Chapter 8 EXERGY A MEASURE OF WORK POTENTIAL

Transcription

1 8- Chapter 8 EXERGY A MEAURE OF ORK POENIAL Exergy, Irreveribility, Reverible ork, and econd-law Efficiency 8-C Reverible work differ from the ueful work by irreveribilitie. For reverible procee both are identical. u rev -I. 8-C Reverible work and irreveribility are identical for procee that volve no actual ueful work. 8-C he dead tate. 8-4C Ye; exergy i a function of the tate of the urroundg a well a the tate of the. 8-5C Ueful work differ from the actual work by the urroundg work. hey are identical for that volve no urroundg work uch a teady-flow. 8-6C Ye. 8-7C No, not necearily. he well with the higher temperature will have a higher exergy. 8-8C he that i at the temperature of the urroundg ha zero exergy. But the that i at a lower temperature than the urroundg ha ome exergy ce we can run a heat enge between thee two temperature level. 8-9C hey would be identical. 8-C he econd-law efficiency i a meaure of the performance of a device relative to it performance under reverible condition. It differ from the firt law efficiency that it i not a converion efficiency. 8-C No. he power plant that ha a lower thermal efficiency may have a higher econd-law efficiency. 8-C No. he refrigerator that ha a lower COP may have a higher econd-law efficiency. 8-C A procee with rev i reverible if it volve no actual ueful work. Otherwie it i irreverible. 8-4C Ye.

2 8-8-5 dmill are to be talled at a location with teady wd to erate power. he mimum number of wdmill that need to be talled i to be determed. Aumption Air i at tandard condition of atm and 5 C Propertie he ga contant of air i.87 kpa.m /kg.k (able A-). Analyi he exergy or work potential of the blowg air i the ketic energy it poee, Exergy ke V (8 m/) kj/kg m /. kj/kg At tandard atmopheric condition (5 C, kpa), the denity and the ma flow rate of air are and hu, P kpa ρ 8. m / kg R (.87 kpa m / kg K)(98 K) m& ρav π D ρ 4 Available Power m& ke (74 kg/)(. kj/kg).74 k V (.8 kg/m )( π / 4)( m) (8 m/) 74 kg/ he mimum number of wdmill that need to be talled i & total 6 k N 5. 6 wdmill &.74 k 8-6 ater i to be pumped to a high elevation lake at time of low electric demand for ue a hydroelectric turbe at time of high demand. For a pecified energy torage capacity, the mimum amount of water that need to be tored the lake i to be determed. Aumption he evaporation of water from the lake i negligible. Analyi he exergy or work potential of the water i the potential energy it poee, hu, m PE gh 6 5 (9.8 m/ Exergy PE mgh kh 6 m / )(75 m) h k /kg.45 kg 75 m

3 8-8-7 A heat reervoir at a pecified temperature can upply heat at a pecified rate. he exergy of thi heat upplied i to be determed. Analyi he exergy of the upplied heat, the rate form, i the amount of power that would be produced by a reverible heat enge, η th,max η th,rev H 98 K 5 K.8 5 K Exergy & max, & rev, η th,rev & (.8)(5, / 6 kj/).4 k HE 98 K & rev 8-8 [Alo olved by EE on encloed CD] A heat enge receive heat from a ource at a pecified temperature at a pecified rate, and reject the wate heat to a k. For a given power put, the reverible power, the rate of irreveribility, and the nd law efficiency are to be determed. Analyi (a) he reverible power i the power produced by a reverible heat enge operatg between the pecified temperature limit, η & th,max rev, η η th,rev th,rev L K.787 H 5 K & (.787)(7 kj/) 55.7 k 5 K 7 kj/ (b) he irreveribility rate i the difference between the reverible power and the actual power put: I & & rev, & k u, (c) he econd law efficiency i determed from it defition, η II u, rev, k 55.7 k 58.% HE K k

4 EE Problem 8-8 i reconidered. he effect of reducg the temperature at which the wate heat i rejected on the reverible power, the rate of irreveribility, and the econd law efficiency i to be tudied and the reult are to be plotted. Analyi he problem i olved ug EE, and the olution i given below. "Input Data" _H 5 [K] _dot_h 7 [kj/] {_L [K]} _dot_ [k] _Lurr 5 [C] "he reverible work i the maximum work done by the Carnot Enge between _H and _L:" Eta_Carnot - _L/_H _dot_rev_dot_h*eta_carnot "he irreveribility i given a:" I_dot _dot_rev-_dot_ "he thermal efficiency i, percent:" Eta_th Eta_Carnot*Convert(, %) "he econd law efficiency i, percent:" Eta_II _dot_/_dot_rev*convert(, %) η II [%] I [kj/] rev [kj/] L [K] ] J / [k e v r L [K]

5 ] [% η I L [K] 5 8 ] J / [k I L [K]

6 8-6 8-E he thermal efficiency and the econd-law efficiency of a heat enge are given. he ource temperature i to be determed. Analyi From the defition of the econd law efficiency, hu, η η th η II η th,rev th,rev L H η th,rev H η th η L II /( η th,rev ) (5 R)/.4 5 R H HE 5 R η th 6% η II 6% 8- A body conta a pecified amount of thermal energy at a pecified temperature. he amount that can be converted to work i to be determed. Analyi he amount of heat that can be converted to work i imply the amount that a reverible heat enge can convert to work, η th,rev max, H rev, (.675)( kj) 6.75 kj 98 K K η th,rev 8 K HE 98 K kj 8- he thermal efficiency of a heat enge operatg between pecified temperature limit i given. he econd-law efficiency of a enge i to be determed. Analyi he thermal efficiency of a reverible heat enge operatg between the ame temperature reervoir i hu, η th,rev H η th η II η th,rev 9 K.8 7 K % C HE C η th.4

7 A houe i mataed at a pecified temperature by electric reitance heater. he reverible work for thi heatg proce and irreveribility are to be determed. Analyi he reverible work i the mimum work required to accomplih thi proce, and the irreveribility i the difference between the reverible work and the actual electrical work conumed. he actual power put i & & H & 8, kj/h. k he COP of a reverible heat pump operatg between the pecified temperature limit i hu, and COP & rev, I& & L / H 88 / 95 HP, rev & COP u, & H HP,rev rev, 4.4. k.5 k k Houe C 8, kj/h 5 C 8-4E A freezer i mataed at a pecified temperature by removg heat from it at a pecified rate. he power conumption of the freezer i given. he reverible power, irreveribility, and the econd-law efficiency are to be determed. Analyi (a) he reverible work i the mimum work required to accomplih thi tak, which i the work that a reverible refrigerator operatg between the pecified temperature limit would conume, H / L 55 / 48 COP R, rev & rev, & COP L R,rev 75 Btu/m hp 4.4 Btu/m (b) he irreveribility i the difference between the reverible work and the actual electrical work conumed, I & & u, &.7..5 hp rev, (c) he econd law efficiency i determed from it defition, & η II & rev u. hp.7 hp 8.9%. hp 75 F R Freezer F 75 Btu/m.7 hp

8 It i to be hown that the power produced by a wd turbe i proportional to the cube of the wd velocity and the quare of the blade pan diameter. Analyi he power produced by a wd turbe i proportional to the ketic energy of the wd, which i equal to the product of the ketic energy of air per unit ma and the ma flow rate of air through the blade pan area. herefore, d power (Efficiency)(Ketic energy)(ma flow rate of air) η η wd wd V ( ρav ) η πv D ρ 8 wd V (Contant) V π D ρ 4 which complete the proof that wd power i proportional to the cube of the wd velocity and to the quare of the blade pan diameter. D V 8-6 A geothermal power produce 4 M power while the exergy detruction the plant i 8.5 M. he exergy of the geothermal water enterg to the plant, the econd-law efficiency of the plant, and the exergy of the heat rejected from the plant are to be determed. Aumption teady operatg condition exit. Ketic and potential energy change are negligible. ater propertie are ued for geothermal water. Analyi (a) he propertie of geothermal water at the let of the plant and at the dead tate are (able A- 4 through A-6) 6 C h kj/kg x.946 kj/kg.k 5 C h 4.8 kj/kg x.67 kj/kg.k he exergy of geothermal water enterg the plant i X & m& h [ h ( ] [( ) kj/kg (5 7 K)( )kJ/kg.K] (44 kg/) 44,55 k 44.5 M (b) he econd-law efficiency of the plant i the ratio of power produced to the exergy put to the plant & η II X& 4, k 44,55 k.4 (c) he exergy of the heat rejected from the plant may be determed from an exergy balance on the plant X & heat, X& & X& 44,55 4, 8,5,5 k. M det

9 8-9 econd-law Analyi of Cloed ytem 8-7C Ye. 8-8C Ye, it can. For example, the t law efficiency of a reverible heat enge operatg between the temperature limit of K and K i 7%. However, the econd law efficiency of thi enge, like all reverible device, i %. 8-9 A cylder itially conta air at atmopheric condition. Air i compreed to a pecified tate and the ueful work put i meaured. he exergy of the air at the itial and fal tate, and the mimum work put to accomplih thi compreion proce, and the econd-law efficiency are to be determed Aumption Air i an ideal ga with contant pecific heat. he ketic and potential energie are negligible. Propertie he ga contant of air i R.87 kpa.m /kg.k (able A-). he pecific heat of air at the average temperature of (984)/6 K are c p.9 kj/kg K and c v.7 kj/kg K (able A-). Analyi (a) e realize that X Φ ce air itially i at the dead tate. he ma of air i Alo, and P V ( kpa)(. m ) m.4 kg R (.87 kpa m / kg K)(98 K) PV P V P ( kpa)(4 K) V V ( L).47 L P (6 kpa)(98 K) c p,avg ln P R ln P 4 K (.9 kj/kg K) ln (.87 kj/kg K) 98 K.68 kj/kg K hu, the exergy of air at the fal tate i (.4 kg).7 kj [ ( ) ( )] X Φ m cv,avg P ( V V ) 6 kpa ln kpa [(.7 kj/kg K)(4-98)K - (98 K)(-.68 kj/kg K) ] ( kpa)(.47-.)m [kj/m kpa] AIR V L P kpa 5 C (b) he mimum work put i the reverible work put, which can be determed from the exergy balance by ettg the exergy detruction equal to zero, X X 44 Net exergy tranfer by heat,work,andma Xdetroyed X Exergy detruction (reverible) rev, (c) he econd-law efficiency of thi proce i η II rev, u,.7 kj. kj 4.% X exergy X.7.7kJ

10 8-8- A cylder i itially filled with R-4a at a pecified tate. he refrigerant i cooled and condened at contant preure. he exergy of the refrigerant at the itial and fal tate, and the exergy detroyed durg thi proce are to be determed. Aumption he ketic and potential energie are negligible. Propertie From the refrigerant table (able A- through A-), v.4875 m / kg P.7 MPa u 74. kj/kg 6 C.56 kj/kg K v v f P.7 MPa u u f 4 C v P. MPa u C 4 C.78 m. kj/kg K 5.84 kj/kg.86m kj/kg / kg.958 kj/kg K / kg Analyi (a) From the cloed exergy relation, {( u u ) ( ) P ( v )} X Φ m v (5 kg){( ) kj/kg (97 K)(.56.) kj/kg K R-4a.7 MPa P cont. and, ( kpa)( )m 5. kj kj /kg kpa m {( u u ) ( ) P ( v )} X Φ m v (5 kg){( ) kj/kg - (97 K)(.958.) kj/kg K } ( kpa)(.86.78)m 8.6 kj kj /kg kpa m (b) he reverible work put, which repreent the mimum work put rev, thi cae can be determed from the exergy balance by ettg the exergy detruction equal to zero, X X 44 Net exergy tranfer by heat,work,andma detroyed Exergy detruction (reverible) X X rev, X exergy X } kj Notg that the proce volve only boundary work, the ueful work put durg thi proce i imply the boundary work exce of the work done by the urroundg air, u, urr, m( P P )( v v ) P ( V V ) P( V V ) P m( v v ) (5 kg)(7 - kpa)( m kj / kg) kpa m. kj Knowg both the actual ueful and reverible work put, the exergy detruction or irreveribility that i the difference between the two i determed from it defition to be X detroyed I kj u, rev,

11 8-8- he radiator of a team heatg i itially filled with uperheated team. he valve are cloed, and team i allowed to cool until the preure drop to a pecified value by tranferrg heat to the room. he amount of heat tranfer to the room and the maximum amount of heat that can be upplied to the room are to be determed. Aumption Ketic and potential energie are negligible. Propertie From the team table (able A-4 through A-6), v.85 m / kg P kpa u kj/kg C 7.58 kj/kg K x 8 C u ( v v ) v v f v fg.45.9 u x u kj/kg f f x Analyi (a) he ma of the team i V. m m v.85 m / kg fg fg kj/kg K.85 kg EAM L P kpa C he amount of heat tranfer to the room i determed from an energy balance on the radiator expreed a or, E E 44 Net energy tranfer by heat, work, and ma ternal, ketic, potential, etc.energie U m( u m( u E 44 u ) u ) (ce KE PE ) (.85 kg)( ) kj/kg. kj (b) he reverible work put, which repreent the maximum work put rev, thi cae can be determed from the exergy balance by ettg the exergy detruction equal to zero, X X 44 Net exergy tranfer by heat,work,andma detroyed Exergy detruction (reverible) X X rev, X exergy X ubtitutg the cloed exergy relation, the reverible work durg thi proce i determed to be rev, m m [( u u ) ( ) P ( v v )] rev, X X [( u u ) ( )] kg) [( )kJ/kg - (7 K)( )kJ/kg K] 8.5 kj (.85 hen thi work i upplied to a reverible heat pump, it will upply the room heat the amount of H COP HP,rev rev rev / L H 8.5 kj - 7/94 6. kj Dicuion Note that the amount of heat upplied to the room can be creaed by ab time by elimatg the irreveribility aociated with the irreverible heat tranfer proce. Φ Φ

12 8-8- EE Problem 8- i reconidered. he effect of the fal team temperature the radiator on the amount of actual heat tranfer and the maximum amount of heat that can be tranferred i to be vetigated. Analyi he problem i olved ug EE, and the olution i given below. _ [C] P_ [kpa] V [L] _8 [C] _o [C] P_o [kpa] "Conervation of energy for cloed i:" E_ - E_ DELAE DELAE m*(u_ - u_) E_ E u_ tenergy(team_iapw,pp_,_) v_ volume(team_iapw,pp_,_) _ entropy(team_iapw,pp_,_) v_ v_ u_ tenergy(team_iapw, vv_,_) _ entropy(team_iapw, vv_,_) mv*convert(l,m^)/v rev-m*(u_ - u_ -(_o7.5)*(_-_)p_o*(v_-v_)) "hen thi work i upplied to a reverible heat pump, the heat pump will upply the room heat the amount of :" _H COP_HP*_rev COP_HP _H/(_H-_L) _H 94 [K] _L 7 [K] H [kj] [kj] [C] rev [kj] J ] [k m R oo to e r f ra n H eat Maximum Actual [C]

13 8-8-E An ulated rigid tank conta aturated liquid-vapor mixture of water at a pecified preure. An electric heater ide i turned on and kept on until all the liquid i vaporized. he exergy detruction and the econd-law efficiency are to be determed. Aumption Ketic and potential energie are negligible. Propertie From the team table (able A-4 through A-6) v v f xv P 5 pia u u f xu x.5 x v v u at. vapor u f fg fg fg v g.988 ft /lbm v g.988 ft /lbm.78.5 (.9.78).988 ft Btu / lbm Btu / lbm R.9 Btu/lbm.569 Btu/lbm R Analyi (a) he irreveribility can be determed from it defition X detroyed where the entropy eration i determed from an entropy balance on the tank, which i an ulated cloed, ubtitutg, 44 Net entropy tranfer by heat and ma X detroyed { Entropy eration 44 entropy m ( ) m( ) (6 lbm)(55 R)( )Btu/lbm R 766 Btu H O 5 pia / lbm (b) Notg that V contant durg thi proce, the and u are identical and are determed from the energy balance on the cloed energy equation, or, E E 44 Net energy tranfer by heat, work, and ma e, e, E 44 ternal, ketic, potential, etc.energie U m( u u ) (6 lbm)( )btu/lbm 45 Btu hen the reverible work durg thi proce and the econd-law efficiency become hu, rev, u, X detroyed Btu η II rev u 9 Btu 45 Btu.9% e

14 A rigid tank i divided to two equal part by a partition. One part i filled with compreed liquid while the other ide i evacuated. he partition i removed and water expand to the entire tank. he exergy detroyed durg thi proce i to be determed. Aumption Ketic and potential energie are negligible. Analyi he propertie of the water are (able A-4 through A-6) v v f P kpa u u f C 6 C.7 m 5.6 kj/kg / kg.8 kj/kg K Notg that v v.7.4 m / kg, P v x 5 kpa u.4.5 kg kpa 6 C AER v v f v fg..4 u x u kj/kg f f x fg fg kj/kg K Vacuum akg the direction of heat tranfer to be to the tank, the energy balance on thi cloed become or, E E 44 Net energy tranfer by heat, work, and ma E 44 ternal, ketic, potential, etc.energie U m( u u ) (.5 kg)( )kj/kg -7.5kJ 7.5 kj he irreveribility can be determed from it defition X detroyed where the entropy eration i determed from an entropy balance on an extended that clude the tank and it immediate urroundg o that the boundary temperature of the extended i the temperature of the urroundg at all time, ubtitutg, 44 Net entropy tranfer by heat and ma X detroyed b, { Entropy eration 44 entropy m( m( ) urr m( ) urr 7.5 kj (98 K) (.5 kg)( )kJ/kg K 98 K.67 kj )

15 EE Problem 8-4 i reconidered. he effect of fal preure the tank on the exergy detroyed durg the proce i to be vetigated. Analyi he problem i olved ug EE, and the olution i given below. _6 [C] P_ [kpa] m.5 [kg] P_5 [kpa] _o5 [C] P_o [kpa] _urr _o "Conervation of energy for cloed i:" E_ - E_ DELAE DELAE m*(u_ - u_) E_ E u_ tenergy(team_iapw,pp_,_) v_ volume(team_iapw,pp_,_) _ entropy(team_iapw,pp_,_) v_ *v_ ] u_ tenergy(team_iapw, vv_,pp_) J k [ _ entropy(team_iapw, vv_,pp_) _ - DELA_y _ [kj/k] /(_urr7) DELA_ym*(_ - _) X_detroyed (_o7)*_ d ye o tr X de P [kpa] X detroyed [kj] [kj] t ou P [kpa] P [kpa]

16 An ulated cylder i itially filled with aturated liquid water at a pecified preure. he water i heated electrically at contant preure. he mimum work by which thi proce can be accomplihed and the exergy detroyed are to be determed. Aumption he ketic and potential energy change are negligible. he cylder i well-ulated and thu heat tranfer i negligible. he thermal energy tored the cylder itelf i negligible. 4 he compreion or expanion proce i quai-equilibrium. Analyi (a) From the team table (able A-4 through A-6), u u kj / kg P 5 kpa v v f at. liquid h h f he ma of the team i V. m m v.5 m kpa kpa / kg.5 m 467. kj/kg /kg.47 kj/kg K.899 kg aturated Liquid H O P 5 kpa e take the content of the cylder a the. hi i a cloed ce no ma enter or leave. he energy balance for thi tationary cloed can be expreed a E E 44 Net energy tranfer by heat, work, and ma E 44 ternal, ketic, potential, etc.energie e, b, U ce U b H durg a contant preure quai-equilibrium proce. olvg for h, e, kj h h kj/kg m.899 kg hu, P h 5 kpa 65. kj/kg x u h u f h h fg x f v v f f x u x v kj/kg K fg fg fg kj/kg e, e m( h h).5.5 (.594.5).67 m he reverible work put, which repreent the mimum work put rev, thi cae can be determed from the exergy balance by ettg the exergy detruction equal to zero, (reverible) X Xdetroyed X rev, X X X 44 Net exergy tranfer by heat,work,andma Exergy detruction 44 exergy ubtitutg the cloed exergy relation, the reverible work put durg thi proce become m ( u u ) ( ) P ( v v ) rev, [ ] (.899 kg){( ) kj/kg (98 K)( ) kj/kg K ( kpa)(.5.67)m / kg[ kj/ kpa m ]} 47.7 kj (b) he exergy detruction (or irreveribility) aociated with thi proce can be determed from it defition X detroyed where the entropy eration i determed from an entropy balance on the cylder, which i an ulated cloed, 44 { 44 ubtitutg, X Net entropy tranfer by heat and ma detroyed Entropy eration entropy m( ) m ( ) (98 K)(.899 kg)( )kj/kg K 75 kj /kg

17 EE Problem 8-6 i reconidered. he effect of the amount of electrical work on the mimum work and the exergy detroyed i to be vetigated. Analyi he problem i olved ug EE, and the olution i given below. x_ P_5 [kpa] V [L] P_P_ {_Ele [kj]} _o5 [C] P_o [kpa] "Conervation of energy for cloed i:" E_ - E_ DELAE DELAE m*(u_ - u_) E Ele E b _b m*p_*(v_-v_) u_ tenergy(team_iapw,pp_,xx_) v_ volume(team_iapw,pp_,xx_) _ entropy(team_iapw,pp_,xx_) u_ tenergy(team_iapw, vv_,pp_) _ entropy(team_iapw, vv_,pp_) mv*convert(l,m^)/v rev_m*(u_ - u_ -(_o7.5) *(_-_)P_o*(v_-v_)) "Entropy Balance:" _ - DELA_y DELA_y m*(_ - _) _ [kj/k] _ [kj/k] "he exergy detruction or irreveribility i:" X_detroyed (_o7.5)*_ J ] [k n e v,i r Ele [kj] Ele rev, X detroyed [kj] [kj] [kj] K ] J / [k d ye o tr X de Ele [kj]

18 An ulated cylder i itially filled with aturated R-4a vapor at a pecified preure. he refrigerant expand a reverible manner until the preure drop to a pecified value. he change the exergy of the refrigerant durg thi proce and the reverible work are to be determed. Aumption he ketic and potential energy change are negligible. he cylder i well-ulated and thu heat tranfer i negligible. he thermal energy tored the cylder itelf i negligible. 4 he proce i tated to be reverible. Analyi hi i a reverible adiabatic (i.e., ientropic) proce, and thu. From the refrigerant table (able A- through A-), v v g P.8 MPa u u g at. vapor he ma of the refrigerant i V.5 m m v.56 m MPa MPa / kg fg.56 m kj/kg / kg.98 kj/kg K.95 kg f x.975 fg.786 P. MPa v v f xv fg ( ).974 m /kg u u x u kj/kg R-4a.8 MPa Reverible he reverible work put, which repreent the maximum work put rev, can be determed from the exergy balance by ettg the exergy detruction equal to zero, X X 44 Net exergy tranfer by heat,work,andma detroyed Exergy detruction (reverible) X X rev, rev, X X Φ exergy X X Φ herefore, the change exergy and the reverible work are identical thi cae. Ug the defition of the cloed exergy and ubtitutg, the reverible work i determed to be rev, Φ Φ 8.5 kj m [( u u ) ( ) P (v v )] m[ ( u u ) P ( v v )] (.95 kg)[( ) kj/kg ( kpa)( )m / kg[kj/kpa m ]

19 E Oxy ga i compreed from a pecified itial tate to a fal pecified tate. he reverible work and the creae the exergy of the oxy durg thi proce are to be determed. Aumption At pecified condition, oxy can be treated a an ideal ga with contant pecific heat. Propertie he ga contant of oxy i R.66 Btu/lbm.R (able A-E). he contant-volume pecific heat of oxy at the average temperature i avg v ( ) / (75 55) / F c, avg Analyi he entropy change of oxy i.64 Btu/lbm R v cv, avg ln R ln v 985 R.5 ft /lbm (.64 Btu/lbm R) ln (.66 Btu/lbm R) ln 55 R ft /lbm.894 Btu/lbm R O ft /lbm 75 F he reverible work put, which repreent the mimum work put rev, thi cae can be determed from the exergy balance by ettg the exergy detruction equal to zero, (reverible) X Xdetroyed X rev, X X X 44 Net exergy tranfer by heat,work,andma Exergy detruction 44 exergy herefore, the change exergy and the reverible work are identical thi cae. ubtitutg the cloed exergy relation, the reverible work put durg thi proce i determed to be w rev, φ φ [( u {(.64 Btu/lbm R)(55-985)R (55 R)(.894 Btu/lbm R) (4.7 pia)(.5)ft 6.7 Btu/lbm u ) ( Alo, the creae the exergy of oxy i φ φ w rev, 6.7 Btu/lbm ) P ( v v )] /lbm[btu/5.49 pia ft ]}

20 8-8-4 An ulated tank conta CO ga at a pecified preure and volume. A paddle-wheel the tank tir the ga, and the preure and temperature of CO rie. he actual paddle-wheel work and the mimum paddle-wheel work by which thi proce can be accomplihed are to be determed. Aumption At pecified condition, CO can be treated a an ideal ga with contant pecific heat at the average temperature. he urroundg temperature i 98 K. Analyi (a) he itial and fal temperature of CO are P V ( kpa)(. m ) 98. K mr (. kg)(.889 kpa m / kg K) PV mr ( kpa)(. m (. kg)(.889 kpa m ) 57.9 K / kg K) avg v ( ) / ( ) / 8 K c, avg.684 kj/kg K. m. kg CO kpa he actual paddle-wheel work done i determed from the energy balance on the CO ga the tank, e take the content of the cylder a the. hi i a cloed ce no ma enter or leave. he energy balance for thi tationary cloed can be expreed a or, E E 44 Net energy tranfer by heat, work, and ma pw, pw, E 44 ternal, ketic, potential, etc. energie U mc ( ) v (. kg)(.684 kj/kg K)( )K 87. kj (b) he mimum paddle-wheel work with which thi proce can be accomplihed i the reverible work, which can be determed from the exergy balance by ettg the exergy detruction equal to zero, (reverible) X Xdetroyed X rev, X X X 44 Net exergy tranfer by heat,work,andma Exergy detruction 44 exergy ubtitutg the cloed exergy relation, the reverible work put for thi proce i determed to be ce rev, m m c [( u u) ( ) P ( v v ) ] [ ( ) ( )] v,avg (. kg) 7.74 kj [(.684 kj/kg K)( )K (98.)(.5 kj/kg K) ] v 57.9 K cv,avg ln R ln (.684 kj/kg K) ln.5 kj/kg K v 98. K pw

21 8-8-4 An ulated cylder itially conta air at a pecified tate. A reitance heater ide the cylder i turned on, and air i heated for 5 m at contant preure. he exergy detruction durg thi proce i to be determed. Aumption Air i an ideal ga with variable pecific heat. Propertie he ga contant of air i R.87 kj/kg.k (able A-). Analyi he ma of the air and the electrical work done durg thi proce are Alo, P V ( kpa)(. m ) m.48 kg R (.87kPa m /kg K)( K) & t ( 5. kj / )(5 6 ) 5kJ e e K h 9. kj / kg and. 7 kj / kg K he energy balance for thi tationary cloed can be expreed a E 44 Net energy tranfer by heat, work, and ma e, E b, e, ternal, ketic, potential, etc. energie U m( h h ) E 44 ce U b H durg a contant preure quai-equilibrium proce. hu, Alo, h h m e, o AIR kpa P cont 5 kj 65 K kj/kg o.48 kg.4964 kj/kg K o o P o o R ln kj/kg K P he exergy detruction (or irreveribility) aociated with thi proce can be determed from it defition X detroyed where the entropy eration i determed from an entropy balance on the cylder, which i an ulated cloed, ubtitutg, 44 Net entropy tranfer by heat and ma X detroyed { Entropy eration 44 entropy m( ) m ( ) ( K)(.48 kg)(.796 kj/kg K) 9.9 kj e

22 8-8-4 A fixed ma of helium undergoe a proce from a pecified tate to another pecified tate. he creae the ueful energy potential of helium i to be determed. Aumption At pecified condition, helium can be treated a an ideal ga. Helium ha contant pecific heat at room temperature. Propertie he ga contant of helium i R.769 kj/kg.k (able A-). he contant volume pecific heat of helium i c v.56 kj/kg.k (able A-). Analyi From the ideal-ga entropy change relation, He 8 kg v ln ln 88 K cv,avg R v 5 K.5 m /kg (.56 kj/kg K) ln (.769 kj/kg K) ln.87 kj/kg K 88 K m /kg he creae the ueful potential of helium durg thi proce i imply the creae exergy, [( u u ) ( ) P ( v )] Φ Φ m v (8 kg){(.56 kj/kg K)(88 5) K (98 K)(.87 kj/kg K) ( kpa)(.5)m 698 kj / kg[kj/kpa m ]} 8-4 One ide of a partitioned ulated rigid tank conta argon ga at a pecified temperature and preure while the other ide i evacuated. he partition i removed, and the ga fill the entire tank. he exergy detroyed durg thi proce i to be determed. Aumption Argon i an ideal ga with contant pecific heat, and thu ideal ga relation apply. Propertie he ga contant of argon i R.8 kj/kg.k (able A-). Analyi akg the entire rigid tank a the, the energy balance can be expreed a E E E Net energy tranfer by heat, work, and ma ce u u() for an ideal ga. ternal, ketic, potential, etc. energie Argon U m( u u) kpa Vacuum 7 C u u he exergy detruction (or irreveribility) aociated with thi proce can be determed from it defition X detroyed where the entropy eration i determed from an entropy balance on the entire tank, which i an ulated cloed, where 44 Net entropy tranfer by heat and ma ubtitutg, { Entropy eration 44 entropy m( ) ( ) V ln ln V m m c,avg ln v R mr V V ( kg)(.8 kj/kg K) ln().4 kj/k X detroyed m ( ) (98 K)(.4 kj/k) 9 kj

23 8-8-44E A hot copper block i dropped to water an ulated tank. he fal equilibrium temperature of the tank and the work potential wated durg thi proce are to be determed. Aumption Both the water and the copper block are compreible ubtance with contant pecific heat at room temperature. he i tationary and thu the ketic and potential energie are negligible. he tank i well-ulated and thu there i no heat tranfer. Propertie he denity and pecific heat of water at the anticipated average temperature of 9 F are ρ 6. lbm/ft and c p. Btu/lbm. F. he pecific heat of copper at the anticipated average temperature of F i c p.95 Btu/lbm. F (able A-E). Analyi e take the entire content of the tank, water copper block, a the, which i a cloed. he energy balance for thi can be expreed a or, where ubtitutg, E E 44 Net energy tranfer by heat, work, and ma U E 44 ternal, ketic, potential, etc. energie U U Cu water [ mc ( )] Cu [ mc( )] water m w ρv (6.lbm/ft )(.5 ft ) 9.5 lbm (7 lbm)(.95 Btu/lbm F)( 86.4 F R ater 75 F 5 F) (9.5 lbm)(. Btu/lbm F)( Copper 5 F 75 F) he wated work potential i equivalent to the exergy detruction (or irreveribility), and it can be determed from it defition X detroyed where the entropy eration i determed from an entropy balance on the, which i an ulated cloed, where 44 Net entropy tranfer by heat and ma ubtitutg, copper water mc mc avg avg { Entropy eration ln ln 44 entropy water copper R (7 lbm)(.9 Btu/lbm R) ln.696 Btu/R 7 R R (9.5 lbm)(. Btu/lbm R) ln.96 Btu/R 55 R X detroyed (55 R)( )Btu/R 4.9 Btu

24 A hot iron block i dropped to water an ulated tank that i tirred by a paddle-wheel. he ma of the iron block and the exergy detroyed durg thi proce are to be determed. Aumption Both the water and the iron block are compreible ubtance with contant pecific heat at room temperature. he i tationary and thu the ketic and potential energie are negligible. he tank i well-ulated and thu there i no heat tranfer. Propertie he denity and pecific heat of water at 5 C are ρ 997 kg/m and c p 4.8 kj/kg. F. he pecific heat of iron at room temperature (the only value available the table) i c p.45 kj/kg. C (able A-). Analyi e take the entire content of the tank, water iron block, a the, which i a cloed. he energy balance for thi can be expreed a where E E 44 Net energy tranfer by heat, work, and ma m water ubtitutg, pw iron 4 kj m m pw, E 44 ternal, ketic, potential, etc. energie U U iron U water pw, [ mc( )] iron [ mc( )] water ρv (997 kg/m )(.m ) 99.7 kg & t (. kj/)( 6 ) 4 kj pw, iron 5. kg L C Iron 85 C ater (.45 kj/kg C)(4 85) C (99.7 kg)(4.8 kj/kg C)(4 ) C (b) he exergy detruction (or irreveribility) can be determed from it defition X detroyed where the entropy eration i determed from an entropy balance on the, which i an ulated cloed, where 44 Net entropy tranfer by heat and ma ubtitutg, iron water mc avg mc avg { Entropy eration ln ln 44 entropy iron water 97 K (5. kg)(.45 kj/kg K) ln 4.7 kj/k 58 K 97 K (99.7 kg)(4.8 kj/kg K) ln 5.65 kj/k 9 K X detroyed (9 K)( ) kj/k 75. kj pw

25 An iron block and a copper block are dropped to a large lake where they cool to lake temperature. he amount of work that could have been produced i to be determed. Aumption he iron and copper block and water are compreible ubtance with contant pecific heat at room temperature. Ketic and potential energie are negligible. Propertie he pecific heat of iron and copper at room temperature are c p, iron.45 kj/kg. C and c p,copper.86 kj/kg. C (able A-). Analyi he thermal-energy capacity of the lake i very large, and thu the temperature of both the iron and the copper block will drop to the lake temperature (5 C) when the thermal equilibrium i etablihed. e take both the iron and the copper block a the, which i a cloed. he energy balance for thi can be expreed a or, ubtitutg, E E 44 Net energy tranfer by heat, work, and ma E 44 ternal, ketic, potential, etc. energie U U iron U [ mc )] [ mc( )] ( iron copper copper Iron 85 C Lake 5 C Copper ( 5 kg)(.45 kj/kg K)( 5 88) K ( kg)(.86 kj/kg K)( 5 88) 964 kj he work that could have been produced i equal to the wated work potential. It i equivalent to the exergy detruction (or irreveribility), and it can be determed from it defition X detroyed. he entropy eration i determed from an entropy balance on an extended that clude the block and the water their immediate urroundg o that the boundary temperature of the extended i the temperature of the lake water at all time, where 44 Net entropy tranfer by heat and ma ubtitutg, X iron copper detroyed mc b, avg mc { Entropy eration ln avg ln 44 entropy iron iron copper ( 5 kg)(.45 kj/kg K) lake copper 88 K ln kj/k 5 K 88 K 5 K ( kg)(.86 kj/kg K) ln.57 kj/k 964 kj (9 K) kj/k 96 kj 88 K K Iron

26 E A rigid tank i itially filled with aturated mixture of R-4a. Heat i tranferred to the tank from a ource until the preure ide rie to a pecified value. he amount of heat tranfer to the tank from the ource and the exergy detroyed are to be determed. Aumption he tank i tationary and thu the ketic and potential energy change are zero. here i no heat tranfer with the environment. Propertie From the refrigerant table (able A-E through A-E), P 4 pia x P ( v.55 6 pia v ) u v v x u u f f f x u x x v fg fg fg Btu / lbm Btu / lbm R ft / lbm v v f v fg x Btu/lbm R u f f x u Analyi (a) he ma of the refrigerant i V ft m v.654 ft / lbm fg fg Btu/lbm 8.4 lbm e take the tank a the, which i a cloed. he energy balance for thi tationary cloed can be expreed a ubtitutg, E E 44 Net energy tranfer by heat, work, and ma m( u u) E 44 ternal, ketic, potential, etc. energie U m( u u ) (8.4 lbm)( ) Btu/lbm 446. Btu R-4a 4 pia ource C (b) he exergy detruction (or irreveribility) can be determed from it defition X detroyed. he entropy eration i determed from an entropy balance on an extended that clude the tank and the region it immediate urroundg o that the boundary temperature of the extended where heat tranfer occur i the ource temperature, ubtitutg, 44 Net entropy tranfer by heat and ma X detroyed b, { Entropy eration 44 entropy m( m( ) ), ource 446. Btu (55 R) (8.4 lbm)(.9.46)btu/lbm R 66.5 Btu 58 R

27 Chicken are to be cooled by chilled water an immerion chiller that i alo gag heat from the urroundg. he rate of heat removal from the chicken and the rate of exergy detruction durg thi proce are to be determed. Aumption teady operatg condition exit. hermal propertie of chicken and water are contant. he temperature of the urroundg medium i 5 C. Propertie he pecific heat of chicken i given to be.54 kj/kg. C. he pecific heat of water at room temperature i 4.8 kj/kg. C (able A-). Analyi (a) Chicken are dropped to the chiller at a rate of 5 per hour. herefore, chicken can be conidered to flow teadily through the chiller at a ma flow rate of &m chicken (5 chicken / h)(. kg / chicken) kg / h.56 kg / akg the chicken flow tream the chiller a the, the energy balance for teadily flowg chicken can be expreed the rate form a (teady) E E E E& E& & 44 & & Rate of net energy tranfer by heat, work, and ma mh & & Rate of change ternal, ketic, potential, etc.energie & & mh & chicken m& (ce ke pe ) chicken hen the rate of heat removal from the chicken a they are cooled from 5 C to ºC become & mc & ) (.56 kg/)(.54 kj/kg.º C)(5 )º C. k c p ( chicken ( p chicken he chiller ga heat from the urroundg a a rate of kj/h.556 kj/. hen the total rate of heat ga by the water i & & & water chicken heat ga k Notg that the temperature rie of water i not to exceed ºC a it flow through the chiller, the ma flow rate of water mut be at leat & water.56 k m& water.56 kg/ c ) (4.8 kj/kg.º C)(º C) ( p water (b) he exergy detruction can be determed from it defition X detroyed. he rate of entropy eration durg thi chillg proce i determed by applyg the rate form of the entropy balance on an extended that clude the chiller and the immediate urroundg o that the boundary temperature i the urroundg temperature: (teady) & & & 44 & { 4444 m& chicken m& m& m& water m& Rate of net entropy tranfer by heat and ma chicken m& m& m& water 4 4 urr urr ) Rate of entropy eration & & Rate of change of entropy & m& chicken ( ) m& water ( 4 ) urr Notg that both tream are compreible ubtance, the rate of entropy eration i determed to be 4 & & m& chickenc p ln m& waterc p ln urr k (.56 kg/)(.54 kj/kg.k) ln (.56 kg/)(4.8 kj/kg.k) ln.8 k/k K Fally, X & detroyed & (98 K)(.8 k/ K).8k

28 An egg i dropped to boilg water. he amount of heat tranfer to the egg by the time it i cooked and the amount of exergy detruction aociated with thi heat tranfer proce are to be determed. Aumption he egg i pherical hape with a radiu of r.75 cm. he thermal propertie of the egg are contant. Energy aborption or releae aociated with any chemical and/or phae change with the egg i negligible. 4 here are no change ketic and potential energie. 5 he temperature of the urroundg medium i 5 C. Propertie he denity and pecific heat of the egg are given to be ρ kg/m and c p. kj/kg. C. Analyi e take the egg a the. hi i a cloed ce no ma enter or leave the egg. he energy balance for thi cloed can be expreed a E E 44 Net energy tranfer by heat, work, and ma ternal, ketic, potential, etc.energie U E 44 egg m( u u) mc( ) hen the ma of the egg and the amount of heat tranfer become πd π (.55 m) m ρv ρ ( kg/m ).889 kg 6 6 mc ( ) (.889 kg)(. kj/kg. C)(7 8) C 8. kj p he exergy detruction can be determed from it defition X detroyed. he entropy erated durg thi proce can be determed by applyg an entropy balance on an extended that clude the egg and it immediate urroundg o that the boundary temperature of the extended i at 97 C at all time: where ubtitutg, Fally, 44 Net entropy tranfer by heat and ma b { Entropy eration 44 entropy b 7 7 m( ) mcavg ln (.889 kg)(. kj/kg.k) ln.588 kj/k kj.588 kj/k 7 K X b detroyed (98 K)(.94 kj / K) kj/k kj (per egg)

29 tale teel ball bearg leavg the oven at a uniform temperature of 9 C at a rate of 4 /m are expoed to air and are cooled to 85 C before they are dropped to the water for quenchg. he rate of heat tranfer from the ball to the air and the rate of exergy detruction due to thi heat tranfer are to be determed. Aumption he thermal propertie of the bearg ball are contant. he ketic and potential energy change of the ball are negligible. he ball are at a uniform temperature at the end of the proce. Propertie he denity and pecific heat of the ball bearg are given to be ρ 885 kg/m and c p.48 kj/kg. C. Analyi (a) e take a gle bearg ball a the. he energy balance for thi cloed can be expreed a E E 44 Net energy tranfer by heat, work, and ma ternal, ketic, potential, etc.energie U ball mc( E 44 m( u ) u he total amount of heat tranfer from a ball i ) πd π (. m) m ρv ρ (885 kg/m ).75 kg 6 6 mc( ) (.75 kg)(.48 kj/kg. C)(9 85) C.756 kj/ball hen the rate of heat tranfer from the ball to the air become & total n& (4 ball/m) (.756 kj/ball) 45.8 kj/m 4. k ball (per ball) herefore, heat i lot to the air at a rate of 4. k. (b) he exergy detruction can be determed from it defition X detroyed. he entropy erated durg thi proce can be determed by applyg an entropy balance on an extended that clude the ball and it immediate urroundg o that the boundary temperature of the extended i at C at all time: where ubtitutg, 44 Net entropy tranfer by heat and ma m( b { Entropy eration ) mc avg 44 entropy ln b 85 7 (.75 kg)(.48 kj/kg.k) ln.5 kj/k kj.5 kj/k.465 kj/k K b hen the rate of entropy eration become Fally, & X & n& ball detroyed & (per ball) (.465 kj/k ball)(4 ball/m).597 kj/m.k.995 k/k ( K)(.995 k/ K).k/K

30 8-8-5 Carbon teel ball are to be annealed at a rate of 5/h by heatg them firt and then allowg them to cool lowly ambient air at a pecified rate. he total rate of heat tranfer from the ball to the ambient air and the rate of exergy detruction due to thi heat tranfer are to be determed. Aumption he thermal propertie of the ball are contant. here are no change ketic and potential energie. he ball are at a uniform temperature at the end of the proce. Propertie he denity and pecific heat of the ball are given to be ρ 78 kg/m and c p.465 kj/kg. C. Analyi (a) e take a gle ball a the. he energy balance for thi cloed can be expreed a E E 44 Net energy tranfer by heat, work, and ma ternal, ketic, potential, etc.energie U ball mc( E 44 m( u ) u he amount of heat tranfer from a gle ball i πd π (.8 m) m ρv ρ (78 kg/m ). kg 6 6 mc ( ) (. kg)(.465 kj/kg. C)(9 ) C 78J p hen the total rate of heat tranfer from the ball to the ambient air become & n& ( ball/h) (.78 kj/ball) 96 kj/h 6 ball ).78kJ (per ball) (b) he exergy detruction (or irreveribility) can be determed from it defition X detroyed. he entropy erated durg thi proce can be determed by applyg an entropy balance on an extended that clude the ball and it immediate urroundg o that the boundary temperature of the extended i at 5 C at all time: where 44 Net entropy tranfer by heat and ma ubtitutg, b m( { Entropy eration 44 entropy ) mc avg ln b.78 kj. kj/k.4 kj/k 8 K b hen the rate of entropy eration become Fally, & X & n& ball & 7 (. kg)(.465 kj/kg.k)ln. kj/k 9 7 (per ball) (.4 kj/k ball)( ball/h).74 kj/h.k.47 k/k detroyed (8 K)(.47 k/ K).46 k 46

31 8-8-5 A tank contag hot water i placed a larger tank. he amount of heat lot to the urroundg and the exergy detruction durg the proce are to be determed. Aumption Ketic and potential energy change are negligible. Air i an ideal ga with contant pecific heat. he larger tank i well-ealed. Propertie he propertie of air at room temperature are R.87 kpa.m /kg.k, c p.5 kj/kg.k, c v.78 kj/kg.k (able A-). he propertie of water at room temperature are ρ kg/m, c w 4.8 kj/kg.k. Analyi (a) he fal volume of the air the tank i V a V a V w m he ma of the air the room i m a PV R a a ( kpa)(.4 m ).474 kg (.87 kpa m /kg K)( 7 K) he preure of air at the fal tate i P ma Ra (.474 kg)(.87 kpa m /kg K)(44 7 K) a V a.5 m he ma of water i mw ρ wv w ( kg/m )(.5 m ) 4.5 kg Air, C 7.9 kpa ater 85 C 5 L An energy balance on the conitg of water and air i ued to determe heat lot to the urroundg [ m c ) m c ( )] (4.5 kg)(4.8 kj/kg.k)(44 85) (.474 kg)(.78 kj/kg.k)(44 ) 489 kj w w ( w a v a (b) An exergy balance written on the ( immediate urroundg) can be ued to determe exergy detruction. But we firt determe entropy and ternal energy change w a U U X m c m w a w c p ln w ln a (85 7) K (4.5 kg)(4.8 kj/kg.k)ln 7.87 kj/k (44 7) K Pa R ln P ( 7) K kpa (.474 kg) (.5 kj/kg.k)ln (.87 kj/kg.k)ln (44 7) K 7.9 kpa.9 kj/k w a det m c m w a X U w ( c ( v w w w a X 8.8 kj a w ) (4.5 kg)(4.8 kj/kg.k)(85-44)k 49 kj ) (.474 kg)(.78 kj/kg.k)( - 44)K.746 kj U a a 49 kj (95 K)(7.87 kj/k) (-.746 kj) (95 K)(.9 kj/k)

32 8-8-5 Heat i tranferred to a piton-cylder device with a et of top. he work done, the heat tranfer, the exergy detroyed, and the econd-law efficiency are to be determed. Aumption he device i tationary and ketic and potential energy change are zero. here i no friction between the piton and the cylder. Analyi (a) he propertie of the refrigerant at the itial and fal tate are (able A- through A-) P kpa.6544 m /kg v C 48. kj/kg u.64 kj/kg.k P 8 kpa v C u.756 m /kg.96 kj/kg.8 kj/kg.k he boundary work i determed to be R-4a.4 kg 4 kpa C mp ( v ) (.4 kg)(8 kpa)( )m /kg.57 kj b, v (b) he heat tranfer can be determed from an energy balance on the m u u ) (.4 kg)( )kJ/kg.57 kj 9.8 kj ( b, (c) he exergy difference between the let and exit tate i X m u [ u ( ) P ( v v )] (.4 kg) 4.6 kj [( )kJ/kg (98 K)(.8.64)kg.K ( kpa)( )m /kg] he ueful work put for the proce i u, b, mp ( v v).57 kj (.4 kg)( kpa)( )m /kg.4 kj he exergy detroyed i the difference between the exergy difference and the ueful work put X X kj det u, (d) he econd-law efficiency for thi proce i η II X u,.4 kj 4.6 kj.78