Argon

63

2.4 Argon
Equations for thermodynamic properties have been cited from the IUPAC Table [1], one for surface tension
from Miller et al.[2], and one for thermal conductivity from reference [3].

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

2.4.2 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:

Argon
libjarg.a
JARG.LIB
arg-ss
ARG–SS.EXE

2.4.3 Important Constants and Others
Molecular Formula:
Relative Molecular Mass:
Gas Constant:Ar
39.948208.13 J/(kg·K)

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

4.998×10 6Pa (49.98 bar)
150.86 K (−122.29 ◦C)
1.8667×10 −3m3 /kg

Triple Point:
Pressure:
Temperature:

0.06875×10 6Pa (0.6875 bar)
83.78 K (−189.37 ◦C)

Reference State:
At 1.01325 bar(1 atm) and 25◦ C(298.15 K)(gas), 154.735 J/(mol·K) and 6197 J/mol are assigned to the speciﬁc
entropy and the speciﬁc enthalpy, respectively.

2.4.4 Formula
Equation of State:
Equation (7) in a function form of P = P (ρ, T ) in reference [1]. Here P =pressure, ρ=density and T =Temperature.

Vapor Pressure:
Equation (5) in reference [1].
Properties on Bubble-Point Curve:
Equation (9) in reference [1].
Properties at Vapor-Liquid equilibrium:saturated liquid: Equations (5) and (9) for speciﬁc volume, equations at page 7 for speciﬁc enthalpy and speciﬁc
entropy, respectively.
saturated vapor: Equations (5) and (7) for speciﬁc volume, equation (7) and equations at page 7 for speciﬁc
enthalpy and speciﬁc entropy, and equations (7) and (9) for isochoric speciﬁc heat and isobaric speciﬁc heat,
respectively. However, the constant CO3 =−360.553×10 4 in eq.(9) has been corrected to CO3 =−360.553×10 7.

64

P-PROPATH: Pure Substances and Mixtures with Fixed Composition

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

References[1] International Thermodynamic Tables of the Fluid State, Argon, 1971, IUPAC, (1972).
[2] J.W.Miller Jr and C.L.Yaws, Chemical Engineering, vol.83, No. 23, (1976), p.127.
[3] Thermal conductivity, TPRC Data Series, vol.3, Plenum, (1970).

Argon65
Table II–2.4–1

No.
1
94
8A
8B
82
8C
8D
2

Name of
Function
AIPPT(P,T)
AJTPT(P,T)
AKPD(P)AKPDD(P)AKPT(P,T)
AKTD(T)
AKTDD(T)
ALAPP(P)3

ALAPT(T)4

ALHP(P)

5

ALHT(T)

6

ALMPD(P)78
9ALMPDD(P)
ALMPT(P,T)
ALMTD(T)

10
11
12
13
14
15
92
90
91
93
16
17

ALMTDD(T)
AMUPD(P)AMUPDD(P)AMUPT(P,T)
AMUTD(T)AMUTDD(T)BPPT(P,T)
BSPT(P,T)
BTPT(P,T)
BVPT(P,T)
CPPD(P)CPPDD(P)18

CPPT(P,T)

Argon Function

Function and Argument(s)Range of Argument(s)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]68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦C]
68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦C]
68.75×103 ≤P≤3.1675×106 [Pa]0.6875≤P≤31.675 [bar]

ALMTD: Thermal Conductivity of Saturated
Liquid [W/(m·K)]
T∗: Temperature [K], [◦ C]

83.78≤T≤140 [K]−189.37≤T≤−133.15 [◦C]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]

68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]10.0×103 ≤P≤100×106 [Pa]83.78≤T≤1100 [K]
0.1≤P≤1000 [bar]−189.37≤T≤826.85 [◦C]
see Fig.II-2-1

19
20

CPTD(T)
CPTDD(T)21

CRP(‘A’)

7A
76

CVPD(P)
CVPDD(P)CPTDD: Isobaric Speciﬁc Heat of Saturated
Vapor [J/(kg·K)]
T∗: Temperature [K], [◦ C]
CRP: Critical Constants
H: ‘A’=‘H’: 189.17×103 [J/kg] Speciﬁc EnthalpyP∗: ‘A’=‘P’: 4.998×106 [Pa], 49.98 [bar] Pressure
S: ‘A’=‘S’: 2.201×103 [J/(kg·K)] Speciﬁc EntropyT∗: ‘A’=‘T’: 150.86 [K], −122.29 [◦ C] Temperature
V: ‘A’=‘V’: 1.8667×10−3 [m3 /kg] Speciﬁc Volume

83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦C]

CVPDD: Isochoric Speciﬁc Heat of Saturated
Vapor [J/(kg·K)]
P∗: Pressure [Pa], [bar]68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]one of ‘H’, ‘P’, ‘S’, ‘T’ and ‘V’66

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2–1 Argon Function (cont’d)

No.
77

Name of
Function
CVPT(P,T)

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

Range of Argument(s)10.0×103 ≤P≤100×106 [Pa]83.78≤T≤1100 [K]
0.1≤P≤1000 [bar]−189.37≤T≤826.85 [◦C]
see Fig.II-2-1

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

83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]

FC: Fundamental Constants
M: ‘A’=‘M’: 39.948 Relative Molecular Mass
R: ‘A’=‘R’: 208.13 [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)]
HPT: Speciﬁc Enthalpy [J/kg]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]10.0×103 ≤P≤100×106 [Pa]0.1≤P≤1000 [bar]see Fig.II-2-3 for S
10.0×103 ≤P≤100×106 [Pa]83.78≤T≤1100 [K]

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’: ‘AR’ Molecular Formula
S: ‘A’=‘S’: ‘ARGON’ Name of Substance
V: ‘A’=‘V’: ‘10.1’ Version Number

0.1≤P≤1000 [bar]−189.37≤T≤826.85 [◦C]
see Fig.II-2-1
68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]0≤X≤1.0 [–]83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
0≤X≤1.0 [–]one of ‘C’, ‘S’ and ‘V’Argon67
Table II–2.4–1 Argon Function (cont’d)

No.
81
87
88
99
30

Name of
Function
PRPT(P,T)
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)

6H
65

TPH2(P,H)
TPS(P,S)

6S
98
70

TPS2(P,S)TPSEUP(P)TPV(P,V)41

TRPL(‘A’)

100
40

TSBP(P)
TSP(P)

Function and Argument(s)Range of Argument(s)PST∗: Saturation Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ 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]

68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [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 [–]68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]10.0×103 ≤P≤100×106 [Pa]83.78≤T≤1100 [K]
0.1≤P≤1000 [bar]−189.37≤T≤826.85 [◦ C]
see Fig.II-2-1
68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]0≤X≤1.0 [–]83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
0≤X≤1.0 [–]TPH∗: Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]H: Speciﬁc Enthalpy [J/kg]

10.0×103 ≤P≤100×106 [Pa]0.1≤P≤1000 [bar]see Fig.II-2-2 for H

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

10.0×103 ≤P≤100×106 [Pa]0.1≤P≤1000 [bar]see Fig.II-2-3 for S

TPV∗: Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]V: Speciﬁc Volume [m3 /kg]
TRPL∗: Properties at Triple Point
P∗:‘A’=‘P’: 68.75×103 [Pa], 0.6875 [bar]Pressure
T∗:‘A’=‘T’: 83.78 [K], −189.37 [◦ C]
Temperature

10.0×103 ≤P≤100×106 [Pa]0.1≤P≤1000 [bar]see Fig.II-2-4 for V
one of ‘P’ and ‘T’

TSP∗: Saturation Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]68P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.4–1 Argon Function (cont’d)

No.
74
75
42

Name of
Function
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)

53

VTD(T)54

VTDD(T)

55

VTX(T,X)

8E
8F
83
8G
8H

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

Function and Argument(s)Range of Argument(s)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]68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]

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

10.0×103 ≤P≤100×106 [Pa]83.78≤T≤1100 [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 [–]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 [–]68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]0.1≤P≤1000 [bar]−189.37≤T≤826.85 [◦ C]
see Fig.II-2-1
68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]0≤X≤1.0 [–]83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
0≤X≤1.0 [–]68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]10.0×103 ≤P≤100×106 [Pa]83.78≤T≤1100 [K]
0.1≤P≤1000 [bar]−189.37≤T≤826.85 [◦ C]
see Fig.II-2-1
68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]0≤X≤1.0 [–]83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
0≤X≤1.0 [–]Argon69
Table II–2.4–1 Argon 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]

68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]HPD(P)≤H≤HPDD(P) [J/kg]
68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]SPD(P)≤S≤SPDD(P) [J/(kg·K)]
68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]UPD(P)≤U≤UPDD(P) [J/kg]
68.75×103 ≤P≤4.998×106 [Pa]0.6875≤P≤49.98 [bar]VPD(P)≤V≤VPDD(P) [m3 /kg]
83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
HTD(T)≤H≤HTDD(T) [J/kg]
83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
STD(T)≤S≤STDD(T) [J/(kg·K)]
83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
UTD(T)≤U≤UTDD(T) [J/kg]
83.78≤T≤150.86 [K]−189.37≤T≤−122.29 [◦ C]
VTD(T)≤V≤VTDD(T) [m3 /kg]

70

P-PROPATH: Pure Substances and Mixtures with Fixed Composition[bar]*10 6 [Pa]1000

-122.29 -93.15
150.86 180

100-43.15
230

[C]
[K]

Argon

500

50

100

10

49.98

4.998

T = 6.476*10 -7 P + 147.62
P:[Pa], T:[K]Critical pointD( S e w- p
atu o
ra intte d cuva rvepor)

Pressure, P

T = 10 -6P + 130
P:[Pa], T:[K]0.6875 0.06875
0.1
0.01
83.78
-189.37200-73.15273.150500
226.85Temperature, T
Fig.II–2.4–1

Range of Arguments(P,T) for CPPT(P,T),CVPT(P,T),HPT(P,T),
SPT(P,T),UPT(P,T) and VPT(P,T).

1100 [K]826.85 [C]Argon71[bar]*10 6 [Pa]
1000

100

Argon

10

49.98

4.998

T = 6.476*10 -7 P + 147.62
P:[Pa], T:[K]T = 1100 K

100Critical point
or

50

tur

ate

ate
Sa tur

dl

iqu

d vap

id

500

Sa

Pressure, P

T = 10 -6P + 130
P:[Pa], T:[K]0.6875 0.06875
0.71

2

4

6

Enthalpy, H [J/kg]
Fig.II–2.4–2

Range of Arguments(P,H) for TPH(P,H).

8

*10 5

72

P-PROPATH: Pure Substances and Mixtures with Fixed Composition[bar]*10 6 [Pa]
1000

100

Argon

100

50

T = 6.476*10 -7 P + 147.62
P:[Pa], T:[K]10

Critical point

u

ate

ui d

Sat

S

r
atu

iq
dl

or

4.998
vap

49.98

d
rate

Pressure, P

500

T = 11 0 0 K

T = 10 -6P + 130
P:[Pa], T:[K]0.6875 0.06875
0

1

2

3

Entropy, S [J/(kg.K)]
Fig.II–2.4–3

Range of Arguments(P,S) for HPS(P,S) and TPS(P,S).

4

4.4

*10 3

Argon73[bar]*10 6 [Pa]
1000

100

Argon

50

T=

100

11 0 0K

T = 6.476*10-7 P + 147.62
P:[Pa], T:[K]10

Critical point
4.998
d liquid

49.98

0.6875 0.06875

Sa tu ra t

S a tu r a t e

Pressure, P

500

T = 10 -6P + 130
P:[Pa], T:[K]0.00071

0.005

ed va p or

0.01

Specific Volume, V [m3 /kg]
Fig.II–2.4–4

Range of Arguments(P,V) for TPV(P,V).

0.015