD(P)95

GAMPT(P,T)

Helium 4(IUPAC−IPTS 1968) Function (cont’d)

Function and Argument(s)Range of Argument(s)FC: Fundamental Constants
M: ‘A’=‘M’: 4.0026 Relative Molecular Mass
R: ‘A’=‘R’: 2077.2 [J/(kg·K)] Gas Constant

one of ‘M’ and ‘R’

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

5.04×103 ≤P≤0.219×106 [Pa]0.0504≤P≤2.19 [bar]5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦ C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦ C]
exclude the critical region shownin Fig.II-2-2

9B
97

GAMTD(T)GAMTDD(T)23

HPD(P)

24

HPDD(P)71

HPS(P,S)

25

26

HPT(P,T)

HPX(P,X)GAMTDD: Ratio of Speciﬁc Heat 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 [–]2.1773≤T≤5.15 [K]−270.9727≤T≤−268 [◦C]
5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]5.04×103 ≤P<3.013×106 [Pa]SPT(P,TLDP(P))≤S≤
SPT(P,1400K) [J/(kg·K)]
3.013×106 ≤P≤70×106 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,1400K) [J/(kg·K)]
0.0504≤P<30.13 [bar]SPT(P,TLDP(P))≤S≤
SPT(P,1126.85◦ C) [J/(kg·K)]
30.13≤P≤700 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,1126.85◦ C) [J/(kg·K)]
5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TLDP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦ C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦ C]
5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]0≤X≤1.0 [–]Helium 4(IUPAC-IPTS 1968)

41

Table II–2.1–1

No.
27

Name of
Function
HTD(T)28

HTDD(T)

29

HTX(T,X)

84

IDENTF(‘A’)

66

PLDT(T)

68

PMLT(T)85

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)

Helium 4(IUPAC−IPTS 1968) Function (cont’d)

Function and Argument(s)Range of Argument(s)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’: ‘HE’ Molecular Formula
S: ‘A’=‘S’: ‘HELIUM 4(IUPAC−IPTS 1968)’
Name of Substance
V: ‘A’=‘V’: ‘10.1’ Version Number
PLDT∗: Pressure on Lambda-line [Pa], [bar]T∗: Temperature [K], [◦ 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]

2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
0≤X≤1.0 [–]one of ‘C’, ‘S’ and ‘V’

1.7678≤T≤2.1773 [K]−271.3822≤T≤−270.9727 [◦ C]
1.7678≤T≤11.023 [K]−271.3822≤T≤−262.127 [◦ C]
46.99×103 ≤P≤0.219×106 [Pa]0.4699≤P≤2.19 [bar]46.99×103 ≤P≤0.219×106 [Pa]0.4699≤P≤2.19 [bar]5.04×103 ≤P≤10.397×106 [Pa]3.5≤T≤300 [K]
10.397×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤300 [K]

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

0.0504≤P≤103.97 [bar]−269.65≤T≤26.85 [◦ C]
103.97≤P≤700 [bar]TMLP(P)≤T≤26.85 [◦ C]
exclude the critical region shownin Fig.II-2-1
3.5≤T≤5.15 [K]−269.65≤T≤−268 [◦ C]
3.5≤T≤5.15 [K]−269.65≤T≤−268 [◦ C]

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

2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ 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]5.04×103 ≤P≤0.218797×106 [Pa]0.0504≤P≤2.18797 [bar]2.1773≤T≤5.15 [K]−270.9727≤T≤−268 [◦C]
5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]42P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.1–1

No.
35

Name of
Function
SPT(P,T)36

SPX(P,X)

37

STD(T)38

STDD(T)

39

STX(T,X)

67

TLDP(P)69

TMLP(P)64

TPH(P,H)

Helium 4(IUPAC−IPTS 1968) Function (cont’d)

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 [–]TLDP∗: Temperature on Lambda-line [K], [◦C]P∗: Pressure [Pa], [bar]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)5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦ C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦ C]
5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]0≤X≤1.0 [–]2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
0≤X≤1.0 [–]5.04×103 ≤P<3.013×106 [Pa]0.0504≤P<30.13 [bar]3.013×106 ≤P≤70×106 [Pa]30.13≤P≤700 [bar]5.04×103 ≤P<3.013×106 [Pa]
HPT(P,TLDP(P))≤H≤
HPT(P,1400K) [J/kg]
3.013×106 ≤P≤70×106 [Pa]
HPT(P,TMLP(P))≤H≤
HPT(P,1400K) [J/kg]
0.0504≤P<30.13 [bar]HPT(P,TLDP(P))≤H≤
HPT(P,1126.85◦ C) [J/kg]
30.13≤P≤700 [bar]HPT(P,TMLP(P))≤H≤
HPT(P,1126.85◦ 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)]

5.04×103 ≤P<3.013×106 [Pa]SPT(P,TLDP(P))≤S≤
SPT(P,1400K) [J/(kg·K)]
3.013×106 ≤P≤70×106 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,1400K) [J/(kg·K)]
0.0504≤P<30.13 [bar]SPT(P,TLDP(P))≤S≤
SPT(P,1126.85◦ C) [J/(kg·K)]
30.13≤P≤700 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,1126.85◦ C) [J/(kg·K)]

6S
98

TPS2(P,S)TPSEUP(P)TPSEUP: Pseudo Boiling Point [K], [◦C]
T∗: Temperature [K], [◦C]

0.228×106 <P≤50×106 [Pa]2.28<P≤500 [bar]Helium 4(IUPAC-IPTS 1968)

43

Table II–2.1–1

No.
70

Name of
Function
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)

Helium 4(IUPAC−IPTS 1968) 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’: 5.04×103 [Pa], 0.0504 [bar]PressureT∗: ‘A’=‘T’: 2.1773 [K], −270.9727 [◦ C]
Temperature

Range of Argument(s)5.04×103 ≤P<3.013×106 [Pa]VPT(P,TLDP(P))≤V≤
VPT(P,1400K) [m3 /kg]
3.013×106 ≤P≤70×106 [Pa]VPT(P,TMLP(P))≤V≤
VPT(P,1400K) [m3 /kg]
0.0504≤P<30.13 [bar]VPT(P,TLDP(P))≤V≤
VPT(P,1126.85◦ C) [m3 /kg]
30.13≤P≤700 [bar]VPT(P,TMLP(P))≤V≤
VPT(P,1126.85◦ C) [m3 /kg]
one of ‘P’ and ‘T’

TSP∗: Saturation Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [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)]

5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [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 [–]5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]5.04×103 ≤P<3.013×106 [Pa]SPT(P,TLDP(P))≤S≤
SPT(P,1400K) [J/(kg·K)]
3.013×106 ≤P≤70×106 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,1400K) [J/(kg·K)]
0.0504≤P<30.13 [bar]SPT(P,TLDP(P))≤S≤
SPT(P,1126.85◦ C) [J/(kg·K)]
30.13≤P≤700 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,1126.85◦ C) [J/(kg·K)]
5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦ C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦C]
5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]0≤X≤1.0 [–]44

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.1–1

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)

Helium 4(IUPAC−IPTS 1968) Function (cont’d)

Function and Argument(s)Range of 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)]

2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]

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]

2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
0≤X≤1.0 [–]5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]5.04×103 ≤P<3.013×106 [Pa]SPT(P,TLDP(P))≤S≤
SPT(P,1400K) [J/(kg·K)]
3.013×106 ≤P≤70×106 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,1400K) [J/(kg·K)]
0.0504≤P<30.13 [bar]SPT(P,TLDP(P))≤S≤
SPT(P,1126.85◦ C) [J/(kg·K)]
30.13≤P≤700 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,1126.85◦ C) [J/(kg·K)]
5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦ C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦ C]
5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]0≤X≤1.0 [–]2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
0≤X≤1.0 [–]5.04×103 ≤P<3.013×106 [Pa]TLDP(P)≤T≤1400 [K]
3.013×106 ≤P≤70×106 [Pa]TMLP(P)≤T≤1400 [K]
0.0504≤P<30.13 [bar]TLDP(P)≤T≤1126.85 [◦ C]
30.13≤P≤700 [bar]TMLP(P)≤T≤1126.85 [◦ C]

Helium 4(IUPAC-IPTS 1968)45

Table II–2.1–1

No.
8G
8H
56

Name of
Function
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)

Helium 4(IUPAC−IPTS 1968) Function (cont’d)

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)]
XTS: 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]

5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]HPD(P)≤H≤HPDD(P) [J/kg]
5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]SPD(P)≤S≤SPDD(P) [J/(kg·K)]
5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]UPD(P)≤U≤UPDD(P) [J/kg]
5.04×103 ≤P≤0.22746×106 [Pa]0.0504≤P≤2.2746 [bar]VPD(P)≤V≤VPDD(P) [m3 /kg]
2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
HTD(T)≤H≤HTDD(T) [J/kg]
2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
STD(T)≤S≤STDD(T) [J/(kg·K)]
2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
UTD(T)≤U≤UTDD(T) [J/kg]
2.1773≤T≤5.2014 [K]−270.9727≤T≤−267.9486 [◦ C]
VTD(T)≤V≤VTDD(T) [m3 /kg]

46

P-PROPATH: Pure Substances and Mixtures with Fixed Composition[bar]*10 6 [Pa]
700

70

3.013

elt

in

g

r
cu

ve

[bar]*10 6 [Pa]T = 3.5 K

30.13

Lambda curve

10.397Upper lambda point

103.97

M

Lower lambda point

Pressure, P

Helium 4

2.28

0.228

2.19

0.219

Critical point

5.15
-268

5.21 [K]-267.94 [C]Vapor pressure curve

0.0504 0.00504
2.1773-270.9727

11-262.15

Temperature, T
Fig.II–2.1–1

Range of Arguments(P,T) for ALMPT(P,T) and PRPT(P,T).

300 [K]
26.85 [C]Helium 4(IUPAC-IPTS 1968)47[bar]*10 6 [Pa]700

70

Lambda curve

3.013

Upper lambda point

30.13

M

Lower lambda point

Pressure, P

Helium 4
elt

in

g

r
cu

ve

[bar]*10 6 [Pa]
2.28

0.228

2.19

0.219

Critical point

5.15
-268

5.21 [K]-267.94 [C]Vapor pressure curve

0.0504 0.00504
2.1773-270.9727

11-262.15

Temperature, T
Fig.II–2.1–2

Range of Arguments(P,T) for AJTPT(P,T),CPPT(P,T) and
GAMPT(P,T).

300 [K]
26.85 [C]