208

P-PROPATH: Pure Substances and Mixtures with Fixed Composition

2.21 Ammonia (Tillner–Roth, Harms–Watzenberg andBaehr)
Equations for thermodynamic properties are based on Tillner–Roth, Harms–Watzenberg and Baehr [1]. The
Equation for viscosity has been cited from Fenghour, Wakeham, Vesovic, Watson, Millat and Vogel [2], that forthermal conductivity from Yata [3], and that for surface tension from Liley and Desai [4].

2.21.1 Temperature Scale
International temperature scale 1990 (ITS-1990)

2.21.2 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:

Ammonialibjnh32.a
JNH32.LIB
nh32-ss
NH32–SS.EXE

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

NH3
17.03026
488.189 J/(kg·K)

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

11.36×10 6Pa (113.6 bar)405.40 K (132.25 ◦C)
4.444×10 −3m3 /kg

Triple Point:
Pressure:
Temperature:

6.063×10 3 Pa (0.06063 bar)
195.495 K (−77.655 ◦C)

Reference State:
At 273.15 K (0◦ C), 200 kJ/kg and 1 kJ/(kg·K) are assigned to the speciﬁc enthalpy and speciﬁc entropy ofsaturated liquid, respectively.

2.21.4 Formula
Equation of State:
Equations (1)–(4) in a function form of Φ = Φ(τ, δ) in reference [1]. Here Φ=speciﬁc helmholtz free energy,τ = 405.40/T , δ = ρ/225, T = temperature (K), ρ = density (kg/m3 ).
Properties at Vapor-Liquid Equilibrium:
The properties at Vapor–Liquid Equilibrium are calculated by Phase–equilibrium condition (Maxwell criterion).
All of those have been cited from reference [1].
Transport Properties:
Viscosiy, thermal conductivity and surface tension are cited from reference [2], [3] and [4], respectively.

References

Ammonia (Tillner–Roth, Harms–Watzenberg and Baehr)

209[1] R. Tillner–Roth, F. Harms–Watzenberg and H. D. Baehr, Eine neue Fundamentalgleichung für Ammoniakm, Proc. 20th DKV–Tagung Heidelberg, Germany, Vol. II, (1993), pp.167[2] A. Fenghour, W. A. Wakeham, V. Vesovic, J. T. R. Watson, J. Millat and E. Vogel, J. Phys. Chem. Ref.
Data, Vol. 24, 5, (1995), pp.1649.
[3] J. Yata, Private communication.
[4] P. E. Liley and P. D. Desai, Thermophysical Properties of Refrigerants (Inch–Pound Edition), American
Society of Heating, Refrigerating and Air-Conditioning Engineers, (1993), pp.204.

210

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.21–1 Ammonia Function

No.
194
8A
8B
82
8C
8D
234

Name ofFunction
AIPPT(P,T)
AJTPT(P,T)
AKPD(P)AKPDD(P)AKPT(P,T)
AKTD(T)
AKTDD(T)
ALAPP(P)
ALAPT(T)
ALHP(P)

5

ALHT(T)

6

ALMPD(P)7

ALMPDD(P)8

ALMPT(P,T)

Function and Argument(s)Range of Argument(s)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)]
ALMPDD: Thermal Conductivity of Saturated
Vapor [W/(m·K)]
ALMPT: Thermal Conductivity [W/(m·K)]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦ C]

6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦ C]
40.8339×103 ≤P≤10.4652×106 [Pa]0.408339≤P≤104.652 [bar]40.8339×103 ≤P≤9.71034×106 [Pa]0.408339≤P≤97.1034 [bar]0<P≤50.0×106 [Pa]223.15≤T≤573.15 [K]
0<P≤500 [bar]-50.0≤T≤300 [◦ C]

9

ALMTD(T)10

ALMTDD(T)11

AMUPD(P)12

AMUPDD(P)13

AMUPT(P,T)

14

AMUTD(T)15

AMUTDD(T)92909193
1617181920

BPPT(P,T)
BSPT(P,T)
BTPT(P,T)
BVPT(P,T)
CPPD(P)CPPDD(P)CPPT(P,T)
CPTD(T)
CPTDD(T)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]

out of range:
395.0 < T < 430.0 [K]
112.5 < ρ < 337.5 [kg/m3 ]223.15≤T≤401.064 [K]-50.0≤T≤127.914 [◦C]
223.15≤T≤396.8669 [K]-50.0≤T≤123.7169 [◦C]
6.06×103 ≤P≤11.36×106 [Pa]6.06×10−2 ≤P≤113.6 [bar]6.06×103 ≤P≤11.36×106 [Pa]6.06×10−2 ≤P≤113.6 [bar]0<P≤50.0×106 [Pa]196.0≤T≤700.0 [K]
0<P≤500 [bar]-77.15≤T≤426.85 [◦C]
196.0≤T≤405.40 [K]-77.15≤T≤132.25 [◦C]
196.0≤T≤405.40 [K]-77.15≤T≤132.25 [◦C]

Ammonia (Tillner–Roth, Harms–Watzenberg and Baehr)

211

Table II–2.21–1 Ammonia Function (cont’d)

No.
21

Name ofFunction
CRP(‘A’)

7A
76
77
7A
78
2A
2B
222C
2D
89

CVPD(P)
CVPDD(P)
CVPT(P,T)
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’)

Function and Argument(s)Range of Argument(s)CRP: Critical ConstantsP∗: ‘A’=‘P’: 11.36×106 [Pa], 113.6 [bar] PressureT∗: ‘A’=‘T’: 405.4 [K], 132.25 [◦ C] Temperature
V: ‘A’=‘V’: 4.444×10−3 [m3 /kg] Speciﬁc Volume

one of ‘P’, ‘T’ and ‘V’

FC: Fundamental Constants
M: ‘A’=‘M’: 17.03026 Relative Molecular Mass
R: ‘A’=‘R’: 488.189 [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)]

6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]0<P≤1000×106 [Pa]SPT(P,196K)≤S≤
SPT(P,700K) [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’: ‘NH3’ Molecular Formula
S: ‘A’=‘S’: ‘AMMONIA’ Name of Substance
V: ‘A’=‘V’: ‘10.1’ Version Number

0<P≤10000 [bar]SPT(P,−77.15◦ C)≤S≤
SPT(P,426.85◦ C) [J/(kg·K)]
0<P≤1000×106 [Pa]196≤T≤700 [K]
0<P≤10000 [bar]−77.15≤T≤426.85 [◦ C]
6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]0≤X≤1.0 [–]195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦ C]
195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦ C]
195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦ C]
0≤X≤1.0 [–]one of ‘C’, ‘S’ and ‘V’212

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.21–1 Ammonia Function (cont’d)

No.
66
68
85
86
81
87
88
99
30

Name ofFunction
PLDT(T)
PMLT(T)
PRPD(P)PRPDD(P)
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)

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

195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦ 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]

10.8207×103 ≤P≤11.36×106 [Pa]10.8207×10−2 ≤P≤113.6 [bar]203.0≤T≤405.40 [K]-70.15≤T≤132.25 [◦ C]
6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [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]
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]

6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]0<P≤1000×106 [Pa]196≤T≤700 [K]
0<P≤10000 [bar]−77.15≤T≤426.85 [◦ C]
6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]0≤X≤1.0 [–]195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦ C]
195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦ C]
195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦ C]
0≤X≤1.0 [–]0<P≤1000×106 [Pa]
HPT(P,196K)≤H≤
HPT(P,700K) [J/kg]
0<P≤10000 [bar]HPT(P,−77.15◦C)≤H≤
HPT(P,426.85◦ C) [J/kg]

6H

TPH2(P,H)

Ammonia (Tillner–Roth, Harms–Watzenberg and Baehr)

213

Table II–2.21–1 Ammonia Function (cont’d)

No.
65

Name ofFunction
TPS(P,S)

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

Range of Argument(s)0<P≤1000×106 [Pa]SPT(P,196K)≤S≤
SPT(P,700K) [J/(kg·K)]
0<P≤10000 [bar]SPT(P,−77.15◦ C)≤S≤
SPT(P,426.85◦ C) [J/(kg·K)]

6S
98
70

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)79

UPS(P,S)

44

UPT(P,T)45

UPX(P,X)

46

UTD(T)

47

UTDD(T)

TPV∗: Temperature [K], [◦ C]
P∗: Pressure [Pa], [bar]V: Speciﬁc Volume [m3 /kg]

TRPL∗: Properties at Triple PointP∗: ‘A’=‘P’: 6.063×103 [Pa], 0.06063 [bar]PressureT∗: ‘A’=‘T’: 195.495 [K], −77.655 [◦ C]
Temperature0<P≤1000×106 [Pa]VPT(P,196K)≤V≤
VPT(P,700K) [m3 /kg]
0<P≤10000 [bar]VPT(P,−77.15◦C)≤V≤
VPT(P,426.85◦ C) [m3 /kg]
one of ‘P’ and ‘T’

TSP∗: Saturation Temperature [K], [◦C]P∗: Pressure [Pa], [bar]6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [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)]

6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [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 [–]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]

6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]0<P≤1000×106 [Pa]SPT(P,196K)≤S≤
SPT(P,700K) [J/(kg·K)]
0<P≤10000 [bar]SPT(P,−77.15◦ C)≤S≤
SPT(P,426.85◦ C) [J/(kg·K)]
0<P≤1000×106 [Pa]196≤T≤700 [K]
0<P≤10000 [bar]−77.15≤T≤426.85 [◦ C]
6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]0≤X≤1.0 [–]195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦ C]
195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦ C]

214

P-PROPATH: Pure Substances and Mixtures with Fixed Composition
Table II–2.21–1 Ammonia Function (cont’d)

No.
48

Name ofFunction
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
8G
8H
56

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

57XPS(P,S)

58

XPU(P,U)59

XPV(P,V)60

XTH(T,H)

61

XTS(T,S)

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

195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦C]
0≤X≤1.0 [–]6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]0<P≤1000×106 [Pa]SPT(P,196K)≤S≤
SPT(P,700K) [J/(kg·K)]

VPT: Speciﬁc Volume [m3/kg]
P∗: Pressure [Pa], [bar]T∗: Temperature [K], [◦C]

0<P≤10000 [bar]SPT(P,−77.15◦ C)≤S≤
SPT(P,426.85◦ C) [J/(kg·K)]
0<P≤1000×106 [Pa]196≤T≤700 [K]

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 [–]0<P≤10000 [bar]−77.15≤T≤426.85 [◦ C]
6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]0≤X≤1.0 [–]195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦C]
195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦C]
195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦C]
0≤X≤1.0 [–]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)]

6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]HPD(P)≤H≤HPDD(P) [J/kg]
6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]SPD(P)≤S≤SPDD(P) [J/(kg·K)]
6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]UPD(P)≤U≤UPDD(P) [J/kg]
6.063×103 ≤P≤11.36×106 [Pa]0.06063≤P≤113.6 [bar]VPD(P)≤V≤VPDD(P) [m3 /kg]
195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦C]
HPD(T)≤H≤HPDD(T) [J/kg]
195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦C]
SPD(T)≤S≤SPDD(T) [J/(kg·K)]

Ammonia (Tillner–Roth, Harms–Watzenberg and Baehr)

215

Table II–2.21–1 Ammonia Function (cont’d)No.
62

Name ofFunction
XTU(T,U)63

XTV(T,V)

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

195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦C]
UPD(T)≤U≤UPDD(P) [J/kg]
195.495≤T≤405.4 [K]−77.655≤T≤132.25 [◦C]
VPD(T)≤V≤VPDD(T) [m3 /kg]