Ammonia–Water(Tillner-Roth and Friend)

511

2.2 Ammonia–Water(Tillner-Roth and Friend)
Thermodynamic properties are evaluated by the formulation of Tillner-Roth et al. [1]. This uses the waterequation of state by Pruss et al. [2] and ammonia equation of state by Tillner-Roth et al. [3]. No provision ismade for transport properties at this moment.
NoticeThis program has some problems in high pressure region. The calculation in the region may notterminate successfully from time to time.

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

2.2.2 The Names of Substance, Library File and Single Shot Program
Substance:
First Component:
Second Component:
Library File for UNIX:
Library File for DOS,Windows95/NT:
Single Shot Program for UNIX:
Single Shot Program for DOS,Windows95/NT:

Ammonia-Water Mixture
Ammonia
Water
libjawmx2.a
JAWMX2.LIB
awmx2-ss
AWMX2–SS.EXE

2.2.3 Important Constants and Others
Table IV-2.2-1 Molecular Formula,Relative Molecular Mass and Gas Constant
Molecular Formula
NH3
H2 O

Ammonia
Water

Relative Molecular Mass
17.03026kg/kmol
18.015268kg/kmol

Gas Constant
488.189×10 3J/(kg·K)
461.5189×10 3J/(kg·K)

Table IV-2.2-2 Critical ConstantAmmonia
Water

Critical temperature
405.40K
132.25 ◦C
647.096K
373.946 ◦C

Critical pressure
11.36×10 6Pa
113.6bar
22.064×10 6Pa
220.64bar

Critical speciﬁc volume
75.7×10 −3m3 /kmol
4.44×10 −3m3 /kg
55.9×10 −3m3 /kmol
3.11×10 −3m3 /kg

Table IV-2.2-3 Reference State Speciﬁed by KSTAN
KSTAN
0

1

othersValues of enthalpy (or internal energy) and entropy at the reference state
Comforms to reference[1]For saturated liquid at the triple-point temperature of both purecomponents , 273.16 K for water and 195.495 K for ammonia ,the internal energy and entropy have been set as :u=0 and s=0
Enthalpy and entropy of saturated liquid of pure ammonia at 273.15K
200kJ/kg and 1kJ/(kg·K), respectively
Enthalpy and entropy of saturated liquid of pure water at 273.15K
200kJ/kg and 1kJ/(kg·K), respectively
The same with when KSTAN=0

512

M-PROPATH: Binary Mixtures

2.2.4 Formula
No correction has been made to the original formulations.

2.2.5 Valid Range
0.01[bar]<p<400[bar]200[K]<T<620[K]2.2.6 Example of User’s PROGRAM UNIT
Sample Program 1
example1.for :
c
c
c
c
c

-------------------------------------------------This program calculateds temperature at bubble
points (p=10[bar])from z=0.0 to 1.0 [kg NH3/kg]
at every 0.1 [kg NH3/kg] interval.
-------------------------------------------------REAL T,P,Z,H,S
INTEGER I,JCALL KPAMES(1,1)
CALL STNKAS(1,1)

c
c
c
C

10

-------------------------------------------------bubble point pressure using
subtb.
-------------------------------------------------P=10.0
DO 10 I=0,10
Z=FLOAT(I)*0.1
CALL SUBTB(J,T,P,Z,V,H,S)
WRITE(*,*) Z,T
CONTINUE
STOP
END

C
c ------------------------------------------c Resultsc ------------------------------------------c 0.000000E+00 179.877300
c 1.000000E-01 149.922400
c 2.000000E-01 125.212800
c 3.000000E-01 101.825800
c 4.000000E-01 80.509940
c 5.000000E-01 62.563330
c 6.000000E-01 48.753480
c 7.000000E-01 39.080770
c 8.000000E-01 32.721220
c 9.000000E-01 28.394670
c
1.000000 24.894940

Sample Program 2
example2.for :cccc--------------------------------------------This program calculates the properties insaturated state at 5.0[bar], T=300[K]---------------------------------------------

Ammonia–Water(Tillner-Roth and Friend)

REAL T,P,X,Y,VL,VV,HL,HV,SL,SVINTEGER J
c
c
c
c
c

--------------------------------------------T=[K], P=[Pa]standard state=(bibliography [1])unit of quantity=[kmol]--------------------------------------------CALL KPAMES(0,1)
CALL STNKAS(0,0)

ccc--------------------------------------------Properties in saturated state--------------------------------------------P=5.0E5
T=300.0
CALL SUBXY(J,T,P,X,Y,VL,VV,HL,HV,SL,SV)
IF(J.NE.0) THEN
WRITE(*,*) ’ERROR IN SUBXY J=’,JELSE
HL=HL*1.0E-6
HV=HV*1.0E-6
SL=SL*1.0E-3
SV=SV*1.0E-3
WRITE(*,*) ’ X[kmol NH3/kmol]=’,X, ’ Y[kmol NH3/kmol]=’,Y
WRITE(*,*) ’VL[M^3/kmol]=’,VL,’ VV[M^3/kmol]=’,VV
WRITE(*,*) ’HL[MJ/kmol]=’,HL,’ HV[MJ/kmol]=’,HV
WRITE(*,*) ’SL[MJ/(kmol.K)] =’,SL,’ SV[MJ/(kmol.K)] =’,SV
ENDIF
STOP
END

C
c
----------------------------------------------------------------c Resultsc----------------------------------------------------------------c
X[kmol NH3/kmol]=
6.012722E-01 Y[kmol NH3/kmol]=
9.987947E-01
c
VL[M^3/kmol]=
2.212924E-02 VV[M^3/kmol]=
4.723189c
HL[MJ/kmol]=
1.458077 HV[MJ/kmol]=
28.437260c
SL[MJ/(kmol.K)] =18.430890 SV[MJ/(kmol.K)] =106.415300

2.2.7 Sample Output of Single Shot Program========================================================================|
Single Shot Program for Ammonia-Water Mixture,||an Application Program by M-PROPATH Ver.11.1||
Thermophysical Properties of Ammonia-Water Mixtures||----------------------------------------------------------------------|| ## First Menu ##|| No.
Current|| 1 --> Go to Second Menu|
| 2 --> Read Help|
| 3 --> Set Logfile[OFF]|| 0 --> Quit|========================================================================
Input No.
2This is help for this program (AWMX-SS2.EXE)
Nomenclature==== First Charactor ====
H : Enthalpy
P : Pressure

513

514

S : Entropy
T : Temperature
V : Volume
X : Ammonia Composition of Liquid
Y : Ammonia Composition of Vapor
Z : Total Composition of Ammonia==== Second Charactor ====
B : Bubble Point
D : Dew Point
L : Liquid
V : Vapor----- Hit RETURN Key ----========================================================================|
Single Shot Program for Ammonia-Water Mixture,||an Application Program by M-PROPATH Ver.11.1||
Thermophysical Properties of Ammonia-Water Mixtures||----------------------------------------------------------------------|| ## First Menu ##|| No.
Current|| 1 --> Go to Second Menu|
| 2 --> Read Help|
| 3 --> Set Logfile[OFF]|| 0 --> Quit|========================================================================
Input No.
3
1: Logfile ON
2: Logfile OFF
Input No.
1
Input Filename
AWMIX.LOG========================================================================|
Single Shot Program for Ammonia-Water Mixture,||an Application Program by M-PROPATH Ver.11.1||
Thermophysical Properties of Ammonia-Water Mixtures||----------------------------------------------------------------------|| ## First Menu ##|| No.
Current|| 1 --> Go to Second Menu|
| 2 --> Read Help|
| 3 --> Set Logfile[ON] SAMPLE.LOG|| 0 --> Quit|========================================================================
Input No.
1===============================================================| ## Second Menu ##|| <Single and Two Phase States>|| No. Input
Output|| 1 --(P,T,Z)-->H HL HV S SL SV V VL VV X Y QUALITY || 2 --(P,Z,H)--> T
HL HV S SL SV V VL VV X Y QUALITY || 3 --(P,Z,S)--> T H HL HVSL SV V VL VV X Y QUALITY || 4 --(P,Z,V)--> T H HL HV S SL SV
VL VV X Y QUALITY ||-------------------------------------------------------------|| <Two Phase State>|| 5 --(P,Z)----> X=Z : TB HB SB VB
Y=Z : TD HD SD VD|| 6 --(T,Z)----> X=Z : PB HB SB VB
Y=Z : PD HD SD VD|| 7 --(P,T)----> Coexisting Phases: X Y HL HV SL SV VL VV||-------------------------------------------------------------|| 8 -----------> Fundamental Constants|| 9 -----------> Conversion of Composition and Relative||
Molcular Mass of Mixture||10 -----------> Change System of Unit, and Standard Values of||Enthalpy and Entropy||99 -----------> Return to First Menu|
| 0 -----------> Quit|===============================================================

M-PROPATH: Binary Mixtures

Ammonia–Water(Tillner-Roth and Friend)

Input No.
10=======================================================
No.
current=======================================================
1 --> Pressure and Temperature[bar, C]2 --> Amount of Substance[kmol]
3 --> Standard Values of h and s [2]0 --> Return to Second Menu=======================================================
Input No.
1===============================
No. <Pressure> <Temperature>===============================
1 -->
Pa
K
2 -->
bar
C
3 -->
bar
K
4 -->
Pa
C
===============================
Input No.
2=======================================================
No.
current=======================================================
1 --> Pressure and Temperature[ bar, C]
2 --> Amount of Substance[kmol]
3 --> Standard Values of h and s [2]0 --> Return to Second Menu=======================================================
Input No.
2===========================No.
Amount of Substance
1 -->
kmol
2 -->
kg
===========================
Input No.
2=======================================================
No.
current=======================================================
1 --> Pressure and Temperature[ bar, C]
2 --> Amount of Substance[ kg ]
3 --> Standard Values of h and s [2]0 --> Return to Second Menu=======================================================
Input No.
3================================================
No.
Standard States and Values of h and s
1 --> As defined in :Reiner Tillner-Roth and Daniel G. Friend
A Helmholtz Free Energy Formulation of
the Thermodynamic Properties of the
Mixtures {Water + Ammonia}, Journal of
Physical and Chemical Reference Data,
27-1,(1996),pp63-96
2 --> Convention of International Institute ofRefrigeration(IIR):
h=200[kJ/kg], s=1.0[kJ/(kg*K)]
Saturated Pure Liquids at 0[C]================================================
Input No.
1

515

516

M-PROPATH: Binary Mixtures=======================================================
No.
current=======================================================
1 --> Pressure and Temperature[ bar, C]
2 --> Amount of Substance[ kg ]
3 --> Standard Values of h and s [1] T-Roth & Friend
0 --> Return to Second Menu=======================================================
Input No.
0===============================================================| ## Second Menu ##|contents not shown===============================================================
Input No.
9==================================================================
Conversion of Composition and Relative Molecular Mass of Mixture==================================================================
1: [kmol/kmol] --> [kg/kg]
and Relative Molecular Mass of Mixture
2: [kg/kg]--> [kmol/kmol] and Relative Molecular Mass of Mixture
0: Return to Second Menu
Input No.
1
Input Z[kmol/kmol]
0.5
Z =.50000000[kmol/kmol]
Z =.48594670[kg/kg]
Relative Molecular Mass of Mixture =17.52276000[kg/kmol]
Relative Molecular Mass of Ammonia =17.03026000[kg/kmol]
Relative Molecular Mass of Water=
18.01527000[kg/kmol]
1: [kmol/kmol] --> [kg/kg]
and Relative Molecular Mass of Mixture
2: [kg/kg]--> [kmol/kmol] and Relative Molecular Mass of Mixture
0: Return to Second Menu
Input No.
2
Input Z[kg/kg]
0.5
Z =.50000000[kg/kg]
Z =.51405330[kmol/kmol]
Relative Molecular Mass of Mixture =17.50892000[kg/kmol]
Relative Molecular Mass of Ammonia =17.03026000[kg/kmol]
Relative Molecular Mass of Water=
18.01527000[kg/kmol]
1: [kmol/kmol] --> [kg/kg]
and Relative Molecular Mass of Mixture
2: [kg/kg]--> [kmol/kmol] and Relative Molecular Mass of Mixture
0: Return to Second Menu
Input No.
0===============================================================| ## Second Menu ##|contents not shown===============================================================
Input No.
8=======================
Fundamental Constants=======================<Constants>
Relative Molecular Mass
Gas Constants
Critical Temperature
Critical Pressure<Ammonia>
17.03026000
488.18900000
405.40000000
132.25000000
113.60000000<Water>18.01527000
461.51890000
647.09600000
373.94600000
220.64000000[kg/kmol][J/(kg*K)]
[K]
[C]
[bar]

Ammonia–Water(Tillner-Roth and Friend)

Critical Volume.75690050E-01.44444450E-02

517.55948040E-01.31055900E-02[m**3/kmol][m**3/kg]----- Hit RETURN Key ----===============================================================| ## Second Menu ##|contents not shown===============================================================
Input No.
1======================================(P,T,Z) --> H, S, V, QUALITY
X, HL, SL, VL
Y, HV, SV, VV======================================
Input P[bar](P=0 : Second Menu)
1
Input T[C]200
Input Z[kg/kg]
0.5
T =200.00000000[C]P =1.00000000[bar]Z =.50000000[kg/kg]
H =2481.23400000[kJ/kg]
S =8.30849400[kJ/(kg.K)] V =.22386150E+01[m**3/kg]
Vapor Region
Input P[bar](P=0 : Second Menu)
1
Input T[C]50.0
Input Z[kg/kg]
0.5
T =50.00000000[C]P =Z =.50000000[kg/kg]
H =S =3.75734900[kJ/(kg*K)] V =X =.18624860[kg/kg]
Y =HL =130.32380000[kJ/kg]
HV =
SL =
912.73970000[J/(kg*K)]
SV =
VL =
.10951560E-02[m**3/kg]VV =QUALITY =.43924260[kg/kg]

1.00000000[bar]875.56820000[kJ/kg].68341210E+00[m**3/kg].90054950[kg/kg]
1826.98200000[kJ/kg]
7.38890700[kJ/(kg*K)].15544890E+01[m**3/kg]

Input P[bar](P=0 : Second Menu)
0===============================================================| ## Second Menu ##|contents not shown===============================================================
Input No.
2======================================(P,Z,H) --> T, S, V, QUALITY
X, HL, SL, VL
Y, HV, SV, VV======================================
Input P[bar](P=0 : Second Menu)
1
Input Z[kg/kg]
0.5
Input H[kJ/kg]
2500.
T =
208.52500000[C]P =Z =.50000000[kg/kg]
H =S =8.34784100[kJ/(kg*K)] V =Vapor Region

1.00000000[bar]2500.00000000[kJ/kg].22795030E+01[m**3/kg]

Input P[bar](P=0 : Second Menu)
0===============================================================| ## Second Menu ##|518

M-PROPATH: Binary Mixturescontents not shown===============================================================
Input No.
3======================================(P,Z,S) --> T, H, V, QUALITY
X, HL, SL, VL
Y, HV, SV, VV======================================
Input P[bar](P=0 : Second Menu)
1
Input Z[kg/kg]
0.5
Input S[k/(kg*K)]0.3
T =-11.38488000[C]P =Z =.50000000[kg/kg]
H =S =300.00000000[J/(kg*K)]V =Liquid Region

1.00000000[bar]-133.57350000[kJ/kg].11689280E-02[m**3/kg]

Input P[bar](P=0 : Second Menu)
0===============================================================| ## Second Menu ##|contents not shown===============================================================
Input No.
4========================================(P,Z,V) --> T, H, S, QUALITY
X, HL, SL, VL
Y, HV, SV, VV========================================
Input P[bar](P=0 : Second Menu)
1.0
Input Z[kg/kg]
0.5
Input V[m**3/kg]
2.
T =150.39830000[C]P =Z =.50000000[kg/kg]
H =S =8.06802600[kJ/(kg*K)] V =Vapor Region

1.00000000[bar]2373.50700000[kJ/kg].20000000E+01[m**3/kg]

Input P[bar](P=0 : Second Menu)
0===============================================================| ## Second Menu ##|contents not shown===============================================================
Input No.
5===============================================(P,Z) --> X=Z : TB, HB, SB, VB
Y=Z : TD, HD, SD, VD===============================================
Input P[bar](P=0 : Second Menu)
1.0
Input Z[kg/kg]
0.5
P =5.00000000[bar]Z =.50000000[kg/kg]
TB =38.31616000[C]TD =128.34460000[C]HB =93.85913000[kJ/kg]
HD =2303.77000000[kJ/kg]
SB =1.09321100[kJ/(kg*K)] SD =7.14666800[kJ/(kg*K)]
VB =.12341500E-02[m**3/kg]
VD =.36748830E+00[m**3/kg]
Input P[bar]0(P=0 : Second Menu)

Ammonia–Water(Tillner-Roth and Friend)519===============================================================| ## Second Menu ##|contents not shown===============================================================
Input No.
6===============================================(T,Z) --> X=Z : PB, HB, SB, VB
Y=Z : PD, HD, SD, VD===============================================
Input Z[kg/kg](Z < 0 : Second Menu)
0.5
Input T[K]80.0
T =80.00000000[C]Z =.50000000[kg/kg]
PB =15.33406000[bar]PD =.92550240[bar]HB =293.33660000[kJ/kg]
HD =2224.19800000[kJ/kg]
SB =1.69010100[kJ/(kg*K)] SD =7.71905800[kJ/(kg*K)]
VB =.13032530E-02[m**3/kg]
VD =.17920140E+01[m**3/kg]
Input Z[kg/kg](Z < 0 : Second Menu)-1===============================================================| ## Second Menu ##|contents not shown===============================================================
Input No.
7==============================================(P,T) --> Coexisting Phases
X, HL, SL, VL
Y, HV, SV, VV==============================================
Input P[bar](P=0 : Second Menu)
1.0
Input T[C]50.
T =50.00000000[C]P =1.00000000[bar]X =.18624860[kg/kg]
Y =.90054950[kg/kg]
HL =130.32380000[kJ/kg]
HV =1826.98200000[kJ/kg]
SL =912.73970000[J/(kg*K)]
SV =7.38890700[kJ/(kg*K)]
VL =.10951560E-02[m**3/kg]
VV =.15544890E+01[m**3/kg]
Input P[bar](P=0 : Second Menu)
0===============================================================| ## Second Menu ##|contents not shown===============================================================
Input No.
0***** See You Again ! *****
Stop - Program terminated.

References[1] R. Tillner-Roth and D. G. Friend, Helmholtz free energy formulation of the thermodynamic properties ofthe mixture { water+ammonia } , Journal of Physical and Chemical Reference Data,27-1,(1996),pp63-96[2] A. Pruss und W. Wagner, Eine neue Fundamental-gleichung fuer das ﬂuide Zustandsgebiet von Wasser
fuer Temperaturen von der Schmelzlinie bis zu 1273 K bei Druecken bis zu 1000MPa, Fortschr.-Ber. VDI
6,No.(320) (VDI verlag Duesseldorf)(1995)[3] R. Tillner-Roth, Harms-Watzenberg und H. D. Bachr, Eine neue Fundamentalgleichung fuer Ammoniak,

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Proc. 20th DKV-Tagung Heidelberg, Germany, vol,167(1993)