esson 6 apour Absorption Refrigeration Systes Based On Aonia- Water Pair ersion ME, IIT Karagpur
Te specific objectives of tis lesson are to:. Introduce aonia-water based vapour absorption refrigeration systes (Section 6.). Discuss te properties of aonia-water ixtures and introduce pressureteperature-concentration (p-t-) and entalpy-teperature-concentration (-T) carts (Section 6.). Analyze soe basic steady flow processes using aonia-water ixtures suc as adiabatic and non-adiabatic ixing, trottling of solution streas and te concept of rectification (Section 6.) At te end of te lecture, te student sould be able to:. Differentiate between water-litiu broide and aonia-water systes vis-àvis teir properties. Explain te concepts of bubble point and dew point teperatures. Obtain terodynaic properties of aonia-water ixtures using p-t- and - T- carts 4. Analyze iportant steady flow processes involving binary ixtures 6.. Introduction In vapour absorption refrigeration systes based on aonia-water pair, aonia is te refrigerant and water is te absorbent. Tese systes are ore versatile tan systes based on water-litiu broide as tey can be used for bot sub-zero (refrigeration) as well above 0 o C (air conditioning) applications. However, tese systes are ore coplex in design and operation due to te saller boiling point teperature difference between te refrigerant and absorbent (about o C). Due to te saller boiling point teperature difference te vapour generated in te generator consists of bot aonia as well as water. If water is allowed to circulate wit aonia in te refrigerant circuit, ten: i. Heat transfer in condenser and evaporator becoes non-isoteral ii. Evaporator teperature increases iii. Evaporation will not be coplete iv. Water ay get accuulated in te evaporator leading to alfunctioning of te plant iv. Circulation ratio increases Since all te above effects are detriental to te perforance of te syste, it is necessary to iniize te concentration of water vapour in aonia at te inlet to te condenser. Tis requires additional coponents, naely a rectification colun and a deplegator between generator and absorber, wic increases te design coplexity and cost and also reduces te syste COP copared to water-litiu broide syste. ersion ME, IIT Karagpur
6.. Properties of aonia-water solutions 6... Coposition Siilar to water-litiu broide solutions, te coposition of aonia-water solution is also expressed eiter in ass fraction () or ole fraction (x). However, for aonia-water solutions, te ass and ole fractions are defined in ters of aonia. For exaple te ass fraction is defined as te ratio of ass of aonia to te total ass of solution, i.e., A = (6.) A + W were A and W are te ass of aonia and water in solution, respectively. Siilarly, te ole fraction of aonia-water solution is defined as: x n A = (6.) n A + n W were n A and n W are te nuber of oles of aonia and water in solution, respectively. Te nuber of oles of aonia and water can easily be obtained fro teir respective asses in solution and olecular weigts, tus; n = A W A = ; and n W (6.) MA M W were M A (= 7.0 kg/kol) and M W (= 8.0 kg/kol) are te olecular weigts of aonia and water respectively. 6... apour pressure of aonia-water solutions iquid aonia and water are copletely iscible in all proportions, ence can for solutions of all concentrations fro 0 to, at noral teperatures. Te effect of aonia in water is to lower te vapour pressure of water, siilarly te effect of water in aonia is to lower aonia s vapour pressure. Tus te total pressure over aoniawater solutions is ade up of partial pressure of aonia and partial pressure of water vapour, and is always in between te saturation pressures of pure aonia and water. If Raoult s law is applied to aonia-water ixtures, ten te total pressure at any teperature, P total is given by: P total = xp A + ( x) P W (6.4) ersion ME, IIT Karagpur
were x is te liquid pase ole fraction of aonia, P A and PW are te saturation pressures of pure aonia and pure water at tat teperature. However, siilar to water-litiu broide solutions, aonia-water solutions also deviate fro ideal solution beaviour predicted by Raoult s law in a negative anner, i.e., at a given teperature of te solution te actual vapour pressure will be less tan tat predicted by Raoult s law (activity coefficient is uc saller tan.0). For exaple, at a ass fraction of 0.4 and teperature of 40 o C, Raoult s law predicts a vapour pressure of 6.47 bar, wereas te easured vapour pressure is.09 bar. Te vapour pressure data of aonia-water solutions is also available in te for of Düring and oter P-T- plots. 6... Coposition of aonia-water vapour Since te vapour above aonia-water liquid consists of bot aonia and water vapour, it is essential to distinguis between te coposition in liquid pase and coposition in vapour pase. Te superscripts and will be used to distinguis between liquid and vapour pase copositions. Tus stands for liquid pase ass fraction and stands for vapour pase ass fraction. Toug te vapour pase coposition, can be obtained by assuing ideal solution beaviour, it is observed tat te actual vapour coposition deviates fro tat predicted by ideal ixture equations. Based on experiental easureents, carts ave been developed for obtaining coposition of aonia-water ixture in vapour pase in equilibriu wit a solution of aonia and water at different teperatures. Figure 6. sows te construction of suc a cart using wic one can obtain te coposition of ixture in vapour pase fro known values of liquid pase ass fraction ( ) and saturated teperature of pure aonia or pressure. ersion ME, IIT Karagpur 4
P T sat,nh Mass fraction of aonia in vapour, Fig.6.. apour-liquid equilibriu cart for aonia-water solution 6..4. Bubble point and dew point for aonia-water ixtures Figure 6. sows a cylinder containing ixture of aonia and water. Te pressure on te ixture is aintained constant wit te elp of a free-floating piston wit fixed weigts. Initially (State ) te cylinder consists of subcooled solution of aoniawater ixture. Now eat is supplied to te syste and te teperature of te solution is increased steadily, te ass fraction of te solution reains constant at initially. At a certain teperature te first vapour bubble appears. Te teperature at wic te first bubble appears is called as bubble point (=T bubble ) of te solution at tat concentration and pressure. Furter eating results in increase in teperature and foration of ore vapour as sown in te figure (State ). If eating is continued furter, ten te teperature ersion ME, IIT Karagpur 5
increases continuously, as ore liquid is converted into vapour, and finally at a particular teperature te last liquid droplet vaporizes. Te teperature at wic te last liquid droplet evaporates is called as dew point teperature (T dew ). Wen eating is continued furter te ixture enters into supereated vapour state (State ). It sould be noted tat unlike pure fluids, te teperature of te aonia-water ixture increases continuously as te liquid undergoes vaporization. Tis is to say tat te pase cange process is caracterized by a teperature glide, wic is te difference between te dew point and bubble point teperatures. If tis process is repeated wit different initial concentrations starting fro 0 (pure water) to (pure aonia) and at te sae pressure, different values of bubble and dew points will be obtained. Of course wen te concentration is 0 (pure water) or (pure aonia) te bubble and dew points coincide. Now if we plot te teperatures (bubble point and dew point) against concentration and join all te bubble points by a curve and all te dew points by anoter curve, ten we would get te equilibriu Teperature vs concentration curve for aonia-water ixtures at tat pressure as sown in Fig.6.. Te loci of all te bubble points is called as bubble point line and te loci of all te dew points is known as te dew point line. Te bubble point line is te saturated liquid line and te dew point line is te saturated vapour line for te ixture at tat pressure. Te region between te bubble and dew point lines is te twopase region were bot liquid and vapour coexist in equilibriu. Different bubble point and dew point lines will be obtained if te experient is carried out wit different pressures. For exaple, Figure 6.4 sows te bubble and dew point lines for two different pressures, P and P. Te sae results can also be obtained if one starts te experient initially wit supereated vapour and ten start cooling it. In tis case, te dew point is te teperature at wic te first liquid droplet fors fro te vapour and te bubble point is te teperature at wic te last vapour bubble condenses. P P P Heat Heat Heat () () () Fig.6.: A siple experient illustrating te principle of bubble and dew points ersion ME, IIT Karagpur 6
T W,Sat P = Constant Supereated vapour T T dew Dew Point line + Bubble Point line T bubble T A,Sat Subcooled liquid 0 Fig.6.: Equilibriu teperature-concentration curve for NH -H O at a constant pressure P > P T P = P P = P 0 (pure H O) (pure NH ) Fig.6.4: Bubble point and dew point curves at two different pressures ersion ME, IIT Karagpur 7
Now since te process is carried out in a closed syste, te ass of bot aonia and water will be conserved. Te concentration of subcooled liquid will be sae as te concentration of supereated vapour. However, in te two-pase region in wic te saturated liquid exists in equilibriu wit saturated vapour, te concentration of liquid and vapour will be different. For exaple, at point in Fig.6., te teperature of saturated liquid and vapour will be sae as tey are in equilibriu, ence, te concentration of liquid will be (intersection of constant teperature line wit bubble point line) and tat of vapour will be (intersection of constant teperature line wit dew point line) as sown in te figure. Obviously te vapour fored initially will be ricer in te low boiling point substance (aonia) and te liquid reaining will be ric in ig boiling point substance (water). For exaple, as sown in Fig.6., te concentration of te first vapour bubble will be and te concentration of te last liquid droplet will be.since te total ass as well as ass of individual coponents is always conserved, we can write ass balance for total ass ( total ) and aonia ( A ) ass at state as: total = + (6.5) A = + = (6.6) total were and are te ass of liquid and vapour at state, respectively. Fro te above equations it can be easily sown tat: =, or (6.7) ( ) = ( ) (6.8) Te above equation is called as te ixing rule or lever rule for te binary ixtures suc as aonia and water. It iplies tat te fraction of liquid and vapour in te two-pase ixture is inversely proportional to te distance between te ixture condition and te saturated liquid and vapour states and, respectively. 6..5. Entalpy of aonia-water ixtures iquid pase: Te entalpy of aonia-water solution in liquid pase, is calculated in a anner siilar to tat of water-litiu broide solutions, i.e., by te equation: A W =. + ( ) + Δ (6.9) ix ersion ME, IIT Karagpur 8
were is te liquid pase ass fraction of aonia, and are liquid pase entalpies of pure aonia and water respectively. Δix is te eat of ixing, wic is negative (exoteric) siilar to water-litiu broide ixtures. Using te above equation one can calculate te specific entalpy of aoniawater solutions at any concentration and teperature provided te eat of ixing is known fro easureents. Tus entalpy carts for solution are plotted as a field of isoters against ass fraction by taking suitable reference values for entalpy of aonia and water. Since pressure does not ave a significant effect on liquid entalpy (except at critical point), norally pressure lines are not sown on typical solution entalpy carts. Also entalpy of subcooled liquid is generally assued to be equal to te saturated entalpy at tat teperature witout loss of uc accuracy. apour pase: Evaluation of entalpy of a ixture of vapours of aonia and water is ore coplicated copared to liquid pase entalpy. Tis is due to te dependence of vapour entalpy on bot teperature and pressure. However, to siplify te proble, it is generally assued tat aonia and water vapour ix witout any eat of ixing. Ten te entalpy of te vapour ixture, is given by: A W A W =. + ( ) (6.0) were. is te vapour pase ass fraction of aonia and A and W are te specific entalpies of aonia vapour and water vapour respectively at te teperature of te ixture. However, since vapour entalpies depend on teperature as well as pressure, one as to evaluate te vapour entalpy at suitable pressure, wic is not equal to te total pressure. An approxiate, but practically useful etod is to evaluate te vapour entalpies of aonia and water at pressures, PA and P W given by: P P A W = yp total = ( y)p total (6.) were y is te vapour pase ole fraction of aonia and P total is te total pressure. It sould be noted tat P A and PW are equal to te partial pressures of aonia and water only if tey beave as ideal gases. However since aonia and water vapour ay not approac te ideal gas beaviour at all teperatures and pressures, in general P A and P W are not equal to te partial pressures. Using tis etod entalpies of aonia-water ixtures in vapour pase ave been obtained as functions of teperature and ass fraction. 6..6. Te coplete entalpy-coposition diagra for aonia-water ixtures: ersion ME, IIT Karagpur 9
Norally, carts of entalpy-teperature-ass fraction are available wic give bot liquid pase as well as vapour entalpy of ixtures. Figure 6.5 sows one suc cart. Figure 6.6 sows te entalpy-coposition diagra at a constant pressure P. In te figure point a represents te condition of saturated liquid ixture at a teperature T wit a liquid pase ass fraction of. Te liquid pase entalpy corresponding to tis condition is given by. Te coposition and entalpy of vapour ixture in equilibriu wit te liquid ixture at teperature T and pressure P are obtained by drawing a vertical line fro a upto te auxiliary line and ten drawing a orizontal line to te rigt fro te intersection of te vertical line wit te auxiliary line. Te intersection of tis orizontal line wit te dew point line a gives te vapour pase ass fraction and te vapour pase entalpy as sown in te figure. Te isoter T in te two-pase region is obtained by joining points a and a as sown in te figure. Point b in te figure lies in te two-pase region. Te specific entalpy of tis point b is given by: b b b = ( ψ ) + ψ (6.) were ψ b is te quality or dryness fraction of te two-pase ixture at b. Since points a, a and b are co-linear, te dryness fraction ψ is given by: b b ψ b = (6.) In actual entalpy-coposition diagras te isoters are not sown in two-pase region as a different set of te exist for eac pressure. It is iportant to note tat it is not possible to fix te state of te ixture (subcooled, saturated, two-pase or supereated) just fro teperature and ass fraction alone, toug one can calculate entalpy of te ixture fro teperature and ass fraction. Tis is due to te reason tat at a given ass fraction and teperature, depending upon te pressure te point can be subcooled or saturated or supereated. For exaple, a liquid ixture wit a ass fraction of 0.4 and teperature of 80 o C as an entalpy of 0 kj/kg, and it will be in subcooled condition if te pressure is 4.9 bar and saturated if te pressure is 8.75 bar. ersion ME, IIT Karagpur 0
Fig.6.5: -T- cart for aonia-water solution ersion ME, IIT Karagpur
P = Constant Dew point line fg,w Auxiliary line a T a b T b fg,a 0 Deterination of teperature of ixture in two-pase region: b Bubble point line Fig.6.6: Entalpy-coposition diagra of NH -H O at a constant pressure P A trial-and-error etod as to be used to deterine te teperature of a point in two-pase region if its entalpy, liquid pase ass fraction and pressure are known. Te trial-and-error etod can be grapical or nuerical. Figure 6.7 sows a grapical etod for finding te teperature of point x in te two-pase region wic is at a known pressure P x, liquid pase ass fraction x and entalpy x. To start wit, point a is obtained as sown in te figure by drawing a vertical line fro point x upto te auxiliary line and ten drawing a orizontal line fro te intersection point a upto te dew point line, te intersection of wic gives a. Ten a straigt line a -x-a is drawn as sown. Next point b is obtained by drawing a vertical line upto te auxiliary line and ten drawing a orizontal line fro b upto te dew point line to get b. Ten line b -x-b is drawn passing troug x. Tis procedure is repeated until convergence is obtained. Nuerically te teperature can be obtained fro te equation, wic needs to be satisfied for eac end of te isoter passing troug x, i.e., x x = x x (6.4) To start wit guess values of and are assued by taking soe point on te bubble point line. Ten saturated vapour properties and are obtained fro te entalpy- coposition carts using te guess values of and. Ten using te above equation, ersion ME, IIT Karagpur
new values of and are obtained. Ten tese new values are used to obtain next set of and. Tis procedure is repeated till te values converge. Once te converged values of and are obtained ten te teperature is read fro te entalpycoposition cart. P x = Constant b a b a x x a b 0 x Fig.6.7: A grapical etod for finding teperature of liquid-vapour ixture 6.. Basic steady-flow processes wit binary ixtures a ) Adiabatic ixing of two streas: Wen two streas of aonia-water solutions are ixed adiabatically as sown in Fig.6.8, one can write ass and energy balance equations as: + = (6.5) + = (6.6) + = (6.7) Fro te above equations, te ass fraction and entalpy of te ixture at are given by: ersion ME, IIT Karagpur
= + ( ) (6.8) = + ( ) (6.9) Adiabatic ixing Caber / / 0 Fig.6.8: Adiabatic ixing of two solution streas Figure 6.9 sows te adiabatic ixing process wit te ixture state lying in two-pase region on te entalpy-coposition diagra. Te ixture state in two-pase region iplies tat soe vaporization as occurred during adiabatic ixing of te two inlet streas and. Te entalpy and coposition of te two-pase ixture at can be obtained by using te equations given above. However, since tis is in two-pase region, te ixture consists of saturated liquid and vapour. Te dryness fraction and teperature of te ixture (T ) ave to be obtained by trial-and-error etod by applying ixing rules. Te fraction of te vapour in te ixture at is ten given by: = = (6.0) b ) Mixing of two streas wit eat transfer: Te process of ixing of two streas wit eat transfer takes place in absorber and generator of absorption refrigeration systes. For exaple, Fig.6.0 sows te ixing of saturated refrigerant vapour (state ) wit saturated solution of refrigerant-absorbent (state ) in te absorber. Te resulting ixture is a solution tat is ric in refrigerant (state ). Since te process is exoteric, eat (Q) is released during tis process. Mass and energy balance equations for tis process can be written as: ersion ME, IIT Karagpur 4
T T 0 Fig.6.9: Adiabatic ixing of two streas on -T- diagra ersion ME, IIT Karagpur 5
+ = + = = + (6.) (6.) + Q (6.) Fro te above equations, te entalpy of te ixture at is given by: Q = + ( ) (6.4) Tus wit eat transfer fro te ixing caber, te exit state lies at a vertical distance of (Q/ ) below te state wic would result witout eat transfer (point ). Te exit point would lie above te state witout eat transfer if eat is transferred to te ixing caber. c) Trottling process: Trottling or isentalpic expansion of aonia-water solution takes place in te solution expansion valve of te absorption refrigeration syste. Figure 6. sows te trottling process on entalpy-coposition diagra. Since bot ass and energy are conserved during tis process, and tere is neiter work nor eat transfer, we obtain: = (6.5) = (6.6) Absorber Q Q/ 0 = Fig.6.0: Mixing of two streas wit eat transfer ersion ME, IIT Karagpur 6
Hence te inlet and outlet states, points and are identical on entalpy-coposition diagra as sown in te figure. However, as tere is possibility of vapour generation due to flasing, te exit condition ay be a ixture of saturated liquid and vapour at te outlet pressure P ten te exit teperature T will be uc lower tan te inlet teperature T. Taking point as in te two-pase region corresponding to te outlet pressure P, one can get te vapour fraction and exit teperature T by trial-end-error etod as discussed earlier. P, Dew point line P T =T =T = T, T P, Bubble point line = Fig.6.: Trottling of aonia-water solution d) Heating and cooling process concept of rectification: Figure 6. sows an arrangeent werein an initially subcooled solution (state ) is eated in a eat excanger A (HX A) in suc a way tat te exit condition lies in te two-pase region. Tis two-pase ixture ten flows into an adiabatic separator (SEP A) were te saturated liquid (state ) and saturated vapour (state 4) are separated. Te saturated vapour at state 4 is ten cooled to state 5 in anoter eat excanger B (HX B) by rejecting eat 4 Q 5. Te resulting two-pase ixture is ten fed to anoter adiabatic separator B (SEP B), were again te saturated liquid (state 6) and saturated vapour (state 7) are separated. It is assued tat te entire process takes place at a constant pressure and is a steady-flow process. ersion ME, IIT Karagpur 7
apour, 7 SEP (B) Saturated liquid, 6 HX (A) 5 HX (B) 4 4Q 5 Q / Isoters P=Constant 4 7 5 6 4Q 5 / 4 Q SEP (A) Saturated liquid, Fig.6.: Heating and cooling of NH -H O solution concept of rectification Now ass and energy balances are applied to eac of te coponents as sown below: Heat excanger A: Mass balance: = (6.7) = (6.8) Energy balance: Separator A: Mass balance: Q = ( ) (6.9) = + (6.0) 4 = + 4 4 (6.) Energy balance: ersion ME, IIT Karagpur 8
= + 4 4 (6.) fro te above equations: 4 4 4 lengt 4 = = = (6.) lengt 4 4 4 lengt = = = (6.4) lengt 4 4 4 Siilar equations can be obtained for eat excanger B and separator B. Te entire process is also sown on entalpy-coposition diagra in Fig.6.. It ay be noted tat fro te above arrangeent consisting of eating, cooling and separation, one finally obtains a vapour at state 7 tat is ric in aonia. Tat is te cobination of eat excangers wit separators is equivalent to te process of rectification. Heat excanger A plays te role of generator, wile eat excanger B plays te role of deplegator. To iprove te process of rectification in actual vapour absorption refrigeration systes, a rectifying colun is introduced between te generator and deplegator. In te rectifying colun, te vapour fro te separator A coes in contact wit te saturated liquid coing fro separator B. As a result, tere will be eat and ass transfer between te vapour and liquid and finally te vapour coes out at a uc iger concentration of aonia. Te practical aonia-water based vapour absorption refrigeration syste incorporating rectifying colun and deplegator in addition to te basic coponents will be discussed in te next lesson. Questions and Answers:. Presence of water vapour in te refrigerant circuit of a NH -H O syste: a) Decreases evaporator teperature b) Increases evaporator teperature c) Increases circulation ratio d) eads to non-isoteral eat transfer in evaporator and condenser Ans. b), c) and d). Copared to H O-iBr systes, a NH -H O syste: a) Requires additional coponents due to te requireent of rectification b) Yields iger COP c) Yields lower COP d) Increases design coplexity and syste cost ersion ME, IIT Karagpur 9
Ans. a), c) and d). Wic of te following stateents regarding te definition of concentration are TRUE: a) A strong solution of H O-iBr iplies a solution ric in refrigerant b) A strong solution of H O-iBr iplies a solution weak in refrigerant c) A strong solution of NH-HO iplies a solution ric in refrigerant d) A strong solution of NH -H O iplies a solution weak in refrigerant Ans. b) and c) 4. Wic of te following stateents regarding NH -H O solution are TRUE: a) Te bubble point teperature is always iger tan dew point teperature b) Te bubble point teperature is always lower tan dew point teperature c) At a given pressure, te bubble point and dew point teperatures are iger tan te saturation teperature of NH but lower tan te saturation teperature of HO d) At a given pressure, te bubble point and dew point teperatures are lower tan te saturation teperature of NH but iger tan te saturation teperature of HO Ans.: b) and c) 5. For NH -H O solution at equilibriu, wic of te following stateents are FASE: a) Te concentration of liquid pase is lower tan te concentration of vapour pase b) Te entalpy of subcooled solution is a function of teperature and pressure c) Te entalpy of supereated vapour is a function of teperature only d) Te state of te ixture can be uniquely deterined by teperature and concentration Ans.: b) and d) 6. Wen a binary solution of NH -H O is trottled adiabatically: a) Teperature always reains constant b) Teperature ay decrease c) Teperature ay increase d) Entalpy always reains constant Ans.: b) and d) 7. A binary ixture of NH - H O is at a teperature of 40 o C and a liquid pase ole fraction x of 0.5. Find te vapour pressure of te solution, if te activity coefficient of te solution is 0.65. Te saturation pressures of aonia and water at 40 o C are 557 kpa and 7.75 kpa, respectively. ersion ME, IIT Karagpur 0
Ans.: Fro Raoult s law, te vapour pressure is given by: P = x.p + ( x).p v,raoult sat,nh sat,ho = 78.9 kpa Using te definition of activity coefficient, a; te actual vapour pressure P is given by: v Pv,act = a.pv, Raoult = 0.65 X 78.9 = 508.4 kpa (Ans.) 8. A binary vapour ixture consisting of aonia and water is at a ole fraction of 0.9 and 0 o C. If te partial pressures of aonia and water vapour in te ixture are 66.5 kpa and.7 kpa, respectively; and te specific vapour entalpies of aonia and water are 47.57 kj/kg and 59.9 kj/kg, respectively, find a) te vapour pressure of te ixture, and b) te specific entalpy of te ixture. Ans.: a) Assue te vapour ixture to beave as a ixture of ideal gases, ten te total pressure of te ixture P is given by: v P = y.p + ( y).p = 554.75 kpa (Ans.) v NH HO b) Te ass fraction of te ixture is given by: A na.m A = = A + W na.m A + nw.m W 7n A = 7n + 8n A W Since te ole fraction of te vapour ixture is 0.9 n A = 9 n W Substituting tis in te expression for ass fraction, we find tat = 0.895 Again assuing te vapour ixture to beave as a ixture of ideal gases; te entalpy of te ixture is given by: =. A + (- ) W = 58.64 kj/kg (Ans.) 9. Find te dryness fraction (quality) and specific entalpy of te two-pase (liquid & vapour) of aonia-water ixture using te following data: iquid pase ass fraction, = 0.0 apour pase ass fraction, = 0.87 Mass fraction of -pase ixture, = 0.50 Specific entalpy of saturated liquid, = 40 kj/kg Specific entalpy of saturated vapour, = 640 kj/kg ersion ME, IIT Karagpur
Ans.: Dryness fraction, ψ = = = 0.5 (Ans.) + Entalpy of te two-pase ixture is given by: = ( ψ) + ψ = 796. kj / kg (Ans.) 9. Two solution streas are ixed in a steady flow device. A eat transfer rate of 4 kw takes place fro te device. Find te exit concentration and entalpy using te data given below: Strea : Mass flow rate, = 0. kg/s Concentration, = 0.7 Entalpy, = 0 kj/kg Strea : Mass flow rate, = 0. kg/s Concentration, = 0.4 Entalpy, = 50 kj/kg Ans.: Fro ass balance of solution and aonia, te exit concentration is given by : ( + ) = = 0.475 (Ans.) ( + ) Fro energy balance of solution and aonia, te exit concentration is given by : [( + ) Q] = = 55 kj / kg (Ans.) ( + ) ersion ME, IIT Karagpur