E v a l u a t i o n o f t h e r m o d y n a m i c p r o p e r t i e s o f a m m o n i a -w a t e r m i x t u r e u p t o 1 0 0 b a r f o r p o w e r a p p l i c a t i o ns y s t e m sN . S h a n k a r G a n e s h * a n d T . S r i n i v a s
Vellore Institute of Technology, Vellore-632014, India.
Accepted September 13, 2010
I n K a l i n a p o w e r g e n e r a t i o n , a s w e l l a s v a p o r a b s o r p t i o n a n d r e f r i g e r a t i o n s y s t e m s a m m o n i a - w a t e rm i x t u r e h a s b e e n u s e d a s w o r k i n g f l u i d s . I n t h i s w o r k , n e w M a t L a b c o d e w a s d e v e l o p e d t o c a l c u l a t e t h et h e r m o d y n a m i c p r o p e r t i e s w h i c h w i l l b e u s e d t o s i m u l a t e K a l i n a c y c l e . T h e p r o g a m d e v e l o p e d i nM a t L a b g i v e s f a s t c a l c u l a t i o n o f t h e t h e r m o d y n a m i c p r o p e r t i e s . T h e c o r r e l a t i o n s p r o p o s e d b y Z i e g l e ra n d T r e p p 1 9 8 4 ) , P a t e k a n d K l o m f a r 1 9 9 5 ) a n d S o l e i m a n i 2 0 0 7 ) w e r e u s e d t o c a l c u l a t e t h e p r o p e r t yd i a g r a m s i n M a t L a b . T h e s o l v e d p r o p e r t i e s a r e b u b b l e p o i n t t e m p e r a t u r e , d e w p o i n t t e m p e r a t u r e ,s p e c i f i c e n t h a l p y , s p e c i f i c e n t r o p y , s p e c i f i c v o l u m e a n d e x e r g y . A f l o w c h a r t w a s d e v e l o p e d t ou n d e r s t a n d t h e c o m p u t a t i o n o f t h e p r o p e r t i e s . T h e p r o p e r t y c h a r t t h a t i s e n t h a l p y - c o n c e n t r a t i o n ,e n t r o p y - c o n c e n t r a t i o n , t e m p e r a t u r e - c o n c e n t r a t i o n a n d e x e r g y - c o n c e n t r a t i o n c h a r t s h a v e b e e np r e p a r e d . T h e p r e s e n t w o r k c a n b e u s e d t o s i m u l a t e t h e p o w e r g e n e r a t i n g s y s t e m s t o g e t t h e f e a s i b i l i t yo f t h e p r o p o s e d i d e a s u p t o 1 0 0 b a r . T h i s w o r k c a n b e u s e d t o c a r r y o u t t h e e x e r g y a n a l y s i s o f K a l i n ap o w e r c y c l e s .K e y o r d s : Ammonia-water mixture, thermodynamic, power generation.
B A C K G R O U N DIn ammonia-water mixture, ammonia has got low boilingpoint which makes it useful for utilizing the waste heatsource and makes the possibility of boiling at lowtemperature. Ammonia-water mixture as non-azeotropic(for a non-azeotropic mixture, the temperature andcomposition continuously change during boiling) nature
will have the tendency to boil and condense at a range oftemperatures which possess a closer match betweenheat source and working fluid mixture. As ammonia havegot a similar molecular weight as that of water, it makes itpossible to utilize the standard steam turbinecomponents.
For determining the thermodynamic properties ofammonia-water mixtures, various studies were published.
Ziegler and Trepp (1984) described an equation for thethermodynamic properties of ammonia-water mixture inabsorption units. In his work, the Gibbs excess energyequation was utilized for determining the specificenthalpy, specific entropy and specific volume. Theydeveloped the properties up to a pressure of 50 bar and
temperature of 500 K. Barhoumi et al. (2004) presentsmodelling of the thermodynamic properties. Feng andYogi (1999) combine the Gibbs free energy method formixture properties and the bubble and dew pointtemperature equations for phase equilibrium were usedPatek and Klomfar (1995) give a fast calculation ofthermodynamic properties. Senthil and Subbarao (2008present fast calculation for determining enthalpy andentropy of the mixtures.
The main objectives of the present work are to combinecorrelations proposed by Ziegler et al. (1984) and carriedout in MatLab, which avoids numerous procedure and
u b b l e p o i n t l i n eD e w p o i n t l i n e
S u b c o o l e d l i q u i d
S u p e r h e a t e d v a p o r
F i g u r e 1 . Equilibrium temperature-concentration curve for NH3- H2O at constant pressure.
time interval in obtaining the result. The presented workcan be used for energy and exergy solutions to powergenerating systems. The exergy details and itsconcentration graph for the ammonia-water mixtures arenot reported out in the literature, which is the gapidentified and presented at various pressures.
T H E R M O D Y N A M I C E V A L U A T I O N O F N H 3 - H 2 O M I X T U R EP R O P E R T I E SFor ammonia-water mixture, to calculate the thermodynamicproperties like specific enthalpy, specific entropy and specificvolume, the need of bubble and dew point temperatures at variouspressures and compositions are very essential and is the prior step.For estimating those temperatures, various correlations have beendeveloped. The correlation developed by Patek and Klomfar (1995)is proposed in this work which avoids tedious iterations required bythe complicated method fugacity coefficient of a component in amixture and the correlation proposed by Ibrahim and Klein (1993).
Figure1 shows the details of bubble point and dew point
temperature variations with ammonia concentration. The loci of allthe bubble points are called the bubble point line and the loci of allthe dew points are called the dew point l ine. The bubble point line isthe saturated liquid line and the region between the bubble and dewpoint lines is the two phase region, where both liquid and vapor co-exist in equilibrium (“Vapor Absorption Refrigeration SystemsBased on Ammonia-Water Pair”, 2004).
C a l c u l a t i n g b u b b l e a n d d e w p o i n t t e m p e r a t u r e sThe bubble point and dew point temperatures of the ammonia-water mixture are found from the correlations in Equations (1) and(2), developed by Patek and Klomfar (1995).
( )i
i
n
om
i
iobp
plnx1aTx)(p,T
−=
(1)
( ) ( )
i
i
n
/4m
iiod p
po
lny1aTyp,T
−=
(2)
Figure 2 shows the bubble and dew point temperatures developedwith the correlation by Patek and Klomfar (1995) up to pressure o100 bar using MATLAB code. A flowchart was prepared tounderstand the mathematical calculations for properties.
D e v e l o p m e n t o f e q u a t i o n sThe properties are derived from Gibbs free energy function fromZiegler and Trepp (1984).
L i q u i d p h a s eThe Gibbs free energy for both liquid and gas phases weredetermined from Equations (3) and (4), developed by Ziegler andTrepp (1984) which is the summation of contributions of the purecomponents, the ideal free energy of mixing and the free excessenergy.
F i g u r e 2 . Bubble and dew point temperatures up to100 bar pressure.
E q u a t i o n o f s t a t e f o r p u r e c o m p o n e n t i n l i q u i d p h a s eThe equation of state for pure components in liquid phase is givenas follows:
( )O
2H2
2op
2p
2aopp2T
4aT
3a
1a
dTT
lpc
TdTlpcop,oT
lTsop,oTlh
pT,
lO
2H
g
−
+−++
+−+−
=
(4)Where,
2T
3bT
2b
1b
T,polpc ++=
(5)
Similarly, the liquid heat capacity at constant pressure can beassumed to be second order in temperature according to Equation(5) (Ziegler and Trepp, 1984).On substituting (5) in Equation (4), thefollowing Equations (6) and (7) were obtained for pure componentsin liquid phase.
F i g u r e 3 . Flowchart to find thermodynamic properties of mixture.
L i q u i d m i x t u r e c o r r e l a t i o nThe Gibbs excess energy gE for liquid mixtures is expressed as:
( )
( )
( ) ( )
( )
+++−
+
+++++−
+
+++++
=
21615
14132
2
121110987
2
654321
xp,T,E
T
e
T
epee12x
T
e3
T
eTpeepee12x
T
e
T
eTpeepee
g
(8)
In Figure 3, the procedure carried out in calculating thethermodynamic properties enthalpy, entropy and volume in bothphases for the compressed region, saturated region, in betweenbubble and dew point region and superheated region wereexplained from the corresponding equations.
For a given pressure, concentration and temperature the bubblepoint and dew point temperatures were calculated and then thegiven temperature is compared with the bubble and dewtemperatures and identifies the respective region as represented inthe flowchart. The flowchart in Figure 3 shows the procedure focalculating the thermodynamic properties of the mixture. For agiven property value, the corresponding regions can be identifiedfrom the flowchart.
E q u a t i o n o f s t a t e f o r p u r e c o m p o n e n t i n g a s p h a s eThe general equation of state for pure component in gas phase isidentified in the following equation.
( ) ( ) ( )
( ) ( )[ ]
+−−
++−=
yylogy1logy1RT
NHyg0Hgy1g
ee
PT,3g
pT,2g
Y)P,(T,g
(9)
For the gas phase, the Gibbs free energy equation is given below:
( )
OH2
O2H
12oT
T3op1111oT
3op12
11T
3p
34c
12oT
Top1111oT
op1211T
p3c
12oT
Top1111oT
op1211T
p3c4
oT
Top33oT
op43T
p2c
opp1cop
pRTln
Tdt
gopC
TdTgopCop,oT
gTsop,oT
gh
pT,gg
+−+
+−
++−++−
+− ++−+−
=
(10)
Where:
( )
2
321T
go
p TdTddc ++=
(11)
Similarly on substituting (11) in Equation (10), the pure components
in gaseous phase from ammonia and water were obtained in
Equations (12) and (13).
( )
( )
O2
H
12oT
T3op1111oT
3op12
11T
3p
34c
12oT
Top1111oT
op1211T
p3c
4oT
Top33oT
op43T
p2copp
1c
op
pelogTR
3T3
oT
3
3d2T2
oT
2
2dToT
1d
op,
oT
gsT
op,
oT
gh
pT,gg
O2H
+−++−+
+−+−++
−+−+−+−
=
(12)
( )
( ) ( ) ( )
( ) ( )
( )
3NH
12o
3o
11o
3o
11
3
4
12o
o
11o
o
113
4o
o
3o
o
32
o1o
e
33o
322
o2
o1oog
oog
pT,3g
T
TP11
T
P12
T
Pc
T
TP11
T
P12
T
Pc
T
TP3
T
P4
T
Pc
PPc
P
PRTlog
TT3
dTT
2
d
TTdp,TTsp,Th
NHg
+−
+
+−+
+−
+−+
+−+−
+−+−
=
(13)
Ganesh and Srinivas. 29
E q u a t i o n o f s t a t e f o r p u r e c o m p o n e n t sSpecific enthalpy at liquid and vapor phases
The molar enthalpy of the liquid phase and gaseous phase werespecified and simplified in Equation (14) to (19). Equation (16) isderived in MATLAB to find the liquid enthalpy in the compressedand saturated regions. Equation (19) is derived in MATLAB to findthe enthalpy in gaseous phase for the saturated and superheatedregions.
The subscript l indicates liquidg indicates gaso indicates ideal gas stateTB = 100KPB = 10bar
( )
( )
( )
( )
( )
−+−
+−+−+−
+−+−+
×××−
−+−
+−+−+−
+−+−+
×−××−
=
3NH
11oT
3op
11T
3p4c411
oT
op
11T
p3c21
3oT
op
3T
p2c4opp1c
3oT
3T33d
2oT
2T22d
oTT1dg
poTo,h
yBT17
R
O2
H11oT
3op
11T
3p4c411
oTop
11Tp3c21
3oT
op
3T
p2c4opp1c
3oT
3T33d
2oT2T
22d
oTT1dg
po,Toh
y1BT18
R
gh
(19)
The coefficients used in Equations 15,17,20,23, 26 and 29 aregiven in (Table 1) and (Table 2).
Specific entropy at liquid and vapor phases
The molar entropy of the liquid and gaseous phases were specifiedand simplified in Equation (20) to (25). Equation (22) is derived inMATLAB to find the liquid entropy in the compressed and saturatedregions. Equation (25) is derived in MATLAB to find the entropy ingaseous phase for the saturated and superheated regions.
T a b l e 1 . Coefficients for the equations for the pure components.
C o e f f i c i e n t A m m o n i a w a t e ra1 3.971423.10
-2 2.748796. 10
-2
a2 -1.790557.10-5
-1.016665.10-5
a3 -1.308905.10-2
-4.452025.10-3
a4 3.752836.10-3
8.389246.10-4
b1 1.634519.101 1.214557.10
1
b2 -6.508119 -1.898065
b3 1.448937 2.911966.10-1
c1 -1.049377.10-2
2.136131.10-2
c2 -8.288224 -3.169291.101
c3 -6.647257.102 -4.634611.10
4
c4 -3.045352.103 0.0
d1 3.673647 4.019170
d2 9.989629.10-2
-5.175550.10-2
d3 3.617622.10-2
1.951939.10-2
hl 4.878573 21.821141h
g 26.468879 60.965058
sl 1.644773 5.733498
sg 8.339026 13.453430
To 3.2252 5.0705
po 2.0000 3.0000
T a b l e 2 . Coefficients for the Gibbs excess energy function.
e1 -4.626129.101
e2 2.060225.10-2
e3 7.292369
e4 -1.032613.10-2
e5 8.074824.101
e6 -8.461214.101
e7 2.452882.101
e8 9.598767.10-3
e9 -1.475383
e10 -5.038107.10-3
e11 -9.640398.101
e12 1.226973.102
e13 -7.582637
e14 6.012445.10-4
e15 5.487018.101
e16 -7.667596.10
1
Specific volume of liquid and vapor phases
The specific volume of the liquid and gaseous phases, werespecified and simplified in Equation (26) to (31). Equation (28) isderived in MATLAB to find the liquid volume in the compressed andsaturated regions. Equation (31) is derived in MATLAB to find thevolume in gaseous phase for the saturated and superheatedregions.
Ganesh and Srinivas. 31
( )
( )xT,
xp,T,l
B
Bl gpp
RTv
∂
∂=
(26)
( ) ( )
( ) ( )[ ]
xT,
xp,T,EgP
xexlogx1elogx1RTP
xp,T,3
NHlg
Px
xp,T,O2H
lgP
x1
Bp
BRTlv
∂
∂++−−
∂
∂
+∂
∂+
∂
∂−
=
(27)
In the same manner specific volumes were solved.
( )
( )
( ) ( ) ( ) ( )( )
−++−++×−××−+
+
+++×××
+
+++×−××
=
142
10842
B
B
NH
24321
B
B
OH
24321
B
B
l
e12xTee12xTeex1x100p
T
.18x1x.17
R
TaTapaa(x)100p
T
17
R
TaTapaax)(1100p
T
18
R
v
3
2
(28)
( )
( )yT,
yp,T,g
B
Bgg
pp
RTv
∂
∂=
(29)
( ) ( )
( ) ( )[ ]
+−−∂
∂
+
∂
∂+
∂
∂−
=
yT,
yeylogy1elogy1RTP
yp,T,3NH
gg
P
y
yp,T,O2H
gg
P
y1
BpBRTg
v
(30)
++++
××××
+
++++
××−××
=
3
2
NH
11
24
11
3
3
21
B
B
OH
11
24
11
3
3
21
B
B
g
T
pc
T
c
T
cc
p
T
18
Ry
100p
T
71
R
T
pc
T
c
T
cc
p
T
18
Ry)(1
100p
T
18
R
v
(31)
R E S U L T S A N D D I S C U S S I O NIn this study, from the simplified Equations 17 and 19 theliquid and vapor enthalpies were calculated and coded inMatLab. Similarly, Equations 22 and 25 were used tocalculate the liquid and vapor entropies. The resultsgenerated using these equations were programmed inMatLab. With MatLab, the graphs were plotted andcompared with the graphs from the Feng and Yog(1999). The graphs obtained from this work, show a veryclose trend of comparison, Feng and Yogi (1999)
F i g u r e 4 . Bubble and dew point temperatures a 34.47 bar.
Figure 4 shows a plot between the temperature and
ammonia mass fraction. Here, the data in the sense ofthe values of temperature at a particular concentration.The temperatures at a particular concentration obtainedfrom Macriss and Goswami (1999) are very close with theproduced result using MatLab. Figure 4 shows the bubblepoint temperature and dew point temperature curves at aspecified pressure and for different concentrations. Thebubble point temperature and dew point temperaturevalues are identical at initial and final concentrationsensuring a closed curve. The differences between ourcomputed values and the data are less than 0.5%.Thesimulated works were carried out in MATLAB, which
shows a closer match with the literature. This work
requires less calculation and can be utilized for thethermodynamic properties.(Table 3) gives the property values at different regions
For a given pressure, temperature and concentration thebubble and dew point temperatures were calculated andthe given temperature will be compared with those twotemperatures and determine in which region the giventemperature lies. If the given temperature is less than thebubble point temperature then region will be acompressed liquid region and for which thecorresponding enthalpy, entropy and volumes wereobtained using MATLAB. In calculating the dryness
fraction, the ammonia mole fraction of vapor phase isobtained from correlation by Soleimani (2007).
y(x,P) = 1− exp[aPbx + (c +d /P) x
2] (32)
The present results found a closer match with the existingresults in the plots at a temperature less than 500
°C and
100 bar. In finding the values of enthalpy, entropy andvolume in between Tb and Td regions the drynessfraction is calculated from the equation developed in (19).
The liquid enthalpy and vapor enthalpy plots wereshown in (Figure 5) and (Figure 6). From (Figure 5), thevariation in the liquid enthalpy decreases first and thenincreases with increase in concentration at a specifiedpressure. The results obtained were validated and showsa closer match with the compared results. Thedifferences are less than 3% for all the data. (Figure 6)shows the variation in the vapor enthalpy curve. The
enthalpy value decreases continuously with the increasein the concentration. The enthalpy concentration withrespect to the parameters pressure and concentration isshown in (Figure 7). The liquid enthalpy plot is obtainedby considering the bubble point temperature andammonia mole fraction of liquid phase. For plotting theauxiliary curve the liquid enthalpy is considered as afunction of bubble point temperature and ammonia molefraction of vapor phase. (Figure 7) of the present workhas got similar curves at saturated liquid and vaporconditions as compared with existing graph by Zieglerand Trepp (1984). The values of enthalpies at anyconcentration and pressure from the result (22) iscompared with the present values and got similar values.
The ammonia mole fraction of vapor phase is obtained bycorrelation by Soleimani (2007). With the utilization ofthese correlations the result shows good agreement withthe previous work. With the combination of correlationsstated in the abstract, the present work was carried outusing a new program code MatLab and shows the similartrends in all the graphs. Work is the properties from thecombination of the three correlations and obtained inMatLab. (Figure 8) shows the entropy of saturated liquidat a specified temperature and various concentrations.
(Figure 8) shows the entropy of saturated liquid at a
specified temperature and various concentrations. Theentropy decreases and increases with the increase inconcentration. The plot obtained is validated with theexisting results and produces a good match. Whereas inthe entropy of saturated vapor from (Figure 9) at a
specified temperature, the plot decreases continuouslywith the increase in concentration. (Figure 10) shows theentropy concentration diagram for ammonia - watermixture at various pressures and concentrations. The gapon the left hand side between the liquid curves is lesscompared with the gap on the right side of the plot whichcan even be extended to 150 bar with the samecorrelations. The values obtained by this plot can beutilized for any thermodynamic cycle. Upon increasingthe pressures vapor curve and auxiliary curve areembedded one over the other forming a close gapbetween each other.
Figures (11 and 12) shows the liquid volume and vapor
volume which has been derived utilizing bubble pointtemperature. With both the plots at a specified pressurethe volume decreases with the increase in theconcentration. Exergy analysis is the maximum usefuwork obtained during an interaction of a system withequilibrium state. The total exergy of a system becomesa summation of physical exergy and chemical exergy.
E = Ech + Eph (33)
Eph = (h-ho)-To(s-so) (34)
Ech = ( )O2H
2
3NH
3
,e
M
x1,e
M
xch
o
OH
ich
o
NH
i
−+
(35)
Where eo
ch, NH3 and eoch, H2O are chemical exergies o
ammonia and water. The standard chemical exergy ofammonia and water are taken from Ahrendts (1980).
The exergy concentration plot for ammonia-water mixtureat various pressures is shown in (Figure 13). The liquidexergy curve decreases to certain concentration andapproaches a near constant relation. The vapor exergy
F i g u r e 1 3 . Exergy concentration diagram for ammonia-water mixture.
curve decreases continuously with the increase inconcentration. The gap on the left hand side between theliquid curves is wider than the right hand side. Theauxiliary lines are contracting at low ammonia fractionswhereas the same lines are expanding at high ammoniafractions. The vapor exergy curve and auxiliary curveshave identical values at initial and final concentrationswhich results in a closed loop. The space between theliquid exergy and the closed loop is reduced with theincrease in pressures.
C o n c l u s i o nTo develop thermodynamic properties of ammonia-watermixtures various correlations were analyzed. In this workthree different correlations were utilized for developingthe results. Bubble and dew point temperatures wereobtained utilizing the correlation of Patek and Klomfar(1995), which reduces iterations, which is been utilizedfor finding the properties enthalpy, entropy and volume.The properties were derived using relations Ziegler andTrepp (1984). The mole fraction of ammonia in vaporphase was solved with the correlation by Soleimani
(2007). With the utility of these correlations, the need otedious iterations used in fugacity method was reducedThe results obtained in this work were validated bycomparing with the published data and found closermatching. Here, the results of the graphs obtained fromMatLab are compared with the existing results andproves the similar trends, which is the evidence and thatis why it was mentioned, as found to have close matchThe exergy for the ammonia-water system have beensimulated with the help of the derived properties, to carryout the second law analysis to power systems.
N o m e n c l a t u r e : a i , b i , c i , d i , e i , m i , n i , Coefficients; hspecific enthalpy, kJ/kg; s , specific entropy, kJ/kg-K; vspecific volume, m
3 /kmol; T , temperature, K; p, pressure
bar; , Gibbs free energy, kJ/kmol; p , specific heacapacity at constant pressure, kJ/kmol-K; R , universagas constant, kJ/kmol-K; x , ammonia mole fraction inliquid phase; y , ammonia mole fraction in vapor phase. S u p e r s c r i p t s : g , Gas phase; l , liquid phase; o , ideal gasstate.
S u b s c r i p t s : b , Bubble point; d , dew point; o , referencestate.
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Ganesh and Srinivas. 39
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