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water as working fluids
Applied Energy 37 (1990) 169-187
Second-Law Analysis of Solar Absorption-Cooling Cycles using Lithium Bromide/Water and Ammonia/Water as Working Fluids A h m e t K a r a k a s , * Nilufer Egrican & S e y h a n U y g u r Department of Mechanical Engineering,ITS) Makina Fakuitesi, Termodinamik Anabililim Dali, The Technical University of Istanbul, Giimussuyu, Istanbul, Turkey
ABSTRACT An availability analysis was carried out for each component in the system, and the results were tabulated. The lithium bromide~water system wasfound to be more effective, on the basis of both first-and second-law analyses, above O°C.
NOTATION a am A AUX b bm
C COL COP CT E G h hH
Redlich-Kwong constant (eqn (30)) Redlich-Kwong constant for binary mixtures (eqn (32)) Absorber Auxiliary source Redlich-Kwong constant (eqn (31)) Redlich-Kwong constant for binary mixtures (eqn (33)) Condenser Collector Coefficient of performance Cooling tower Evaporator Generator Enthalpy Molar enthalpy Total enthalpy
* To whom all correspondence should be addressed. 169 Applied Energy 0306-2619/90/$03.50 O 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain
170 HE rh P PI P2 QcoL R s so ST T TE TG TV TWV u° v W I~ X y
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur Heat exchanger Mass-flow rate Pressure The first pump (Fig. 1) The second pump (Fig. 1) Heat flow rate Flow rate of the heat collected on the collector plates Universal gas constant Entropy Ideal-gas entropy Storage tank Temperature Evaporation temperature Generator-leaving temperature Throttling valve Three-way valve Ideal-gas internal energy Specific volume Molar volume Work Work flow rate Mole fraction Concentration
Greek Symbols 6 Difference e Effectiveness el Effectiveness (eqn (25)) e2 Effectiveness (eqn (26)) t/ Efficiency ~b Availability Aq~ Availability difference X; Sum Subscripts A Absorber AUX Auxiliary source C Condenser Car Carnot COL Collector cr Critical CT Cooling tower
Second-law analysis of solar absorption-cooling cycles
E env G H HE i 1 O P1 P2 R S ST TVI TVII TWV
171
Evaporation Environment Generator Source Heat exchanger Inlet Outlet Ambient conditions The first pump (Fig. 1) The second pump (Fig. 1) Refrigerant Solvent Storage tank The first throttling valve (Fig. 1) The second throttling valve (Fig. 1) Three-way valve
INTRODUCTION An absorption-cooling cycle differs from a vapor-compression system in that it requires a negligible amount of work. In such systems, a solution, including an absorbent and a refrigerant, is used as the working fluid. The compression and expansion parts in a conventional refrigeration system are 12 r
,ib~
N
.
I I ,,I
q
•
Fig. 1. Schematic diagram of solar-assisted absorption-cooling cycle.
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
172
replaced by a generator, which is used for separating the refrigerant from the solution, and an absorber, where the refrigerant is absorbed in an absorption cooling system. The main source of energy is taken from a solar collector. However, another source is assumed to be available when the energy coming from the sun is not sufficient. The total energy needed consists of the heat given to the generator and the work done on the solution pump (Fig. 1). Thus, the thermodynamic analysis of an absorption cycle requires the examination of the thermodynamic properties of the two component fluids and the transformation of the heat energy.
DESCRIPTION OF THE CYCLE The refrigerant fluids, NH 3 for the ammonia/water system and H20 for the lithium bromide/water system, are separated in the generator by means of heat given to this component. 1-4 The mass-flow rate of the refrigerant depends on the temperature to which the solution is heated. After if has reached the desired temperature, the refrigerant goes through the condenser and evaporator (Fig. 2). Meanwhile, the weak solution, which has less of the refrigerant fluid as a result of dissolving in the generator, expands in the throttling valve and goes through the absorber. Here it absorbs the refrigerant coming through the evaporator, and a strong solution forms, which has more of the refrigerant as a result of this absorption. The strong solution is then pumped to the generator through the solution pump. The heat released in the condenser and absorber is rejected by the coolingwater system. The cooling water cools down in the cooling tower and is sent to the absorber. The required heat for the generator is supplied from the hotwater cycle by means of the collector plates and the storage tank. When the solar energy is insufficient, the auxiliary source is used.
To .....
'
Po
"r<
Fig. 2.
v Behaviour of the refrigerant fluid in the pure state.
Second-law analysis of solar absorption-cooling cycles
173
T H E FIRST LAW ANALYSIS By using the basic principles of thermodynamics, and neglecting the work given to the pump, a coefficient of performance may be defined as the rate of heat taken by the evaporator to the heat given to the generator: c o p = OE/Oo
(1)
An important amount of the heat is supplied by the collector. The meaning of COP in this system is thus the success in transforming the required energy to the given type. Another definition may be written as:
= OE/OcoL
(2)
T H E SECOND-LAW ANALYSIS This is based on the availability concept 5 and on reducing the availability definition for a steady-state flow. Let us take a system that has heat transfer only with its environment and is undergoing a reversible process. According to the first law: 6Qo - 6 W = dU
(3)
By the second law for the reversible process: dS = Oo/To
(~w = ~ Wu~efu~+ ~ Wenv
(4) (5)
and, for a steady-state system: Wnow= Po Vo - P1 I/"1
(6)
where the environment state is outlet and the state 1 is the inlet of the flow. If eqns (3)-(6) are combined, the relation: Wuseful= (H1 - T o S I ) - ( H o - ToSo)
(7)
which defines the maximum work, may be obtained for a system undergoing a reversible process from a given state to the environmental conditions. If there is a heat flux from a source at the temperature TH to the system, the maximum work obtained from this transformation can be written by means of the Carnot efficiency as: ]'~max = ?~Car0 ~---(1 - To/TH)O.
(8)
This quantity is the available energy because it is the maximum available work obtained by the transformation of this amount of heat.
174
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
CALCULATING
THE AVAILABILITY
The definition o f availability is: 4)1 = (hi - TosI) - (ho - Toso)
(9)
The availability difference for a steady-state flow that is valid for every c o m p o n e n t in this study is: A4) = Zth,4), - Eth,4), - 0n(1 - To/TH)
(10)
where i and 1 represent the inlets and the outlets o f the c o m p o n e n t , respectively. Applying this definition to each o f the c o m p o n e n t s in the system, the following equations can be formed: A4)A = rh54)5 + m,,(4),, - 4),3) - rh44), -- rh,o4),o A4)AUX = FH15(4)19 -- 4 ) 1 5 ) -
QAWX(1 -- r o / T u )
(11) (12)
A4)c = rh12(4)12 - 4)1'1) + rh2(4)2 - 4)1)
(13)
A4)coL = rh21(4)22 -- 4)21)- QcoL( 1 -- To/Tn)
(14)
A ¢ C T ---- Ff/25(4)26 -- 4)25) Jr" Yf/l 3(4)13 -- 4)12)
(15)
A4)~ = rh4(4) 4 - 4)3) + rh23(4)24 - 4)23)
(16)
A4)G = Yf/14)1 "[- th84)8 "[-/'f/14(4)14 -- 4)19) -- Ff/74)7
(17)
A4)HE ~---rh7(4)7 -- 4)6) "[-/'h9(4)9 -- 4)8)
(18)
A4)PI = Fh5(4)6 -- 4)5)
(19)
A4)p2 =
(20)
- 4)20)
A4)ST = rh17(4)17 -- 4)16) + rh2o(4):o -- 4)22) A4)TVl = rh:(4)3 -- 4)2) A4)TVII =
Fh9(4)lO --
4)9)
A4)TWV -~-/9~/164)16 "Jl- FH 154)15 -- rh14.4)14
(21) (22) (23)
(24)
The decrease in the availability m e a n s that the lost w o r k or the e n t r o p y generation increases. The effectiveness assumed according to the second law m a y be defined in various ways. One o f these is the ratio o f the availability change o f the aim (i.e. the availability difference in the evaporator) to the sum o f the availability differences for all the other components. el = A4)E/ZA4)for all the other components
(25)
The second definition is the ratio o f the availability difference in the e v a p o r a t o r to the one that occurs in the collector (i.e. the c o m p o n e n t in which the cost process is obtained). e 2 ~-- A4)E/A4)¢o L
(26)
Second-law analysis of solar absorption-cooling cycles
175
If we wish to use the energy source with maximum effectiveness in the long term, the first approach is more realistic. The second definition, on the other hand, is more general because it changes only owing to the cooling load and climatic conditions. The curves representing the change of the effectiveness are different for each working fluid. The formulae for calculating the availability are applied to each component of both the lithium bromide/water and the ammonia/water systems. For the LiBr/H20 system, the P, T, h, s diagram is used in the calculation of the COP, availability and effectiveness parameters. 6 In determining the COP and effectiveness for the ammonia/water system and the availabilities for each component of the system, the Redlich-Kwong equation of state modified for the binary mixtures is used for the working fluid. 2 The Redlich-Kwong equation of state, and enthalpy and entropy equations derived from it, are as follows:
P = [RT/(v - b)] - [a/{v(v + b)Tl/2}]
(27)
h-= u ° + P15 + [(3aT- 1/2)/2b] In IU05 + b)l
(28)
= s o + R Iln (~ - b)/R TI + ( a T - 3/2/2b) In I(~ + b)/~l
(29)
The u ° and s o values in these equations are, respectively, the ideal-gasstate internal energy and entropy. The constants a and b are defined as: a = 0"427 48R 2 T2r'5/Pcr
(30)
b = 0"086 64RT~r/Pcr
(31)
Modifying these constants for binary mixtures, gives: a m
=
a , X 2 + 2(1 - kRs)(aRas)l/2XRXs + as X2
(32)
and
b m = bRX R + bsX s
(33)
By substituting these into eqn (27), the Redlich-Kwong equation of state for binary mixtures can be obtained. Performing phase-equilibrium calculations leads to:
]i= XRU° + XS u° + Pe + (3am/2bm T1/2) In I~/(~ + bm)l
(34)
g= Xr~s° + Xs s° + R l n I(0 - bm)/(RTXs)I + (am/2bm T3/2) In I(f/(~ + bm)l + RXR In IXsXRI
(35)
and
The coefficient k~s in eqn (32) represents the unlike interaction between
176
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
the refrigerant and solvent molecules. Its value for the ammonia/water molecule pair is -0.3. The calculated availabilities for each component of both the lithium bromide/water and ammonia/water systems are given in Tables 1-4. In these tables, the amount of the heat transferred to the collector, QcoL, the generator-leaving temperature, TG, and the evaporation temperature, TE, are taken as the considered parameters. On changing these parameters, results are obtained for various conditions, and figures illustrating these results are preserved. TABLE I The Calculated Thermodynamic Properties based on the Redlich-Kwong Equation for a Mixture of N H a / H 2 0
Location (see Fig. 1)
P (kPa)
T (°C)
h (kJ/kg)
s (kJ/kg K)
rh (kg/s)
y (kg NH3/ kg sol)
q~ (kJ/kg)
1 728"61 100"00 1 673"74 5"81 3"89 1"00 302"035 2 728"61 15"00 253" 16 0"96 3"89 1"00 351"005 3 462"48 2"00 253"16 0"97 3'89 1'00 347"975 4 462"48 2'00 1445"63 5'31 3'89 1"00 225"425 5 462"48 15'00 83"33 0'86 7' 11 0"66 -- 3"780 6 728"61 18"00 83"33 0"92 7"11 0"66 -21"960 7 728"61 33"00 108"50 1"06 7"11 0'66 -- 37"988 8 728'61 100"00 385"71 1"56 3"22 0'25 --32"291 9 728'61 82'00 314"28 1'37 3"22 0'25 --46"454 10 462"48 79"00 314"28 1"32 3"22 0"25 -- 32"667 11 4"25 30"00 949'01 3"15 5"00 2"484 12 4"25 30"00 1 777"91 5"89 5"00 1"982 13 4"25 10"00 42'01 0"15 4"85 3"787 14 70"14 77"00 322"32 1"04 2"92 14"730 15 70"14 77"00 322"32 1"04 0"44 14"730 16 70"14 77"00 322"32 1"04 1"48 14"730 17 70"14 90"00 2 660"10 7"48 1"48 401"190 18 70"14 9 0 " 0 0 26600"10 7'48 2"92 401"190 19 70"14 510'00 3 514"28 9"14 2'92 751"481 20 100"00 30"00 125"79 0"44 1"36 0'000 21 200"00 31'00 125"86 0"44 1"36 --0'536 22 100"00 100"00 2 676"20 7"36 1"36 453"650 23 385'507 ................................................................................................................................. ~b2,~- q~23 = 0"245 kJ/kg 24 385.507 25 2.320 ................................................................................................................................. ~b26 - ~b25 = 0-361 kJ/kg 26 2.320
TABLE 2 COP. Availability-Difference a n d Effectiveness Values for a n A m m o n i a / W a t e r System at QcoL = 6 814.32 kW, T E = 2°C a n d T~ = IOOOC
Component
Availability difference Adp (kJ/s)
Generator Evaporator Heat exchanger T h r o t t l i n g valve I Three-way valve Pump I Collector Condenser Absorber Storage tank Cooling tower T h r o t t l i n g valve II P u m p II
- 810.207 - 382'291 - 159"635 - 11'787 - 14.730 - 0.728 - 662.042 187.984 - 805-107 -43-323 9.591 44.393 - 129-260
QG = 9 308.533 kW. QE = 4 642'28 kW. C O P = 0"50. el =0"16. e2 = 0'58.
COP
(a)
r~ =2i: 0"7
LiBr/H20
o+ 0.5
5O COP
60
70
80
90
100
+o
['C-'I(b)
rE =10C
0.7
.....~...~0
0-6.
04..
5b Fig. 3.
~
7o
+b
9o
1c~
T h e change in C O P with T6. (a), TE = 2°C; (b), Tt = 10°C,
+o['c]
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
178
TABLE 3 The Thermodynamic Properties for a Binary Mixture of L i B r / H 2 0 Based on Ref. 6
Location (see Fig. 1)
P (kPa)
T (°C)
h (kJ/kg)
s (kJ/kg K)
rh (kg/s)
y (kg 1120/ kg sol)
dp (kJ/kg)
1 5"63 100"00 2 686'96 8"71 1"97 1"00 53"936 2 5'63 35'00 146'68 0"51 1-97 1"00 0'165 3 0"66 2"00 146"68 0"53 1"97 1'00 - 7'925 4 0'66 2"00 2 501'48 9"13 1'97 1"00 -258"531 5 0-66 35"00 251"04 2"02 12'17 0'43 - 14"079 6 5"63 38-00 251-04 2'04 12"17 0"43 - 18"018 7 5-63 72'00 326'00 2-28 12'17 0"43 - 18"414 8 5"63 100"00 378"34 1-89 10"20 0"32 65"212 9 5'63 60"00 292'88 1"85 10"20 0"32 - 9"006 10 0"66 55"00 292'88 1"85 10"20 0-32 - 8-037 11 4"25 30"00 949"01 3'15 4"02 1-545 12 4-25 30"00 1 876"24 6"21 4-02 1"110 13 4"25 10"00 42"01 0"15 3'85 2'848 14 70"14 77"00 322"32 1'04 2"92 13'791 15 70"14 77'00 322-32 1'04 0"44 13"791 16 70'14 77"00 322"32 1-04 1"48 13"791 17 70'14 90"00 2660"10 7"48 1'48 400-251 18 70"14 90"00 2660'10 7"48 2"92 400"251 19 70"14 108"00 2693'80 7-57 2"92 406"499 20 100"00 30"00 125"79 0-44 1"36 --0"939 21 200"00 31"00 125'86 0.44 1"36 - 1-475 22 100-00 100"00 2 676"20 7"36 1"36 452-711 23 385'507 ................................................................................................................................. tP24 - q~23 = 0-245 kJ/kg 24 385"507 25 2-320 ................................................................................................................................. ~26 - qb2s = 0-361 kJ/kg 26 2"320
The values of COP, el and e 2 are analysed with respect to three parameters: (i) The generator-leaving temperature, TG (which is restricted by the thermodynamic properties of the working fluid); (ii) the evaporation temperature, TE (which is dependent on the cooling load; and (iii) the amount of heat collected by the solar collector QcoL (which is restricted by the climatic conditions). The changes in COP at constant QcoL and TE are shown in Figs 3(a) and (b) for temperatures above O°C. The change in QG with T~ is illustrated in
Second-law analysis of solar absorption-cooling cycles TABLE
179
4
COP. Availability Difference and Effectiveness Values for a Lithium Bromide/Water System at QcoL = 6 814'32 kW, T E = 2°C and TC = 100°C
Component
Availability difference Ad? {kJ/kg)
Generator Evaporator Heat exchanger Throttling valve I Three-way valve Pump I Collector Condenser Absorber Storage tank Cooling tower Throttling valve II P u m p II
- 151.196 - 399'266 - 761.851 - 15"938 - 13'791 - 0.729 - 661-134 - 107-677 - 414.708 -44'230 7.528 9"890 -47"938
Qc = QE = COP = el = g2 =
6 913"279 kW. 4 642.28 kW. 0"67. 0"29. 0"60.
9500
8500 7500 Li Br/H20 6500
~'~
50
60
70
80
Fig. 4. The change in Qo with Tc. TE = 2°C.
100
TA'C]
Ahmet Karakas, Nilufer Egrican, Seyha. Uygur
180
rE : io'c 9500,
8500'
7500 ~tBr/HzO 6500
50
60
70
80
90
100
To'7"['cj
Fig. 5. The change in QG with T~. TE = 10°C. £1 0.4 ~ 0.3
TE = 2 "C
..=
o.z
~
~
L~/~O
_
NH,/~O
0-1
50
60
70
80
90
100
'10 T/['C]
(a) LiBr/HzO
0.3
0.2 0.1
NH~/.H~.. TE =I0"C
50
60
70
80
90
,00
(b) Fig. 6.
T h e c h a n g e in el w i t h TG. (a), T e = 2°C; (b), Te = 10°C.
110 r~T'c]
181
Second-law analysis of solar absorption-cooling cycles
Figs 4 and 5. As expected, QG versus TG curves correspond to the COP versus TG curves. Figure 6(a), (b) represents the change e t for a constant Q¢ot and TE above 0°C. Figures 7(a), (b) and 8(a), (b) illustrate the dependence ofe 1 on QcoL and prove that the irreversibility in the collector plates increases with the amount of heat collected, so that the design of the collector plates has an influence on
0-7
0-3
0.1 0.0
~ .~_
so
60
,o
80
so
,oo
~o['cJ
(a)
0'7
o~
T~=2"C
~ ' ~ -
~
~
LiBr/H20
0.1 80
90
100
T¢
E'gJ
(b) Fig. 7. The change in ~ as a function of To and QCOL. TE =2°C- (a), NH3/H20;
(b), LiBr/HsO.
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
182
0.6
T~=IO'C
0.2
~0
....
. so
~o
~
.
. 6o
.
. 70
=.__
.
. 80
~
~
.
. 9o
re-1 ~
loo
r~l-C l
(a)
O-7
0.5
0.3
~soo .
5500
kiBr/H20 o.1 80
90
100
1tO l s
(b)
Fig. 8. The change in e,l as a function of TG and QcoL. T~= 10°C. (a), NH3/H20; (b), LiBr/H20.
reducing the lost work, The slow change in Et for LiBr/H20 can be observed from Figs 9 and 10(b). Figure 11 indicates the el - T6 change for both o f the fluid pairs. The increases in entropy generation, A~b, in the generator, condenser, and absorber are balanced by the decrease in irreversibility in the heat exchanger. This balance is not valid for N H s / H z O because of the different t h e r m o d y n a m i c properties of the solution. 2'*'6 The heat transfer in
50
60
70
coN~.2~.~
~
~~ ~ ~ A ~ o a
80 90 100 TG[•c.]"~ 80 90 100 (a) (b) Fig. 9. The change in availability difference with TG. Tr = 10~C.(a), NH3/H20; (b) LiBr/H20.
100
~
100
500
300
NH3/H20
(~coL =6800 kW
7oo
900
300
500
/
700
~.~
/
900
1 I00
13(}(}
A~[k~J
110
T~
Li Br/ H20
[~]
QCOL:6800 kW
TE =10"(]
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
184
,,~~
,~[,J] 8oo
600
ZJ C0L=6800 k~/ 200
NH3/H20 so
60
~o
80
so
~o[~
1oo
(a)
1000
8O0 TE =2"C
LiBr/H20 400
200
~~ ~
CO~E~ER m
oo
so
~oo
11o
To ['cJ
(b) Fig. 10. The change in availability difference with TG. TE=2°C. (a), N H 3 H 2 0 , (b) LiBr/H20.
185
Second-law analysis of solar absorption-cooling cycles ~ ....
E,
TE: = 2"C TE: =10"C
0"/-* 0"3
NH 3/t-lz0
/
LiBr/H20
,o
Fig. II.
,oo
The change in ~,i as a function of TG and T E.
the heat exchanger is between the solutions leaving the generator and absorber. For NH3/H20, the refrigerant concentration of the solutions between the points leaving the generator and the absorber differs too much as To increases. For LiBr/H20 around the limit resulting from crystallization, the difference and entropy changes become smaller. The rate of availability decrease thus slows down. However, this advantage of LiBr/H20 leads to an economic disadvantage. As the concentrations of the weak and strong solutions approach each other, the amount of the working fluid needed increases (Figs 12, 13(a), (b)). The opposite characteristics of the irreversibility curves for the condenser represented in Figs 9 and 10(a), (b) result from the fact that the heat transfer in this component occurs between the same kinds of fluid for LiBr/H20.
[kg/s]
30
25
~ ....
Te :2"C TE :lO'C
~Li
\\
20
NH3/H,0 ~
~
15
~
~
Br/H20 ~
5 50 Fig. 12.
60
70
80
90
100
The change in the mass-flow rate of the strong solution with
TO ['C]
To
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
186
[.g/s] 30
,o, 25
QcoL:6800 kW
Br ,o
,o
~ : IOeC~
5
80
90
100
110
T°~C]
(a)
15..
qcoL = 6800 kW NH3/HzO
10..
Te: -SaC rE:'7°°c
5.
~o
~o
7o
80
9o
,oo ToT'C]
(b) Fig. 13.
The change in mass-flow rate of the strong solution as a function of TG and TE.
(a), LiBr/H20; (b), NH3/H20.
CONCLUSIONS For the effective operation of an absorption-cooling system, correct choices of the working fluid and the design parameters of the components must be made. Where the temperature is above 0°C, the lithium bromide/water system is more effective than the ammonia/water system and has high values of COP. However, the lithium bromide/water system involves more design problems than the ammonia/water system because the pressures corresponding to the convenient temperatures are sub-atmospheric. This disadvantage can be partly reduced by considering the minimum entropy generation when choosing the design parameters of the components of the lithium bromide/water system. Solar energy is especially useful for obtaining
Second-law analysis of solar absorption-cooling cycles
187
a high degree of effectiveness. As may be seen from eqns (2) and (10), r/and q~ decrease with increasing heat flux from the solar collector. The influence of this inverse proportion on el is illustrated on Figs 7(a), (b) and 8(a), (b). Large a m o u n t s of heat flux are necessary, on the other hand, for high values of Tc. In order to avoid the high values of TC, it is preferable to use an auxiliary source of heat, instead of the solar collector, when the high Tc is needed or to design the collector plates to achieve m i n i m u m entropy generation.
REFERENCES 1. Duffle, J. A. & Beckman, W. A., Solar Engineering of Thermal Processes, John Wiley & Sons, New York, 1980. 2. Gomez, A. L. & Mansoori, G. A., Thermodynamic equation-of-state approach for the choice of the working fluids of the absorption cooling cycles. Solar Energy, 31 (1983) 557-66. 3. Bosnjakovic, F., Technical Thermodynamics (translated by P. L. Blackshear), Holt, Reinhart & Wiston, New York, 1965. 4. Egrican, N., The second law analysis of absorption cooling cycles, Heat Recovery Systems & CHP, 8 (1988) 549-58. 5. Brzustowski, T. A. & Golem, P. J., Second law analysis of the energy process. Part I: Energy- an introduction. Trans. ASME, 4 (1976-77) 209-21. 6. Lower, A., Thermodynamische Eigenschaften und Warmediagramme des Binaren Systems Lithiumbromide/Wasser. Kaltetechnic, 13(5) (1961). 7. Bejan, A., Second Law Analysis (Advances in Heat Transfer, Vol. 15), Plenum Press, New York, 1982.
Second-Law Analysis of Solar Absorption-Cooling Cycles using Lithium Bromide/Water and Ammonia/Water as Working Fluids A h m e t K a r a k a s , * Nilufer Egrican & S e y h a n U y g u r Department of Mechanical Engineering,ITS) Makina Fakuitesi, Termodinamik Anabililim Dali, The Technical University of Istanbul, Giimussuyu, Istanbul, Turkey
ABSTRACT An availability analysis was carried out for each component in the system, and the results were tabulated. The lithium bromide~water system wasfound to be more effective, on the basis of both first-and second-law analyses, above O°C.
NOTATION a am A AUX b bm
C COL COP CT E G h hH
Redlich-Kwong constant (eqn (30)) Redlich-Kwong constant for binary mixtures (eqn (32)) Absorber Auxiliary source Redlich-Kwong constant (eqn (31)) Redlich-Kwong constant for binary mixtures (eqn (33)) Condenser Collector Coefficient of performance Cooling tower Evaporator Generator Enthalpy Molar enthalpy Total enthalpy
* To whom all correspondence should be addressed. 169 Applied Energy 0306-2619/90/$03.50 O 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain
170 HE rh P PI P2 QcoL R s so ST T TE TG TV TWV u° v W I~ X y
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur Heat exchanger Mass-flow rate Pressure The first pump (Fig. 1) The second pump (Fig. 1) Heat flow rate Flow rate of the heat collected on the collector plates Universal gas constant Entropy Ideal-gas entropy Storage tank Temperature Evaporation temperature Generator-leaving temperature Throttling valve Three-way valve Ideal-gas internal energy Specific volume Molar volume Work Work flow rate Mole fraction Concentration
Greek Symbols 6 Difference e Effectiveness el Effectiveness (eqn (25)) e2 Effectiveness (eqn (26)) t/ Efficiency ~b Availability Aq~ Availability difference X; Sum Subscripts A Absorber AUX Auxiliary source C Condenser Car Carnot COL Collector cr Critical CT Cooling tower
Second-law analysis of solar absorption-cooling cycles
E env G H HE i 1 O P1 P2 R S ST TVI TVII TWV
171
Evaporation Environment Generator Source Heat exchanger Inlet Outlet Ambient conditions The first pump (Fig. 1) The second pump (Fig. 1) Refrigerant Solvent Storage tank The first throttling valve (Fig. 1) The second throttling valve (Fig. 1) Three-way valve
INTRODUCTION An absorption-cooling cycle differs from a vapor-compression system in that it requires a negligible amount of work. In such systems, a solution, including an absorbent and a refrigerant, is used as the working fluid. The compression and expansion parts in a conventional refrigeration system are 12 r
,ib~
N
.
I I ,,I
q
•
Fig. 1. Schematic diagram of solar-assisted absorption-cooling cycle.
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
172
replaced by a generator, which is used for separating the refrigerant from the solution, and an absorber, where the refrigerant is absorbed in an absorption cooling system. The main source of energy is taken from a solar collector. However, another source is assumed to be available when the energy coming from the sun is not sufficient. The total energy needed consists of the heat given to the generator and the work done on the solution pump (Fig. 1). Thus, the thermodynamic analysis of an absorption cycle requires the examination of the thermodynamic properties of the two component fluids and the transformation of the heat energy.
DESCRIPTION OF THE CYCLE The refrigerant fluids, NH 3 for the ammonia/water system and H20 for the lithium bromide/water system, are separated in the generator by means of heat given to this component. 1-4 The mass-flow rate of the refrigerant depends on the temperature to which the solution is heated. After if has reached the desired temperature, the refrigerant goes through the condenser and evaporator (Fig. 2). Meanwhile, the weak solution, which has less of the refrigerant fluid as a result of dissolving in the generator, expands in the throttling valve and goes through the absorber. Here it absorbs the refrigerant coming through the evaporator, and a strong solution forms, which has more of the refrigerant as a result of this absorption. The strong solution is then pumped to the generator through the solution pump. The heat released in the condenser and absorber is rejected by the coolingwater system. The cooling water cools down in the cooling tower and is sent to the absorber. The required heat for the generator is supplied from the hotwater cycle by means of the collector plates and the storage tank. When the solar energy is insufficient, the auxiliary source is used.
To .....
'
Po
"r<
Fig. 2.
v Behaviour of the refrigerant fluid in the pure state.
Second-law analysis of solar absorption-cooling cycles
173
T H E FIRST LAW ANALYSIS By using the basic principles of thermodynamics, and neglecting the work given to the pump, a coefficient of performance may be defined as the rate of heat taken by the evaporator to the heat given to the generator: c o p = OE/Oo
(1)
An important amount of the heat is supplied by the collector. The meaning of COP in this system is thus the success in transforming the required energy to the given type. Another definition may be written as:
= OE/OcoL
(2)
T H E SECOND-LAW ANALYSIS This is based on the availability concept 5 and on reducing the availability definition for a steady-state flow. Let us take a system that has heat transfer only with its environment and is undergoing a reversible process. According to the first law: 6Qo - 6 W = dU
(3)
By the second law for the reversible process: dS = Oo/To
(~w = ~ Wu~efu~+ ~ Wenv
(4) (5)
and, for a steady-state system: Wnow= Po Vo - P1 I/"1
(6)
where the environment state is outlet and the state 1 is the inlet of the flow. If eqns (3)-(6) are combined, the relation: Wuseful= (H1 - T o S I ) - ( H o - ToSo)
(7)
which defines the maximum work, may be obtained for a system undergoing a reversible process from a given state to the environmental conditions. If there is a heat flux from a source at the temperature TH to the system, the maximum work obtained from this transformation can be written by means of the Carnot efficiency as: ]'~max = ?~Car0 ~---(1 - To/TH)O.
(8)
This quantity is the available energy because it is the maximum available work obtained by the transformation of this amount of heat.
174
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
CALCULATING
THE AVAILABILITY
The definition o f availability is: 4)1 = (hi - TosI) - (ho - Toso)
(9)
The availability difference for a steady-state flow that is valid for every c o m p o n e n t in this study is: A4) = Zth,4), - Eth,4), - 0n(1 - To/TH)
(10)
where i and 1 represent the inlets and the outlets o f the c o m p o n e n t , respectively. Applying this definition to each o f the c o m p o n e n t s in the system, the following equations can be formed: A4)A = rh54)5 + m,,(4),, - 4),3) - rh44), -- rh,o4),o A4)AUX = FH15(4)19 -- 4 ) 1 5 ) -
QAWX(1 -- r o / T u )
(11) (12)
A4)c = rh12(4)12 - 4)1'1) + rh2(4)2 - 4)1)
(13)
A4)coL = rh21(4)22 -- 4)21)- QcoL( 1 -- To/Tn)
(14)
A ¢ C T ---- Ff/25(4)26 -- 4)25) Jr" Yf/l 3(4)13 -- 4)12)
(15)
A4)~ = rh4(4) 4 - 4)3) + rh23(4)24 - 4)23)
(16)
A4)G = Yf/14)1 "[- th84)8 "[-/'f/14(4)14 -- 4)19) -- Ff/74)7
(17)
A4)HE ~---rh7(4)7 -- 4)6) "[-/'h9(4)9 -- 4)8)
(18)
A4)PI = Fh5(4)6 -- 4)5)
(19)
A4)p2 =
(20)
- 4)20)
A4)ST = rh17(4)17 -- 4)16) + rh2o(4):o -- 4)22) A4)TVl = rh:(4)3 -- 4)2) A4)TVII =
Fh9(4)lO --
4)9)
A4)TWV -~-/9~/164)16 "Jl- FH 154)15 -- rh14.4)14
(21) (22) (23)
(24)
The decrease in the availability m e a n s that the lost w o r k or the e n t r o p y generation increases. The effectiveness assumed according to the second law m a y be defined in various ways. One o f these is the ratio o f the availability change o f the aim (i.e. the availability difference in the evaporator) to the sum o f the availability differences for all the other components. el = A4)E/ZA4)for all the other components
(25)
The second definition is the ratio o f the availability difference in the e v a p o r a t o r to the one that occurs in the collector (i.e. the c o m p o n e n t in which the cost process is obtained). e 2 ~-- A4)E/A4)¢o L
(26)
Second-law analysis of solar absorption-cooling cycles
175
If we wish to use the energy source with maximum effectiveness in the long term, the first approach is more realistic. The second definition, on the other hand, is more general because it changes only owing to the cooling load and climatic conditions. The curves representing the change of the effectiveness are different for each working fluid. The formulae for calculating the availability are applied to each component of both the lithium bromide/water and the ammonia/water systems. For the LiBr/H20 system, the P, T, h, s diagram is used in the calculation of the COP, availability and effectiveness parameters. 6 In determining the COP and effectiveness for the ammonia/water system and the availabilities for each component of the system, the Redlich-Kwong equation of state modified for the binary mixtures is used for the working fluid. 2 The Redlich-Kwong equation of state, and enthalpy and entropy equations derived from it, are as follows:
P = [RT/(v - b)] - [a/{v(v + b)Tl/2}]
(27)
h-= u ° + P15 + [(3aT- 1/2)/2b] In IU05 + b)l
(28)
= s o + R Iln (~ - b)/R TI + ( a T - 3/2/2b) In I(~ + b)/~l
(29)
The u ° and s o values in these equations are, respectively, the ideal-gasstate internal energy and entropy. The constants a and b are defined as: a = 0"427 48R 2 T2r'5/Pcr
(30)
b = 0"086 64RT~r/Pcr
(31)
Modifying these constants for binary mixtures, gives: a m
=
a , X 2 + 2(1 - kRs)(aRas)l/2XRXs + as X2
(32)
and
b m = bRX R + bsX s
(33)
By substituting these into eqn (27), the Redlich-Kwong equation of state for binary mixtures can be obtained. Performing phase-equilibrium calculations leads to:
]i= XRU° + XS u° + Pe + (3am/2bm T1/2) In I~/(~ + bm)l
(34)
g= Xr~s° + Xs s° + R l n I(0 - bm)/(RTXs)I + (am/2bm T3/2) In I(f/(~ + bm)l + RXR In IXsXRI
(35)
and
The coefficient k~s in eqn (32) represents the unlike interaction between
176
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
the refrigerant and solvent molecules. Its value for the ammonia/water molecule pair is -0.3. The calculated availabilities for each component of both the lithium bromide/water and ammonia/water systems are given in Tables 1-4. In these tables, the amount of the heat transferred to the collector, QcoL, the generator-leaving temperature, TG, and the evaporation temperature, TE, are taken as the considered parameters. On changing these parameters, results are obtained for various conditions, and figures illustrating these results are preserved. TABLE I The Calculated Thermodynamic Properties based on the Redlich-Kwong Equation for a Mixture of N H a / H 2 0
Location (see Fig. 1)
P (kPa)
T (°C)
h (kJ/kg)
s (kJ/kg K)
rh (kg/s)
y (kg NH3/ kg sol)
q~ (kJ/kg)
1 728"61 100"00 1 673"74 5"81 3"89 1"00 302"035 2 728"61 15"00 253" 16 0"96 3"89 1"00 351"005 3 462"48 2"00 253"16 0"97 3'89 1'00 347"975 4 462"48 2'00 1445"63 5'31 3'89 1"00 225"425 5 462"48 15'00 83"33 0'86 7' 11 0"66 -- 3"780 6 728"61 18"00 83"33 0"92 7"11 0"66 -21"960 7 728"61 33"00 108"50 1"06 7"11 0'66 -- 37"988 8 728'61 100"00 385"71 1"56 3"22 0'25 --32"291 9 728'61 82'00 314"28 1'37 3"22 0'25 --46"454 10 462"48 79"00 314"28 1"32 3"22 0"25 -- 32"667 11 4"25 30"00 949'01 3"15 5"00 2"484 12 4"25 30"00 1 777"91 5"89 5"00 1"982 13 4"25 10"00 42'01 0"15 4"85 3"787 14 70"14 77"00 322"32 1"04 2"92 14"730 15 70"14 77"00 322"32 1"04 0"44 14"730 16 70"14 77"00 322"32 1"04 1"48 14"730 17 70"14 90"00 2 660"10 7"48 1"48 401"190 18 70"14 9 0 " 0 0 26600"10 7'48 2"92 401"190 19 70"14 510'00 3 514"28 9"14 2'92 751"481 20 100"00 30"00 125"79 0"44 1"36 0'000 21 200"00 31'00 125"86 0"44 1"36 --0'536 22 100"00 100"00 2 676"20 7"36 1"36 453"650 23 385'507 ................................................................................................................................. ~b2,~- q~23 = 0"245 kJ/kg 24 385.507 25 2.320 ................................................................................................................................. ~b26 - ~b25 = 0-361 kJ/kg 26 2.320
TABLE 2 COP. Availability-Difference a n d Effectiveness Values for a n A m m o n i a / W a t e r System at QcoL = 6 814.32 kW, T E = 2°C a n d T~ = IOOOC
Component
Availability difference Adp (kJ/s)
Generator Evaporator Heat exchanger T h r o t t l i n g valve I Three-way valve Pump I Collector Condenser Absorber Storage tank Cooling tower T h r o t t l i n g valve II P u m p II
- 810.207 - 382'291 - 159"635 - 11'787 - 14.730 - 0.728 - 662.042 187.984 - 805-107 -43-323 9.591 44.393 - 129-260
QG = 9 308.533 kW. QE = 4 642'28 kW. C O P = 0"50. el =0"16. e2 = 0'58.
COP
(a)
r~ =2i: 0"7
LiBr/H20
o+ 0.5
5O COP
60
70
80
90
100
+o
['C-'I(b)
rE =10C
0.7
.....~...~0
0-6.
04..
5b Fig. 3.
~
7o
+b
9o
1c~
T h e change in C O P with T6. (a), TE = 2°C; (b), Tt = 10°C,
+o['c]
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
178
TABLE 3 The Thermodynamic Properties for a Binary Mixture of L i B r / H 2 0 Based on Ref. 6
Location (see Fig. 1)
P (kPa)
T (°C)
h (kJ/kg)
s (kJ/kg K)
rh (kg/s)
y (kg 1120/ kg sol)
dp (kJ/kg)
1 5"63 100"00 2 686'96 8"71 1"97 1"00 53"936 2 5'63 35'00 146'68 0"51 1-97 1"00 0'165 3 0"66 2"00 146"68 0"53 1"97 1'00 - 7'925 4 0'66 2"00 2 501'48 9"13 1'97 1"00 -258"531 5 0-66 35"00 251"04 2"02 12'17 0'43 - 14"079 6 5"63 38-00 251-04 2'04 12"17 0"43 - 18"018 7 5-63 72'00 326'00 2-28 12'17 0"43 - 18"414 8 5"63 100"00 378"34 1-89 10"20 0"32 65"212 9 5'63 60"00 292'88 1"85 10"20 0"32 - 9"006 10 0"66 55"00 292'88 1"85 10"20 0-32 - 8-037 11 4"25 30"00 949"01 3'15 4"02 1-545 12 4-25 30"00 1 876"24 6"21 4-02 1"110 13 4"25 10"00 42"01 0"15 3'85 2'848 14 70"14 77"00 322"32 1'04 2"92 13'791 15 70"14 77'00 322-32 1'04 0"44 13"791 16 70'14 77"00 322"32 1-04 1"48 13"791 17 70'14 90"00 2660"10 7"48 1'48 400-251 18 70"14 90"00 2660'10 7"48 2"92 400"251 19 70"14 108"00 2693'80 7-57 2"92 406"499 20 100"00 30"00 125"79 0-44 1"36 --0"939 21 200"00 31"00 125'86 0.44 1"36 - 1-475 22 100-00 100"00 2 676"20 7"36 1"36 452-711 23 385'507 ................................................................................................................................. tP24 - q~23 = 0-245 kJ/kg 24 385"507 25 2-320 ................................................................................................................................. ~26 - qb2s = 0-361 kJ/kg 26 2"320
The values of COP, el and e 2 are analysed with respect to three parameters: (i) The generator-leaving temperature, TG (which is restricted by the thermodynamic properties of the working fluid); (ii) the evaporation temperature, TE (which is dependent on the cooling load; and (iii) the amount of heat collected by the solar collector QcoL (which is restricted by the climatic conditions). The changes in COP at constant QcoL and TE are shown in Figs 3(a) and (b) for temperatures above O°C. The change in QG with T~ is illustrated in
Second-law analysis of solar absorption-cooling cycles TABLE
179
4
COP. Availability Difference and Effectiveness Values for a Lithium Bromide/Water System at QcoL = 6 814'32 kW, T E = 2°C and TC = 100°C
Component
Availability difference Ad? {kJ/kg)
Generator Evaporator Heat exchanger Throttling valve I Three-way valve Pump I Collector Condenser Absorber Storage tank Cooling tower Throttling valve II P u m p II
- 151.196 - 399'266 - 761.851 - 15"938 - 13'791 - 0.729 - 661-134 - 107-677 - 414.708 -44'230 7.528 9"890 -47"938
Qc = QE = COP = el = g2 =
6 913"279 kW. 4 642.28 kW. 0"67. 0"29. 0"60.
9500
8500 7500 Li Br/H20 6500
~'~
50
60
70
80
Fig. 4. The change in Qo with Tc. TE = 2°C.
100
TA'C]
Ahmet Karakas, Nilufer Egrican, Seyha. Uygur
180
rE : io'c 9500,
8500'
7500 ~tBr/HzO 6500
50
60
70
80
90
100
To'7"['cj
Fig. 5. The change in QG with T~. TE = 10°C. £1 0.4 ~ 0.3
TE = 2 "C
..=
o.z
~
~
L~/~O
_
NH,/~O
0-1
50
60
70
80
90
100
'10 T/['C]
(a) LiBr/HzO
0.3
0.2 0.1
NH~/.H~.. TE =I0"C
50
60
70
80
90
,00
(b) Fig. 6.
T h e c h a n g e in el w i t h TG. (a), T e = 2°C; (b), Te = 10°C.
110 r~T'c]
181
Second-law analysis of solar absorption-cooling cycles
Figs 4 and 5. As expected, QG versus TG curves correspond to the COP versus TG curves. Figure 6(a), (b) represents the change e t for a constant Q¢ot and TE above 0°C. Figures 7(a), (b) and 8(a), (b) illustrate the dependence ofe 1 on QcoL and prove that the irreversibility in the collector plates increases with the amount of heat collected, so that the design of the collector plates has an influence on
0-7
0-3
0.1 0.0
~ .~_
so
60
,o
80
so
,oo
~o['cJ
(a)
0'7
o~
T~=2"C
~ ' ~ -
~
~
LiBr/H20
0.1 80
90
100
T¢
E'gJ
(b) Fig. 7. The change in ~ as a function of To and QCOL. TE =2°C- (a), NH3/H20;
(b), LiBr/HsO.
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
182
0.6
T~=IO'C
0.2
~0
....
. so
~o
~
.
. 6o
.
. 70
=.__
.
. 80
~
~
.
. 9o
re-1 ~
loo
r~l-C l
(a)
O-7
0.5
0.3
~soo .
5500
kiBr/H20 o.1 80
90
100
1tO l s
(b)
Fig. 8. The change in e,l as a function of TG and QcoL. T~= 10°C. (a), NH3/H20; (b), LiBr/H20.
reducing the lost work, The slow change in Et for LiBr/H20 can be observed from Figs 9 and 10(b). Figure 11 indicates the el - T6 change for both o f the fluid pairs. The increases in entropy generation, A~b, in the generator, condenser, and absorber are balanced by the decrease in irreversibility in the heat exchanger. This balance is not valid for N H s / H z O because of the different t h e r m o d y n a m i c properties of the solution. 2'*'6 The heat transfer in
50
60
70
coN~.2~.~
~
~~ ~ ~ A ~ o a
80 90 100 TG[•c.]"~ 80 90 100 (a) (b) Fig. 9. The change in availability difference with TG. Tr = 10~C.(a), NH3/H20; (b) LiBr/H20.
100
~
100
500
300
NH3/H20
(~coL =6800 kW
7oo
900
300
500
/
700
~.~
/
900
1 I00
13(}(}
A~[k~J
110
T~
Li Br/ H20
[~]
QCOL:6800 kW
TE =10"(]
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
184
,,~~
,~[,J] 8oo
600
ZJ C0L=6800 k~/ 200
NH3/H20 so
60
~o
80
so
~o[~
1oo
(a)
1000
8O0 TE =2"C
LiBr/H20 400
200
~~ ~
CO~E~ER m
oo
so
~oo
11o
To ['cJ
(b) Fig. 10. The change in availability difference with TG. TE=2°C. (a), N H 3 H 2 0 , (b) LiBr/H20.
185
Second-law analysis of solar absorption-cooling cycles ~ ....
E,
TE: = 2"C TE: =10"C
0"/-* 0"3
NH 3/t-lz0
/
LiBr/H20
,o
Fig. II.
,oo
The change in ~,i as a function of TG and T E.
the heat exchanger is between the solutions leaving the generator and absorber. For NH3/H20, the refrigerant concentration of the solutions between the points leaving the generator and the absorber differs too much as To increases. For LiBr/H20 around the limit resulting from crystallization, the difference and entropy changes become smaller. The rate of availability decrease thus slows down. However, this advantage of LiBr/H20 leads to an economic disadvantage. As the concentrations of the weak and strong solutions approach each other, the amount of the working fluid needed increases (Figs 12, 13(a), (b)). The opposite characteristics of the irreversibility curves for the condenser represented in Figs 9 and 10(a), (b) result from the fact that the heat transfer in this component occurs between the same kinds of fluid for LiBr/H20.
[kg/s]
30
25
~ ....
Te :2"C TE :lO'C
~Li
\\
20
NH3/H,0 ~
~
15
~
~
Br/H20 ~
5 50 Fig. 12.
60
70
80
90
100
The change in the mass-flow rate of the strong solution with
TO ['C]
To
Ahmet Karakas, Nilufer Egrican, Seyhan Uygur
186
[.g/s] 30
,o, 25
QcoL:6800 kW
Br ,o
,o
~ : IOeC~
5
80
90
100
110
T°~C]
(a)
15..
qcoL = 6800 kW NH3/HzO
10..
Te: -SaC rE:'7°°c
5.
~o
~o
7o
80
9o
,oo ToT'C]
(b) Fig. 13.
The change in mass-flow rate of the strong solution as a function of TG and TE.
(a), LiBr/H20; (b), NH3/H20.
CONCLUSIONS For the effective operation of an absorption-cooling system, correct choices of the working fluid and the design parameters of the components must be made. Where the temperature is above 0°C, the lithium bromide/water system is more effective than the ammonia/water system and has high values of COP. However, the lithium bromide/water system involves more design problems than the ammonia/water system because the pressures corresponding to the convenient temperatures are sub-atmospheric. This disadvantage can be partly reduced by considering the minimum entropy generation when choosing the design parameters of the components of the lithium bromide/water system. Solar energy is especially useful for obtaining
Second-law analysis of solar absorption-cooling cycles
187
a high degree of effectiveness. As may be seen from eqns (2) and (10), r/and q~ decrease with increasing heat flux from the solar collector. The influence of this inverse proportion on el is illustrated on Figs 7(a), (b) and 8(a), (b). Large a m o u n t s of heat flux are necessary, on the other hand, for high values of Tc. In order to avoid the high values of TC, it is preferable to use an auxiliary source of heat, instead of the solar collector, when the high Tc is needed or to design the collector plates to achieve m i n i m u m entropy generation.
REFERENCES 1. Duffle, J. A. & Beckman, W. A., Solar Engineering of Thermal Processes, John Wiley & Sons, New York, 1980. 2. Gomez, A. L. & Mansoori, G. A., Thermodynamic equation-of-state approach for the choice of the working fluids of the absorption cooling cycles. Solar Energy, 31 (1983) 557-66. 3. Bosnjakovic, F., Technical Thermodynamics (translated by P. L. Blackshear), Holt, Reinhart & Wiston, New York, 1965. 4. Egrican, N., The second law analysis of absorption cooling cycles, Heat Recovery Systems & CHP, 8 (1988) 549-58. 5. Brzustowski, T. A. & Golem, P. J., Second law analysis of the energy process. Part I: Energy- an introduction. Trans. ASME, 4 (1976-77) 209-21. 6. Lower, A., Thermodynamische Eigenschaften und Warmediagramme des Binaren Systems Lithiumbromide/Wasser. Kaltetechnic, 13(5) (1961). 7. Bejan, A., Second Law Analysis (Advances in Heat Transfer, Vol. 15), Plenum Press, New York, 1982.