Nitrogen105

2.10 Nitrogen
Equations for thermodynamic properties have been cited from the IUPAC Tables[1], those for transport properties from Stephan et al.[2], and those for other properties from Jacobsen et al.[3].

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

2.10.2 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:

Nitrogenlibjn2.a
JN2.LIBn2-ss
N2–SS.EXE

2.10.3 Important Constants and Others
Molecular Formula:
Relative Molecular Mass:
Gas Constant:N2
28.0134
296.8115 J/(kg·K)

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

3.4000×10 6Pa (34.000 bar)126.20 K (−146.95 ◦C)
3.1847×10 −3m3 /kg

Triple Point:
Pressure:
Temperature:

0.01253×10 6Pa (0.1253 bar)
63.148 K (−210.002 ◦C)

Reference State:
At 1.01325 bar(1 atm) and 25◦C(298.15 K), 0 J/(kg·K) is assigned to the speciﬁc entropy of the ideal gas. At
25◦ C(298.15 K), 0 J/kg is assigned to the speciﬁc enthalpy of the ideal gas.

2.10.4 Formula
Equation of State:
Equation (9) in a function form of P = P (ρ, T ) in reference [1]. Here P =pressure, ρ=density and T =Temperature.

Vapor Pressure:
Equation (2) in reference [1].
Properties at Vapor-Liquid Equilibrium:
Equations (2) and (9) for speciﬁc volume, equation (12) for speciﬁc enthalpy, equation (15) for speciﬁc entropy
and equation (19) for isobaric speciﬁc heat, respectively. All of these have been cited from reference [1]. However,
the third term in the right side of equation (19),32

Cp (ρ, T ) = Cpid(T ) − R + R[

Ni (XC)i ]w
0 +···i=1

106

P-PROPATH: Pure Substances and Mixtures with Fixed Composition

has been corrected to32

Cp (ρ, T ) = Cpid(T ) − R − R[

Ni (XC)i ]w
0 +···
i=1

Pressure and Temperature on Melting Line:
Equation (1) in reference [1].
Transport Properties:
Viscosity and thermal conductivity from Equations (1) and (5) in reference [2], respectively.
The Other Properties:
Surface tension and static dielectric constant from equations (19) and (20) in reference [3], respectively.

References[1] S.Angus, B.Armstrong and K.M.de Reuck, Nitrogen International Thermodynamic Table of the Fluid
State-6, IUPAC, (1979).
[2] K.Stephan, R.Krauss and A.Laesecke, J. Phys. Chem. Ref. Data, 16–4, (1987), pp.993–1023.
[3] R.T.Jacobsen, R.B.Stewart, R.D.McCarty and H.J.M. Hanley, N.B.S. Technical Note 648, (December,1973).

Nitrogen107
Table II–2.10–1

No.
1
94

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

Nitrogen Function

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

Range of Argument(s)12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦ C]

8A
8B
82

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

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

12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦ 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)10

ALMTDD(T)11

AMUPD(P)12

AMUPDD(P)13

AMUPT(P,T)

14

AMUTD(T)15

AMUTDD(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]
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]

12.53×103 ≤P<3.4×106 [Pa]0.1253≤P<34 [bar]63.148≤T<126.2 [K]−210.002≤T<−146.95 [◦ C]
12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
12.53×103 ≤P<3.4×106 [Pa]0.1253≤P<34 [bar]12.53×103 ≤P<3.4×106 [Pa]0.1253≤P<34 [bar]12.53×103 ≤P≤100×106 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤1000 [bar]TMLP(P)≤T≤826.85 [◦ C]
63.148≤T<126.2 [K]−210.002≤T<−146.95 [◦ C]
63.148≤T<126.2 [K]−210.002≤T<−146.95 [◦ C]
12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]12.53×103 ≤P≤100×106 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤1000 [bar]TMLP(P)≤T≤826.85 [◦ C]
63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]

108

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.10–1

No.
92

90

91

93

Name of
Function
BPPT(P,T)

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’)

7A
76

CVPD(P)
CVPDD(P)77

CVPT(P,T)

Nitrogen Function (cont’d)

Function and Argument(s)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’: 30.703×103 [J/kg] Speciﬁc EnthalpyP∗: ‘A’=‘P’: 3.4×106 [Pa], 34.0 [bar] Pressure
S: ‘A’=‘S’: 4.2266×103 [J/(kg·K)] Speciﬁc EntropyT∗: ‘A’=‘T’: 126.2 [K], −146.95 [◦ C] Temperature
V: ‘A’=‘V’: 3.1847×10−3 [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)12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦ C]
12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦ C]
12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦ C]
12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦ C]
12.53×103 ≤P<3.4×106 [Pa]0.1253≤P<34 [bar]12.53×103 ≤P<3.4×106 [Pa]0.1253≤P<34 [bar]12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦ C]
63.148≤T<126.2 [K]−210.002≤T<−146.95 [◦ C]
63.148≤T<126.2 [K]−210.002≤T<−146.95 [◦ C]
one of ‘H’, ‘P’, ‘S’, ‘T’ and ‘V’

12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦ C]

7B
78

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

63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]

Nitrogen

109
Table II–2.10–1

No.
2A
2B
22

Name of
Function
EPSPD(P)EPSPDD(P)EPSPT(P,T)

Nitrogen Function (cont’d)

Function and Argument(s)EPSPT: Static Dielectric Constant [–]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

Range of Argument(s)12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1000 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤726.85 [◦C]

2C
2D
89

EPSTD(T)EPSTDD(T)FC(‘A’)9A
96

GAMPD(P)GAMPDD(P)95

GAMPT(P,T)

FC: Fundamental Constants
M: ‘A’=‘M’: 28.0134 Relative Molecular Mass
R: ‘A’=‘R’: 296.8115 [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]

12.53×103 ≤P≤3.398×106 [Pa]0.1253≤P≤33.98 [bar]12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦C]

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)

29

HTX(T,X)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)]

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 [–]63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]12.53×103 ≤P≤109 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,1100K) [J/(kg·K)]
0.1253≤P≤10000 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,826.85◦ C) [J/(kg·K)]
12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦C]
12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]0≤X≤1.0 [–]63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
0≤X≤1.0 [–]110

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.10–1

No.
84

Name of
Function
IDENTF(‘A’)

66
68

PLDT(T)
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)35

SPT(P,T)36

SPX(P,X)

37

STD(T)38

STDD(T)

39

STX(T,X)

67
69

TLDP(P)
TMLP(P)

Nitrogen Function (cont’d)

Function and Argument(s)Range of Argument(s)IDENTF: CHARACTER TYPE FUNCTION
for Package Identiﬁcation (Length 20)
C: ‘A’=‘C’: ‘N2’ Molecular Formula
S: ‘A’=‘S’: ‘NITROGEN’ Name of Substance
V: ‘A’=‘V’: ‘10.1’ Version Number

one of ‘C’, ‘S’ and ‘V’

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]

63.148≤T≤190.4 [K]−210.002≤T≤−82.75 [◦ C]
12.53×103 ≤P<3.4×106 [Pa]0.1253≤P<34 [bar]12.53×103 ≤P<3.4×106 [Pa]0.1253≤P<34 [bar]12.53×103 ≤P≤100×106 [Pa]TMLP(P)≤T≤1100 [K]

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

0.1253≤P≤1000 [bar]TMLP(P)≤T≤826.85 [◦C]
63.148≤T<126.2 [K]−210.002≤T<−146.95 [◦ C]
63.148≤T<126.2 [K]−210.002≤T<−146.95 [◦ C]

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

63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ 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]

12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [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 [–]TMLP∗: Temperature on Melting Curve [K], [◦C]P∗: Pressure [Pa], [ bar]

12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦C]
12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]0≤X≤1.0 [–]63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
0≤X≤1.0 [–]12.53×103 ≤P≤109 [Pa]0.1253≤P≤10000 [bar]Nitrogen111
Table II–2.10–1

No.
64

Name of
Function
TPH(P,H)

Nitrogen Function (cont’d)

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

Range of Argument(s)12.53×103 ≤P≤109 [Pa]
HPT(P,TMLP(P))≤H≤
HPT(P,1100K) [J/kg]
0.1253≤P≤10000 [bar]HPT(P,TMLP(P))≤H≤
HPT(P,826.85◦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)]

12.53×103 ≤P≤109 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,1100K) [J/(kg·K)]
0.1253≤P≤10000 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,826.85◦ 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

UPT(P,T)45

UPX(P,X)

46

UTD(T)TPSEUP: Pseudo Boiling Point [K], [◦ C]
T∗: Temperature [K], [◦ C]
TPV∗: Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]V: Speciﬁc Volume [m3 /kg]

TRPL∗: Properties at Triple PointP∗: ‘A’=‘P’: 12.53×103 [Pa], 0.1253 [bar] PressureT∗: ‘A’=‘T’: 63.148 [K], −210.002 [◦ C] Temperature

3.4×106 <P≤100×106 [Pa]34<P≤1000 [bar]12.53×103 ≤P≤109 [Pa]VPT(P,TMLP(P))≤V≤
VPT(P,1100K) [m3 /kg]
0.1253≤P≤10000 [bar]VPT(P,TMLP(P))≤V≤
VPT(P,826.85◦C) [m3 /kg]
one of ‘P’ and ‘T’

TSP∗: Saturation Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [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)]

12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [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 [–]UTD: Speciﬁc Internal Energy of Saturated
Liquid [J/kg]
T∗: Temperature [K], [◦ C]

12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]12.53×103 ≤P≤109 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,1100K) [J/(kg·K)]
0.1253≤P≤10000 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,826.85◦ C) [J/(kg·K)]
12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦ C]
12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]0≤X≤1.0 [–]63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦C]

112

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.10–1

No.
47

Name of
Function
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)

Nitrogen Function (cont’d)

Function and Argument(s)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 [–]WPT: Velocity of Sound [m/s]P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

Range of Argument(s)63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
0≤X≤1.0 [–]12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]12.53×103 ≤P≤109 [Pa]SPT(P,TMLP(P))≤S≤
SPT(P,1100K) [J/(kg·K)]
0.1253≤P≤10000 [bar]SPT(P,TMLP(P))≤S≤
SPT(P,826.85◦ C) [J/(kg·K)]
12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦C]
12.53×103 ≤P≤3.4×106 [Pa]0.1253≤P≤34 [bar]0≤X≤1.0 [–]63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
63.148≤T≤126.2 [K]−210.002≤T≤−146.95 [◦ C]
0≤X≤1.0 [–]12.53×103 ≤P≤109 [Pa]TMLP(P)≤T≤1100 [K]
0.1253≤P≤10000 [bar]TMLP(P)≤T≤826.85 [◦C]

8G
8H
56

WTD(T)WTDD(T)
XPH(P,H)57

XPS(P,S)58

XPU(P,U)

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]

12.53×103 ≤P<3.4×106 [Pa]0.1253≤P<34 [bar]HPD(P)≤H≤HPDD(P) [J/kg]
12.53×103 ≤P<3.4×106 [Pa]0.1253≤P<34 [bar]SPD(P)≤S≤SPDD(P) [J/(kg·K)]
12.53×103 ≤P<3.4×106 [Pa]0.1253≤P<34 [bar]UPD(P)≤U≤UPDD(P) [J/kg]

Nitrogen

113
Table II–2.10–1

No.
59

Name of
Function
XPV(P,V)60

XTH(T,H)

61

XTS(T,S)62

XTU(T,U)63

XTV(T,V)

Nitrogen Function (cont’d)

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

12.53×103 ≤P<3.4×106 [Pa]0.1253≤P<34 [bar]VPD(P)≤V≤VPDD(P) [m3 /kg]
63.148≤T<126.2 [K]−210.002≤T<−146.95 [◦C]HTD(T)≤H≤HTDD(T) [J/kg]
63.148≤T<126.2 [K]−210.002≤T<−146.95 [◦C]
STD(T)≤S≤STDD(T) [J/(kg·K)]
63.148≤T<126.2 [K]−210.002≤T<−146.95 [◦C]UTD(T)≤U≤UTDD(T) [J/kg]
63.148≤T<126.2 [K]−210.002≤T<−146.95 [◦C]
VTD(T)≤V≤VTDD(T) [m3 /kg]