Chapter 7 ENTROPY. 7-3C The entropy change will be the same for both cases since entropy is a property and it has a fixed value at a fixed state.

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1 7- Chapter 7 ENROY Entropy and the Increae of Entropy rciple 7-C No. he δ Q repreent the net heat tranfer durg a cycle, which could be poitive. 7-C No. A ytem may produce more (or le) work than it receive durg a cycle. A team power plant, for example, produce more work than it receive durg a cycle, the difference beg the net work put. 7-C he entropy change will be the ame for both cae ce entropy i a property and it ha a fixed value at a fixed tate. 7-4C No. In eral, that tegral will have a different value for different procee. However, it will have the ame value for all reverible procee. 7-5C Ye. 7-6C hat tegral hould be performed along a reverible path to determe the entropy change. 7-7C No. An iothermal proce can be irreverible. Example: A ytem that volve paddle-wheel work while log an equivalent amount of heat. 7-8C he value of thi tegral i alway larger for reverible procee. 7-9C No. Becaue the entropy of the urroundg air creae even more durg that proce, makg the total entropy change poitive. 7-0C It i poible to create entropy, but it i not poible to detroy it. 7-C If the ytem undergoe a reverible proce, the entropy of the ytem cannot change with a heat tranfer. Otherwie, the entropy mut creae ce there are no offettg entropy change aociated with reervoir exchangg heat with the ytem.

2 7-7-C he claim that work will not change the entropy of a fluid pag through an adiabatic teady-flow ytem with a gle let and let i true only if the proce i alo reverible. Sce no real proce i reverible, there will be an entropy creae the fluid durg the adiabatic proce device uch a pump, compreor, and turbe. 7-C Sometime. 7-4C Never. 7-5C Alway. 7-6C Increae. 7-7C Increae. 7-8C Decreae. 7-9C Sometime. 7-0C Ye. hi will happen when the ytem i log heat, and the decreae entropy a a reult of thi heat lo i equal to the creae entropy a a reult of irreveribilitie. 7-C hey are heat tranfer, irreveribilitie, and entropy tranport with ma. 7-C Greater than. 7- A rigid tank conta an ideal ga that i beg tirred by a paddle wheel. he temperature of the ga rema contant a a reult of heat tranfer. he entropy change of the ga i to be determed. Aumption he ga the tank i given to be an ideal ga. Analyi he temperature and the pecific volume of the ga rema contant durg thi proce. herefore, the itial and the fal tate of the ga are the ame. hen ce entropy i a property. herefore, ΔS y 0 00 kj IDEAL GAS 40 C Heat 0 C

3 7-7-4 Air i compreed teadily by a compreor. he air temperature i mataed contant by heat rejection to the urroundg. he rate of entropy change of air i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. Air i an ideal ga. 4 he proce volve no ternal irreveribilitie uch a friction, and thu it i an iothermal, ternally reverible proce. ropertie Notg that h h() for ideal gae, we have h h ce 5 C. Analyi We take the compreor a the ytem. Notg that the enthalpy of air rema contant, the energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma herefore, Q & & E& W& W Rate of change ternal, ketic, potential, etc.energie E& Q& kw & Notg that the proce i aumed to be an iothermal and ternally reverible proce, the rate of entropy change of air i determed to be ΔS& air Q&,air y kw kw/k 98 K Q AIR cont. kw 7-5 Heat i tranferred directly from an energy-ource reervoir to an energy-k. he entropy change of the two reervoir i to be calculated and it i to be determed if the creae of entropy prciple i atified. Aumption he reervoir operate teadily. Analyi he entropy change of the ource and k i given by Q ΔS H H Q L L 00 kj 00 kj 0.08 kj/k 00 K 600 K Sce the entropy of everythg volved thi proce ha creaed, thi tranfer of heat i poible.

4 It i aumed that heat i tranferred from a cold reervoir to the hot reervoir contrary to the Clauiu tatement of the econd law. It i to be proven that thi violate the creae entropy prciple. Aumption he reervoir operate teadily. Analyi Accordg to the defition of the entropy, the entropy change of the high-temperature reervoir hown below i H ΔS H Q H 00 kj 00 K 0.08 kj/k Q 00 kj and the entropy change of the low-temperature reervoir i L ΔS L Q L 00 kj kj/k 600 K he total entropy change of everythg volved with thi ytem i then ΔS ΔS H ΔS kj/k total L which violate the creae entropy prciple ce the entropy i decreag, not creag or tayg fixed. 7-7 Heat i tranferred from a hot reervoir to a cold reervoir. he entropy change of the two reervoir i to be calculated and it i to be determed if the econd law i atified. Aumption he reervoir operate teadily. Analyi he rate of entropy change of everythg volved thi tranfer of heat i given by Q& ΔS& H H Q& L L kw 800 K kw 00 K kw/k H L kw Sce thi rate i poitive (i.e., the entropy creae a time pae), thi tranfer of heat i poible.

5 E A reverible air conditioner with pecified reervoir temperature i conidered. he entropy change of two reervoir i to be calculated and it i to be determed if thi air conditioner atifie the creae entropy prciple. Aumption he air conditioner operate teadily. Analyi Accordg to the thermodynamic temperature cale, Q & H Q& L H L 570 R ( 6,000 Btu/h) 8,70 Btu/h 50 R he rate of entropy change of the hot reervoir i then ΔS& H Q& H H 8,70 Btu/h 67.9 Btu/h R 570 R Similarly, the rate of entropy change of the cold reervoir i ΔS& L Q& L L 6,000 Btu/h 67.9 Btu/h R 50 R he net rate of entropy change of everythg thi ytem i ΔS & ΔS& H ΔS& Btu/h R total L he net rate of entropy change i zero a it mut be order to atify the econd law. Q & H Q & L 570 R R 50 R W & net,

6 A reverible heat pump with pecified reervoir temperature i conidered. he entropy change of two reervoir i to be calculated and it i to be determed if thi heat pump atifie the creae entropy prciple. Aumption he heat pump operate teadily. Analyi Sce the heat pump i completely reverible, the combation of the coefficient of performance expreion, firt Law, and thermodynamic temperature cale give CO L / H (8 K) /(94 K) H, rev he power required to drive thi heat pump, accordg to the coefficient of performance, i then W& & CO Q H 00 kw net, H, rev kw 6.7 Accordg to the firt law, the rate at which heat i removed from the low-temperature energy reervoir i Q& L Q& W& H 00 kw.74 kw net, 96.6 kw he rate at which the entropy of the high temperature reervoir change, accordg to the defition of the entropy, i ΔS& H Q& H H 00 kw 0.40 kw/k 94 K and that of the low-temperature reervoir i ΔS& L Q& L L 96.6 kw 0.40 kw/k 8 K he net rate of entropy change of everythg thi ytem i ΔS & ΔS& H ΔS& kw/k total L a it mut be ce the heat pump i completely reverible. 00 kw Q & L C H 0 C W & net

7 E Heat i tranferred iothermally from the workg fluid of a Carnot enge to a heat k. he entropy change of the workg fluid i given. he amount of heat tranfer, the entropy change of the k, and the total entropy change durg the proce are to be determed. Analyi (a) hi i a reverible iothermal proce, and the entropy change durg uch a proce i given by ΔS Q Notg that heat tranferred from the workg fluid i equal to the heat tranferred to the k, the heat tranfer become Q ( R)( 0.7 Btu/R) Btu 88.5 Btu fluid fluidδsfluid 555 Qfluid, (b) he entropy change of the k i determed from ΔS Q 88.5 Btu 555 R k, k k 0.7 Btu/R (c) hu the total entropy change of the proce i S ΔS ΔS ΔS total fluid k SINK 95 F hi i expected ce all procee of the Carnot cycle are reverible procee, and no entropy i erated durg a reverible proce. Heat 95 F Carnot heat enge

8 R-4a enter an evaporator a a aturated liquid-vapor at a pecified preure. Heat i tranferred to the refrigerant from the cooled pace, and the liquid i vaporized. he entropy change of the refrigerant, the entropy change of the cooled pace, and the total entropy change for thi proce are to be determed. Aumption Both the refrigerant and the cooled pace volve no ternal irreveribilitie uch a friction. Any temperature change occur with the wall of the tube, and thu both the refrigerant and the cooled pace rema iothermal durg thi proce. hu it i an iothermal, ternally reverible proce. Analyi Notg that both the refrigerant and the cooled pace undergo reverible iothermal procee, the entropy change for them can be determed from ΔS Q (a) he preure of the refrigerant i mataed contant. herefore, the temperature of the refrigerant alo rema contant at the aturation value, 5.6 C 57.4 K (able A-) ka hen, ΔS (b) Similarly, ΔS refrigerant pace Q Q refrigerant, refrigerant pace, pace 80 kj kj/k 57.4 K 80 kj 0.67 kj/k 68 K R-4a 60 ka -5 C 80 kj (c) he total entropy change of the proce i S S ΔS ΔS kj/k total refrigerant pace

9 7-9 Entropy Change of ure Subtance 7-C Ye, becaue an ternally reverible, adiabatic proce volve no irreveribilitie or heat tranfer. 7-C Accordg to the conervation of ma prciple, dmcv m m dt & & dm m& dt An entropy balance adapted to thi ytem become ds urr dt d( m) m& dt 0 When thi i combed with the ma balance, and the contant entropie are removed from the derivative, it become ds urr dt dm dt dm 0 dt Multiplyg by dt and tegratg the reult yield or ΔS urr ( ) Δm 0 Δ S ) Δm urr ( 7-4C Accordg to the conervation of ma prciple, dmcv m m dt & & dm m& dt An entropy balance adapted to thi ytem become ds urr dt d( m) m& 0 dt When thi i combed with the ma balance, it become ds urr dt dm dt dm dt 0 Multiplyg by dt and tegratg the reult yield ΔS urr m m ( m m) 0 Sce all the entropie are ame, thi reduce to ΔS urr 0 Hence, the entropy of the urroundg can only creae or rema fixed.

10 R-4a i expanded a turbe durg which the entropy rema contant. he enthalpy difference i to be determed. Analyi he itial tate i uperheated vapor and thu 50 pia 75 F h 9.95 Btu/lbm 0.8 Btu/lbm R (from EES) he entropy i contant durg the proce. he fal tate i alo uperheated vapor and the enthalpy at thi tate i 0 F h 0.8 Btu/lbm R Btu/lbm (from EES) Note that the propertie at the let and exit tate can alo be determed from able A-E by terpolation but the value will not be a accurate a thoe by EES. he change the enthalpy acro the turbe i then Δh h h Btu/lbm 7-6E A piton-cylder device that i filled with water i heated. he total entropy change i to be determed. Analyi he itial pecific volume i v V.5 ft m.5 ft lbm /lbm which i between v f and v g for 00 pia. he itial quality and the entropy are then (able A-5E) x v v f v fg ( ) ft /lbm ( ) ft /lbm H O 00 pia lbm.5 ft f x fg Btu/lbm R (0.8075)(0.989 Btu/lbm R).4 Btu/lbm R he fal tate i uperheated vapor and 500 F 00 pia.5706 Btu/lbm R (able A - 6E) Hence, the change the total entropy i ΔS m( ) ( lbm)( ) Btu/lbm R Btu/R v

11 7-7-7 Water i compreed a compreor durg which the entropy rema contant. he fal temperature and enthalpy are to be determed. Analyi he itial tate i uperheated vapor and the entropy i 60 C 5 ka h kj/kg 8.5 kj/kg K (from EES) Note that the propertie can alo be determed from able A-6 by terpolation but the value will not be a accurate a thoe by EES. he fal tate i uperheated vapor and the propertie are (able A-6) 00 ka 8.5 kj/kg K h C 6.0 kj/kg 7-8E R-4a i expanded ientropically a cloed ytem. he heat tranfer and work production are to be determed. Aumption he ytem i tationary and thu the ketic and potential energy change are zero. here are no work teraction volved other than the boundary work. he thermal energy tored the cylder itelf i negligible. 4 he compreion or expanion proce i quai-equilibrium. Analyi A there i no area under the proce le hown on the - diagram and thi proce i reverible, Q 0 Btu he energy balance for thi ytem can be expreed a E E 44 Net energy tranfer by heat, work, and ma W W Change ternal, ketic, potential, etc.energie ΔU m( u m( u he itial tate propertie are ΔEytem 44 u ) u ) R-4a lbm 00 pia 00 F 00 F 00 pia u Btu/lbm Btu/lbm R (able A -E) he fal tate propertie for thi ientropic proce are (able A-E) 0 pia Btu/lbm R x u u fg x f f u.5 ( )(87.45) Btu/lbm fg Subtitutg, W m( u u ) (lbm)( ) Btu/lbm 9.05 Btu

12 7-7-9 An ulated rigid tank conta a aturated liquid-vapor mixture of water at a pecified preure. An electric heater ide i turned on and kept on until all the liquid vaporized. he entropy change of the water durg thi proce i to be determed. Analyi From the team table (able A-4 through A-6) 00 ka v v f xv fg x 0.5 f x v v at. vapor kj/kg K 0.00 fg.08 hen the entropy change of the team become ( 0.5)( ) ( 0.5)( 6.056) 0.44 m /kg.868 kj/kg K ( ) ( kg)( ) kj/kg 8.0 kj/k ΔS m K H O kg 00 ka W e 7-40 [Alo olved by EES on encloed CD] A rigid tank i divided to two equal part by a partition. One part i filled with compreed liquid water while the other ide i evacuated. he partition i removed and water expand to the entire tank. he entropy change of the water durg thi proce i to be determed. Analyi he propertie of the water are (able A-4) Notg that 00 ka v v f 60 C C m /kg 0.8 kj/kg K ( )( ) m /kg v v 5 ka x v m /kg hen the entropy change of the water become ( ) (.5 kg)( ) ΔS m v v f v fg x f fg ( )( 7.5) kj/kg K kj/kg K 0.4 kj/k.5 kg compreed liquid 00 ka 60 C Vacuum

13 7-7-4 EES roblem 7-40 i reconidered. he entropy erated i to be evaluated and plotted a a function of urroundg temperature, and the value of the urroundg temperature that are valid for thi problem are to be determed. he urroundg temperature i to vary from 0 C to 00 C. Analyi he problem i olved ug EES, and the reult are tabulated and plotted below. "Input Data" []00 [ka] []60 [C] m.5 [kg] []5 [ka] Fluid$'Steam_IAWS' V[]m*pv[] pv[]volume(fluid$,[], []) "pecific volume of team at tate, m^/kg" []entropy(fluid$,[],[]) "entropy of team at tate, kj/kgk" V[]*V[] "Steam expand to fill entire volume at tate " "State i identified by [] and pv[]" pv[]v[]/m "pecific volume of team at tate, m^/kg" []entropy(fluid$,[],vpv[]) "entropy of team at tate, kj/kgk" []temperature(fluid$,[],vpv[]) DELAS_ym*([]-[]) "otal entopy change of team, kj/k" "What doe the firt law tell u ab thi problem?" "Conervation of Energy for the entire, cloed ytem" E_ - E_ DELAE_y "neglectg change KE and E for the ytem:" DELAE_ym*(tenergy(Fluid$, [], vpv[]) - tenergy(fluid$,[],[])) E_ 0 "How do you terpert the energy leavg the ytem, E_? Recall thi i a contant volume ytem." Q_ E_ "What i the maximum value of the Surroundg temperature?" "he maximum poible value for the urroundg temperature occur when we et S_ 0Delta S_yum(DeltaS_urr)" Q_net_urrQ_ S_ 0 S_ DELAS_yQ_net_urr/urr "Etablih a parametric table for the variable S_, Q_net_urr, _urr, and DELAS_y. In the arametric able wdow elect _urr and ert a range of value. hen place '{' and '}' ab the S_ 0 le; pre F to olve the table. he reult are hown lot Wdow. What value of _urr are valid for thi problem?"

14 7-4 S Q net,urr urr ΔS y [kj/k] [kj] [K] [kj/k] S [kj/k] urr [K]

15 E A cylder i itially filled with R-4a at a pecified tate. he refrigerant i cooled and condened at contant preure. he entropy change of refrigerant durg thi proce i to be determed Analyi From the refrigerant table (able A-E through A-E), 0 pia 00 F 0.6 Btu/lbm R 50 F 0 pia f F Btu/lbm R hen the entropy change of the refrigerant become ( ) ( lbm)( ) Btu/lbm 0.64 Btu/R ΔS m R R-4a 0 pia 00 F Q

16 An ulated cylder i itially filled with aturated liquid water at a pecified preure. he water i heated electrically at contant preure. he entropy change of the water durg thi proce i 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 From the team table (able A-4 through A-6), Alo, v v f 50 ka h h at. ka ka ka m /kg 467. kj/kg.47 kj/kg K 00 kj H O 50 ka Sat. liquid V m m 4.75 kg v m /kg We take the content of the cylder a the ytem. hi i a cloed ytem ce no ma enter or leave. he energy balance for thi tationary cloed ytem can be expreed a E 44 Net energy tranfer by heat, work, and ma W E e, W b, W e, Change ternal, ketic, potential, etc.energie ΔU m( h h ) ΔEytem 44 ce ΔU W b ΔH durg a contant preure quai-equilibrium proce. Solvg for h, hu, h W 00 kj kg e, h m 50 ka x h 90. kj/kg h f h h fg x hen the entropy change of the water become f 90. kj/kg fg ( 0.08)( ).684 kj/kg K ( ) ( 4.75 kg)( ) kj/kg 5.7 kj/k ΔS m K

17 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 fal temperature the cylder and the work done by the refrigerant 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 (a) hi i a reverible adiabatic (i.e., ientropic) proce, and thu. From the refrigerant table (able A- through A-), Alo, v v g 0.8 Ma u u at. Ma g@0.8 Ma g@0.8 Ma m /kg kj/kg kj/kg K and V 0.05 m m.95 kg v m /kg 0.4 Ma x u u fg x f f u 6.6 fg ( )( 7.45).9 kj/kg R-4a 0.8 Ma 0.05 m Ma at@ C (b) We take the content of the cylder a the ytem. hi i a cloed ytem ce no ma enter or leave. he energy balance for thi adiabatic cloed ytem can be expreed a E E 44 Net energy tranfer by heat, work, and ma W W b, b, Change ternal, ketic, potential, etc.energie ΔU m( u u ) ΔEytem 44 Subtitutg, the work done durg thi ientropic proce i determed to be W ( ) (.95 kg)( ) 7.09 kj m u kj/kg b, u

18 EES roblem 7-44 i reconidered. he work done by the refrigerant i to be calculated and plotted a a function of fal preure a the preure varie from 0.8 Ma to 0.4 Ma. he work done for thi proce i to be compared to one for which the temperature i contant over the ame preure range. Analyi he problem i olved ug EES, and the reult are tabulated and plotted below. rocedure IothermWork(_,x_,m_y,_:Work Iotherm,Q_iotherm,DELAE_iotherm,_iother m) _iothermemperature(r4a,_,xx_) _iotherm u_ INENERGY(R4a,_,xx_) v_ volume(r4a,_,xx_) _ entropy(r4a,_,xx_) u_ INENERGY(R4a,_,) _ entropy(r4a,_,) "he proce i reverible and Iothermal thu the heat tranfer i determed by:" Q_iotherm (7)*m_y*(_ - _) DELAE_iotherm m_y*(u_ - u_) E_ Q_iotherm E_ DELAE_iothermE_ Work iotherme_ END "Known:" _ 800 [ka] x_.0 V_y 0.05[m^] "_ 400 [ka]" "Analyi: " " reat the rigid tank a a cloed ytem, with no heat tranfer, neglect change KE and E of the R4a." "he ientropic work i determed from:" E_ - E_ DELAE_y E_ Work ien E_ 0 DELAE_y m_y*(u_ - u_) u_ INENERGY(R4a,_,xx_) v_ volume(r4a,_,xx_) _ entropy(r4a,_,xx_) V_y m_y*v_ "Rigid ank: he proce i reverible and adiabatic or ientropic. hen _ and _ pecify tate." u_ INENERGY(R4a,_,_) ien temperature(r4a,_,_) Call IothermWork(_,x_,m_y,_:Work Iotherm,Q_iotherm,DELAE_iotherm,_i otherm)

19 7-9 [ka] Work,ien [kj] Work,iotherm [kj] Q iotherm [kj] Work [kj] Iothermal Ientropic [ka] Q ientropic 0 kj Q iotherm [kj] [ka]

20 Saturated Refrigerant-4a vapor at 60 ka i compreed teadily by an adiabatic compreor. he mimum power put to the compreor i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. Analyi he power put to an adiabatic compreor will be a mimum when the compreion proce i reverible. For the reverible adiabatic proce we have. From the refrigerant table (able A- through A-), Alo, v v g 60 ka h h at. vapor 900 ka h &m v V ka g@60 ka g@60 ka kj/kg 0.48 m /kg 4. kj/kg kj/kg K m /m 6.0 kg/m 0.7 kg/ 0.48 m /kg R-4a here i only one let and one exit, and thu m& m& m&. We take the compreor a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& Rate of change ternal, ketic, potential, etc.energie E& & W& & & & mh mh (ce Q Δke Δpe 0) W& m& ( h h ) Subtitutg, the mimum power upplied to the compreor i determed to be W & ( 0.7 kg/)( ) 9.7 kw kj/kg

21 An ulated cylder i itially filled with uperheated team at a pecified tate. he team i compreed a reverible manner until the preure drop to a pecified value. he work put durg thi proce i 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 team table (able A-4 through A-6), Alo, v m /kg 00 ka u 57.0 kj/kg 50 C kj/kg K Ma u 77.8 kj/kg V 0.05 m m kg v m /kg H O 00 ka 50 C We take the content of the cylder a the ytem. hi i a cloed ytem ce no ma enter or leave. he energy balance for thi adiabatic cloed ytem can be expreed a E E 44 Net energy tranfer by heat, work, and ma W b, ΔEytem 44 Change ternal, ketic, potential, etc. energie ΔU m( u u ) Subtitutg, the work put durg thi adiabatic proce i determed to be W ( ) ( kg)( ) 6.0 kj m u kj/kg b, u

22 EES roblem 7-47 i reconidered. he work done on the team i to be determed and plotted a a function of fal preure a the preure varie from 00 ka to Ma. Analyi he problem i olved ug EES, and the reult are tabulated and plotted below. "Known:" _ 00 [ka] _ 50 [C] V_y 0.05 [m^] "_ 000 [ka]" "Analyi: " Fluid$'Steam_IAWS' " reat the piton-cylder a a cloed ytem, with no heat tranfer, neglect change KE and E of the Steam. he proce i reverible and adiabatic thu ientropic." "he ientropic work i determed from:" E_ - E_ DELAE_y E_ 0 [kj] E_ Work_ DELAE_y m_y*(u_ - u_) u_ INENERGY(Fluid$,_,_) v_ volume(fluid$,_,_) _ entropy(fluid$,_,_) V_y m_y*v_ " he proce i reverible and adiabatic or ientropic. hen _ and _ pecify tate." u_ INENERGY(Fluid$,_,_) ien temperature(fluid$,_,_) [ka] Work [kj] Work [kj] Work on Steam 00 ka 50 C [ka]

23 A cylder i itially filled with aturated water vapor at a pecified temperature. Heat i tranferred to the team, and it expand a reverible and iothermal manner until the preure drop to a pecified value. he heat tranfer and the work put for thi proce 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 and iothermal. Analyi From the team table (able A-4 through A-6), 00 C u u at. vapor g 800 ka u g@00 C 6.40 kj/kg K 6. kj/kg 594. kj/kg kj/kg K he heat tranfer for thi reverible iothermal proce can be determed from ( ) (47 K)(. kg)( )kJ/kg 9.9 kj Q ΔS m K We take the content of the cylder a the ytem. hi i a cloed ytem ce no ma enter or leave. he energy balance for thi cloed ytem can be expreed a E 44 Net energy tranfer by heat, work, and ma Q E W W b, b, Change ternal, ketic, potential, etc. energie ΔU m( u Q ΔEytem 44 m( u u ) u ) H O 00 C at. vapor cont Q Subtitutg, the work done durg thi proce i determed to be W b, 9.9 kj (. kg)( ) kj/kg 75.6 kj

24 EES roblem 7-49 i reconidered. he heat tranferred to the team and the work done are to be determed and plotted a a function of fal preure a the preure varie from the itial value to the fal value of 800 ka. Analyi he problem i olved ug EES, and the reult are tabulated and plotted below. "Known:" _ 00 [C] x_.0 m_y. [kg] {_ 800"[ka]"} "Analyi: " Fluid$'Steam_IAWS' " reat the piton-cylder a a cloed ytem, neglect change KE and E of the Steam. he proce i reverible and iothermal." E_ - E_ DELAE_y E_ Q_ E_ Work_ DELAE_y m_y*(u_ - u_) _ preure(fluid$,_,x.0) u_ INENERGY(Fluid$,_,x.0) v_ volume(fluid$,_,x.0) _ entropy(fluid$,_,x.0) V_y m_y*v_ Work [KJ] " he proce i reverible and iothermal. hen _ and _ pecify tate." u_ INENERGY(Fluid$,_,_) _ entropy(fluid$,_,_) Q_ (_7)*m_y*(_-_) [ka] [ka] Q [kj] Work [kj] Q [kj] [ka]

25 Water i compreed ientropically a cloed ytem. he work required i to be determed. Aumption he ytem i tationary and thu the ketic and potential energy change are zero. here are no work teraction volved other than the boundary work. he thermal energy tored the cylder itelf i negligible. 4 he compreion or expanion proce i quai-equilibrium. Analyi he energy balance for thi ytem can be expreed a E E 44 Net energy tranfer by heat, work, and ma W he itial tate propertie are u u f f xu x fg fg ΔEytem 44 Change ternal, ketic, potential, etc.energie ΔU m( u u ) 4.00 (0.84)(46.6) 95. kj/kg 0.5 (0.84)(8.7488) 7.76 kj/kg K Sce the entropy i contant durg thi proce, Ma Subtitutg, w 7.76 kj/kg K u.6 kj/kg (able A - 6) u u (.6 95.) kj/kg 80.4 kj/kg Water 0 C x 0.84

26 R-4a undergoe an iothermal proce a cloed ytem. he work and heat tranfer are to be determed. Aumption he ytem i tationary and thu the ketic and potential energy change are zero. here are no work teraction volved other than the boundary work. he thermal energy tored the cylder itelf i negligible. 4 he compreion or expanion proce i quai-equilibrium. Analyi he energy balance for thi ytem can be expreed a E E 44 Net energy tranfer by heat, work, and ma W Q ΔEytem 44 Change ternal, ketic, potential, etc.energie ΔU m( u u ) he itial tate propertie are 40 ka 0 C u kj/kg.04 kj/kg K (able A -) For thi iothermal proce, the fal tate propertie are (able A-) x C u u he heat tranfer i determed from q f f x u x fg fg (0.0)(6.6).9 kj/kg (0.0)(0.67) kj/kg K ( ) (9 K)( ) kj/kg K 7.4 kj/kg 0 he negative ign how that the heat i actually tranferred from the ytem. hat i, q 7.4 kj/kg he work required i determed from the energy balance to be w q ( u u) 7.4 kj/kg ( ) kj/kg 6.95 kj/kg R-4a 40 ka 0 C 7-5 he total heat tranfer for the proce - hown the figure i to be determed. Analyi For a reverible proce, the area under the proce le - diagram i equal to the heat tranfer durg that proce. hen, Q - Q - Q ds - ds ( C) ( S S) ( S S ) (60 7) (55 7) K ( )kj/k (60 7 K)( )kj/kg K 8 kj S (kj/k)

27 he total heat tranfer for the proce - hown the figure i to be determed. Analyi For a reverible proce, the area under the proce le - diagram i equal to the heat tranfer durg that proce. hen, Q - ds ( S S) (500 7) (00 7) K (.0 0.)kJ/K kj ( C) S (kj/k) 7-55 he heat tranfer for the proce - hown the figure i to be determed. Analyi For a reverible proce, the area under the proce le - diagram i equal to the heat tranfer durg that proce. hen, q - d d ( ) 0 (0 7) (0 7) K (.0 0.0)kJ/kg K 4.0 kj/kg ( C) (kj/kg K) 7-56E he total heat tranfer for the proce - hown the figure i to be determed. Analyi For a reverible proce, the area under the proce le - diagram i equal to the heat tranfer durg that proce. hen, Q - ds ( ) ( ) (00 460) R (.0 0.) Btu/lbm R 608 Btu/lbm ( F) (Bu/lbm R)

28 he change the entropy of R-4a a it i heated at contant preure i to be calculated ug the relation d (δq /) t rev, and it i to be verified by ug R-4a table. Analyi A R-4a i converted from a aturated liquid to a aturated vapor, both the preure and temperature rema contant. hen, the relation d (δq /) t rev reduce to dh d When thi reult i tegrated between the aturated liquid and aturated vapor tate, the reult i (able A-) g f h g h f h 00 ka 00 ka 06.0 kj/kg 0.78kJ/kg K ( ) K Fdg the reult directly from the R-4a table kj/kg K (able A-) g f 00 ka he two reult are practically identical.

29 Steam i expanded an ientropic turbe. he work produced i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. he proce i ientropic (i.e., reverible-adiabatic). Analyi here i only one let and one exit, and thu m & m& m&. We take the turbe a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& mh & W& Rate of change ternal, ketic, potential, etc.energie E& mh & & m& ( h h ) he let tate propertie are Ma 60 C W& h 59.9 kj/kg kj/kg K (able A - 6) For thi ientropic proce, the fal tate propertie are (able A-5) 00 ka kj/kg K x h fg h x f f h 47.5 (0.997)(57.5) 58.9 kj/kg fg Ma 60 C Ma 00 ka urbe 00 ka Subtitutg, w h h ( ) kj/kg 6.0 kj/kg

30 R-4a i compreed an ientropic compreor. he work required i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. he proce i ientropic (i.e., reverible-adiabatic). Analyi here i only one let and one exit, and thu m & m& m&. We take the compreor a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teadyflow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& mh & W& W& Rate of change ternal, ketic, potential, etc.energie E& mh & & m& ( h h) he let tate propertie are 0 F x h 0.08 Btu/lbm 0.59 Btu/lbm R For thi ientropic proce, the fal tate enthalpy i 00 pia Subtitutg, 0.59 Btu/lbm R w h.8 Btu/lbm (able A -E) (able A -E) h h ( ) Btu/lbm 0. Btu/lbm 00 pia 0 F Compreor 0 F at. vapor 00 pia

31 Steam i expanded an ientropic turbe. he work produced i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. he proce i ientropic (i.e., reverible-adiabatic). Analyi here i one let and two exit. We take the turbe a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& m& h W& From a ma balance, m& m& 0.05m& 0.95m& Rate of change ternal, ketic, potential, etc.energie E& m& & h m& h m& h m& h W& m& (0.05)(5 kg/) 0.5 kg/ (0.95)(5 kg/) 4.75 kg/ Notg that the expanion proce i ientropic, the enthalpie at three tate are determed a follow: 50 ka 00 C h h 68.4 kj/kg kj/kg K (able A - 6) 4 Ma 5 kg/ 700 ka 4 Ma 0.7 Ma 50 ka Steam turbe 50 ka 00 C 4 Ma kj/kg K h 979. kj/kg (able A - 6) Subtitutg, W & 700 ka kj/kg K m& h m& h 68 kw m& h h 09. kj/kg (able A - 6) (5 kg/)(979. kj/kg) (0.5 kg/)(09. kj/kg) (4.75 kg/)(68.4 kj/kg)

32 7-7-6 Heat i added to a preure cooker that i mataed at a pecified preure. he mimum entropy change of the thermal-energy reervoir upplyg thi heat i to be determed. Aumption Only water vapor ecape through the preure relief valve. Analyi Accordg to the conervation of ma prciple, dmcv m m dt & & dm m& dt An entropy balance adapted to thi ytem become ds urr dt d( m) m& 0 dt When thi i combed with the ma balance, it become ds urr dt d( m) dt dm dt 0 Multiplyg by dt and tegratg the reult yield ΔS urr m m ( m m) 0 he propertie at the itial and fal tate are (from able A-5 at 00 ka) v v f f f v v f xv x xv x he itial and fal mae are m m fg fg fg fg (0.0)( ) m.50 (0.0)(5.5968).0899 kj/kg K (0.50)( ) m.50 (0.50)(5.5968) 4.86 kj/kg K V V 0.m v v m /kg f xv fg V V 0.m v v m /kg f xv fg he entropy of ecapg water vapor i Subtitutg, ΔS urr 00 ka 7.70 kj/kg K ΔS urr.7 kg 0.55 kg m ( m (0.55)(4.86) (.7)(.0899) (7.70)(0.55.7) 0 m ΔS he entropy change of the thermal energy reervoir mut then atify ΔS urr kj/k urr /kg /kg m )

33 7-7-6 Heat i added to a preure cooker that i mataed at a pecified preure. Work i alo done on water. he mimum entropy change of the thermal-energy reervoir upplyg thi heat i to be determed. Aumption Only water vapor ecape through the preure relief valve. Analyi Accordg to the conervation of ma prciple, dmcv m m dt & & dm m& dt An entropy balance adapted to thi ytem become ds urr dt d( m) m& 0 dt When thi i combed with the ma balance, it become ds urr dt d( m) dt dm dt 0 Multiplyg by dt and tegratg the reult yield ΔS urr m m ( m m) 0 he propertie at the itial and fal tate are (from able A-5 at 00 ka) v v f f f v v f xv x xv x he itial and fal mae are m m fg fg fg fg (0.0)( ) m.50 (0.0)(5.5968).0899 kj/kg K (0.50)( ) m.50 (0.50)(5.5968) 4.86 kj/kg K V V 0.m v v m /kg f xv fg V V 0.m v v m /kg f xv fg he entropy of ecapg water vapor i Subtitutg, ΔS urr 00 ka 7.70 kj/kg K ΔS urr.7 kg 0.55 kg m ( m (0.55)(4.86) (.7)(.0899) (7.70)(0.55.7) 0 m ΔS he entropy change of the thermal energy reervoir mut then atify ΔS urr kj/k urr /kg /kg m )

34 A cylder i itially filled with aturated water vapor mixture at a pecified temperature. Steam undergoe a reverible heat addition and an ientropic proce. he procee are to be ketched and heat tranfer for the firt proce and work done durg the econd proce are to be determed. Aumption he ketic and potential energy change are negligible. he thermal energy tored the cylder itelf i negligible. Both procee are reverible. Analyi (b) From the team table (able A-4 through A-6), 00 C h h x 0.5 x h hg kj/kg 00 C u kj/kg u g 7.54 kj/kg K 5 ka u f xh fg 47.9 kj/kg 49.7 (0.5)(56.4) kj/kg We take the content of the cylder a the ytem. hi i a cloed ytem ce no ma enter or leave. he energy balance for thi cloed ytem can be expreed a E 44 Net energy tranfer by heat, work, and ma Q E W b, For proce -, it reduce to Q ΔEytem 44 Change ternal, ketic, potential, etc.energie ΔU m( u u ) m( h ) (5 kg)( )kj/ kg 564kJ, h (c) For proce -, it reduce to W m( u ) (5 kg)( )kj/ kg 9kJ, b, u H O 00 C x 0.5 Q 700 Steam IAWS [ C] ka ka [kj/kg-k]

35 Steam expand an adiabatic turbe. Steam leave the turbe at two different preure. he proce i to be ketched on a - diagram and the work done by the team per unit ma of the team at the let are to be determed. Aumption he ketic and potential energy change are negligible. Analyi (b) From the team table (able A-4 through A-6), 500 C h 4. kj/kg 6 Ma kj/kg K 0 ka h 79.6 kj/kg x 0.8 A ma balance on the control volume give m & & & where m m m& m& 0.m& 0.9m& We take the turbe a the ytem, which i a control volume. he energy balance for thi teady-flow ytem can be expreed the rate form a or E& E& m& h W& m& h W& w h w, h,,, m& h m& h 0.m& h 0.9m& h 0.h 0.h 0.9h 0.9h Ma h 9. kj/kg 4. (0.)(9.) (0.9)(79.6) 69. kj/kg he actual work put per unit ma of team at the let i w η w (0.85)(69. kj/kg) 99.9 kj/kg, [ C] ka 000 ka 0 ka 6 Ma 500 C urbe 0 ka Steam IAWS Ma [kj/kg-k]

36 E An ulated rigid can itially conta R-4a at a pecified tate. A crack develop, and refrigerant ecape lowly. he fal ma the can i to be determed when the preure ide drop to a pecified value. Aumption he can i well-ulated and thu heat tranfer i negligible. he refrigerant that rema the can underwent a reverible adiabatic proce. Analyi Notg that for a reverible adiabatic (i.e., ientropic) proce,, the propertie of the refrigerant the can are (able A-E through A-E) 40 pia 70 F 0 pia v v F f x v Btu/lbm R x fg f fg 0.08 hu the fal ma of the refrigerant the can i ( 0.55)( ) ft /lbm R-4 40 pia 70 F Leak m V v. ft ft /lbm lbm

37 7-7 Entropy Change of Incompreible Subtance 7-66C No, becaue entropy i not a conerved property A hot copper block i dropped to water an ulated tank. he fal equilibrium temperature of the tank and the total entropy change are to be determed. Aumption Both the water and the copper block are compreible ubtance with contant pecific heat at room temperature. he ytem i tationary and thu the ketic and potential energie are negligible. he tank i well-ulated and thu there i no heat tranfer. ropertie he denity and pecific heat of water at 5 C are ρ 997 kg/m and c p 4.8 kj/kg. C. he pecific heat of copper at 7 C i c p 0.86 kj/kg. C (able A-). Analyi We take the entire content of the tank, water copper block, a the ytem. hi i a cloed ytem ce no ma croe the ytem boundary durg the proce. he energy balance for thi ytem can be expreed a or, where E E 44 Net energy tranfer by heat, work, and ma ΔU 0 ΔU ΔEytem 44 Change ternal, ketic, potential, etc.energie Cu ΔU water [ mc( )] Cu [ mc( )] water mwater ρv (997 kg/m )(0.0 m ) 9.6 kg 0 Ug pecific heat value for copper and liquid water at room temperature and ubtitutg, 0 (50 kg)(0.86 kj/kg C)( 80) C (9.6 kg)(4.8 kj/kg C)( 5) C C he entropy erated durg thi proce i determed from WAER Copper 50 kg 0 L hu, ΔS ΔS copper water mc mc avg avg ln ln ( 50 kg)( 0.86 kj/kg K) 00.0 K ln.40 kj/k 5 K 00.0 K 98 K ( 9.6 kg)( 4.8 kj/kg K) ln.44 kj/k ΔS ΔS ΔS kj/k total copper water

38 Computer chip are cooled by placg them aturated liquid R-4a. he entropy change of the chip, R-4a, and the entire ytem are to be determed. Aumption he ytem i tationary and thu the ketic and potential energy change are zero. here are no work teraction volved. here i no heat tranfer between the ytem and the urroundg. Analyi (a) he energy balance for thi ytem can be expreed a E E 44 Net energy tranfer by heat, work, and ma Change ternal, ketic, potential, etc.energie 0 ΔU ΔEytem 44 [ m( u u )] chip [ m( u u) ] R-4a he heat releaed by the chip i [ m( u u )] [ m( u u )] chip R-4a [ 0 ( 40) ] K 0.8 kj Qchip mc( ) (0.00 kg)(0. kj/kg K) he ma of the refrigerant vaporized durg thi heat exchange proce i m Q Q 0.8 kj kj/kg R 4a R 4a g, u g u f u 40 C kg Only a mall fraction of R-4a i vaporized durg the proce. herefore, the temperature of R-4a rema contant durg the proce. he change the entropy of the R-4a i (at -40 F from able A- ) ΔS R 4a mg, g, m f, f, m f, f, ( )( ) ( )(0) (0.005)(0) kJ/K (b) he entropy change of the chip i ΔS chip mc ln (c) he total entropy change i ( 40 7)K (0.00 kg)(0. kj/kg K)ln kj/k (0 7)K Δ S S ΔS ΔS ( ) kj/k total R-4a chip he poitive reult for the total entropy change (i.e., entropy eration) dicate that thi proce i poible.

39 A hot iron block i dropped to water an ulated tank. he total entropy change durg thi proce i to be determed. Aumption Both the water and the iron block are compreible ubtance with contant pecific heat at room temperature. he ytem i tationary and thu the ketic and potential energie are negligible. he tank i well-ulated and thu there i no heat tranfer. 4 he water that evaporate, condene back. ropertie he pecific heat of water at 5 C i c p 4.8 kj/kg. C. he pecific heat of iron at room temperature i c p 0.45 kj/kg. C (able A-). Analyi We take the entire content of the tank, water iron block, a the ytem. hi i a cloed ytem ce no ma croe the ytem boundary durg the proce. he energy balance for thi ytem can be expreed a or, Subtitutg, E E 44 Net energy tranfer by heat, work, and ma ΔU 0 ΔU ΔEytem 44 Change ternal, ketic, potential, etc.energie iron ΔU water [ mc( )] iron [ mc( )] water (5 kg)(0.45 kj/kg K)( 0 0 o o 50 C) (00 kg)(4.8 kj/kg K)( 8 C) C he entropy erated durg thi proce i determed from WAER 8 C Iron 50 C hu, ΔS ΔS S iron water mc avg mc ln avg ln ( 5 kg)( 0.45 kj/kg K) 99.7 K ln 8. kj/k 6 K 99.7 K 9 K ( 00 kg)( 4.8 kj/kg K) ln.4 kj/k ΔS ΔS ΔS kj/k total iron water Dicuion he reult can be improved omewhat by ug pecific heat at average temperature.

40 An alumum block i brought to contact with an iron block an ulated encloure. he fal equilibrium temperature and the total entropy change for thi proce are to be determed. Aumption Both the alumum and the iron block are compreible ubtance with contant pecific heat. he ytem i tationary and thu the ketic and potential energie are negligible. he ytem i well-ulated and thu there i no heat tranfer. ropertie he pecific heat of alumum at the anticipated average temperature of 450 K i c p 0.97 kj/kg. C. he pecific heat of iron at room temperature (the only value available the table) i c p 0.45 kj/kg. C (able A-). Analyi We take the ironalumum block a the ytem, which i a cloed ytem. he energy balance for thi ytem can be expreed a or, E E 44 Net energy tranfer by heat, work, and ma [ mc( Subtitutg, ΔU )] alum alum 0 ΔU ΔEytem 44 Change ternal, ketic, potential, etc.energie ΔU iron [ mc( (0 kg)(0.45 kj/kg K)( 0 )] iron 0 00 C) (0 kg)(0.97 kj/kg K)( o 68.4 o C 44.4 K he total entropy change for thi proce i determed from Iron 0 kg 00 C o 00 C) 0 Alumum 0 kg 00 C hu, ΔS ΔS iron alum mc mc avg avg ln ln ( 0 kg)( 0.45 kj/kg K) 44.4 K ln.55 kj/k 7 K 44.4 K 47 K ( 0 kg)( 0.97 kj/kg K) ln.46 kj/k ΔStotal ΔSiron ΔSalum kj/k

41 EES roblem 7-70 i reconidered. he effect of the ma of the iron block on the fal equilibrium temperature and the total entropy change for the proce i to be tudied. he ma of the iron i to vary from to 0 kg. he equilibrium temperature and the total entropy change are to be plotted a a function of iron ma. Analyi he problem i olved ug EES, and the reult are tabulated and plotted below. "Known:" iron 00 [C] {m_iron 0 [kg]} al 00 [C] m_al 0 [kg] C_al 0.97 [kj/kg-k] "Fromable A- at the anticipated average temperature of 450 K." C_iron 0.45 [kj/kg-k] "Fromable A- at room temperature, the only value available." "Analyi: " " reat the iron plu alumum a a cloed ytem, with no heat tranfer, no work, neglect change KE and E of the ytem. " "he fal temperature i found from the energy balance." E_ - E_ DELAE_y E_ 0 E_ 0 DELAE_y m_iron*delau_iron m_al*delau_al DELAu_iron C_iron*( iron - iron) DELAu_al C_al*( al - al) "the iron and alumum reach thermal equilibrium:" iron al _ DELAS_iron m_iron*c_iron*ln(( iron7) / ( iron7)) DELAS_al m_al*c_al*ln(( al7) / ( al7)) DELAS_total DELAS_iron DELAS_al m iron [kg] m iron ΔS total [kj/kg] [kg] [C] ΔS total [kj/kg] m iron [kg]

42 An iron block and a copper block are dropped to a large lake. he total amount of entropy change when both block cool to the lake temperature i to be determed. Aumption Both the water and the iron block are compreible ubtance with contant pecific heat at room temperature. Ketic and potential energie are negligible. ropertie he pecific heat of iron and copper at room temperature are c iron 0.45 kj/kg. C and c copper 0.86 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. hen the entropy change of the block become ΔS ΔS iron copper mc avg mc ln avg ln ( 50 kg)( 0.45 kj/kg ) We take both the iron and the copper block, a the ytem. hi i a cloed ytem ce no ma croe the ytem boundary durg the proce. he energy balance for thi ytem can be expreed a or, E E 44 Net energy tranfer by heat, work, and ma Q Q 88 K K ln kj/k 5 K 88 K 5 K ( 0 kg)( 0.86 kj/kg K) ln.57 kj/k ΔEytem 44 Change ternal, ketic, potential, etc.energie ΔU ΔU iron ΔU copper [ mc( )] iron [ mc( )] copper Lake 5 C Iron 50 kg 80 C Copper 0 kg 80 C Subtitutg, Q ( 50 kg)( 0.45 kj/kg K)( 5 88) K ( 0 kg)( 0.86 kj/kg K)( 5 88) 964 kj K hu, ΔS Q 964 kj 88 K lake, lake lake 6.80 kj/k hen the total entropy change for thi proce i ΔS ΔS ΔS ΔS kj/k total iron copper lake

43 An adiabatic pump i ued to compre aturated liquid water a reverible manner. he work put i to be determed by different approache. Aumption Steady operatg condition exit. Ketic and potential energy change are negligible. Heat tranfer to or from the fluid i negligible. Analyi he propertie of water at the let and exit of the pump are (able A-4 through A-6) h 9.8 kj/kg 0 ka kj/kg x 0 v m /kg 5 Ma h v kj/kg m (a) Ug the entropy data from the compreed liquid water table w /kg h h kj/kg (b) Ug let pecific volume and preure value w v ( ) ( m /kg)(5,000 0) ka 5.4 kj/kg Error 0.% (b) Ug average pecific volume and preure value w [ / ( ) m /kg](5,000 0) 5.0 kj/kg v ( ) ka avg Error 0% 0 ka 5 Ma pump Dicuion he reult how that any of the method may be ued to calculate reverible pump work.

44 7-44 Entropy Change of Ideal Gae 7-74C For ideal gae, c p c v R and V V V V hu, ln ln ln ln ln ln ln ln ln R c R R c R c R c p v v v V V 7-75C For an ideal ga, dh c p d and v R/. From the econd d relation, d R d c d R d c vd dh d p p Integratg, ln ln R c p Sce c p i aumed to be contant. 7-76C No. he entropy of an ideal ga depend on the preure a well a the temperature. 7-77C Settg Δ 0 give C p R p p c R R c ln ln 0 ln ln But ( ) k k p p p p c c k k k k c c c c R hu,. / ce v v 7-78C he r and v r are called relative preure and relative pecific volume, repectively. hey are derived for ientropic procee of ideal gae, and thu their ue i limited to ientropic procee only. 7-79C he entropy of a ga can change durg an iothermal proce ce entropy of an ideal ga depend on the preure a well a the temperature.

45 C he entropy change relation of an ideal ga implify to Δ c p ln( / ) for a contant preure proce and Δ c v ln( / ) for a contant volume proce. Notg that c p > c v, the entropy change will be larger for a contant preure proce. 7-8 he entropy difference between the two tate of oxy i to be determed. Aumption Oxy i an ideal ga with contant pecific heat. ropertie he pecific heat of oxy at the average temperature of (97)/88 C46 K i c p kj/kg K (able A-b). Analyi From the entropy change relation of an ideal ga, (7 7)K Δoxy c p ln R ln (0.960 kj/kg K)ln kj/kg K (9 7)K ce the preure i ame at the itial and fal tate. 7-8 he entropy change of helium and nitro i to be compared for the ame itial and fal tate. Aumption Helium and nitro are ideal gae with contant pecific heat. ropertie he propertie of helium are c p 5.96 kj/kg K, R.0769 kj/kg K (able A-a). he pecific heat of nitro at the average temperature of (477)/7 C500 K i c p.056 kj/kg K (able A-b). he ga contant of nitro i R kj/kg K (able A-a). Analyi From the entropy change relation of an ideal ga, Δ Δ He N c p ln R ln (7 7)K (5.96 kj/kg K)ln (.0769 kj/kg K)ln (47 7)K 0.86 kj/kg K c p ln 0. kj/kg K R ln (7 7)K (.056 kj/kg K)ln (0.968 kj/kg K)ln (47 7)K Hence, helium undergoe the larget change entropy. 00 ka 000 ka 00 ka 000 ka

46 E he entropy change of air durg an expanion proce i to be determed. Aumption Air i an ideal ga with contant pecific heat. ropertie he pecific heat of air at the average temperature of (50050)/75 F i c p 0.4 Btu/lbm R (able A-Eb). he ga contant of air i R Btu/lbm R (able A-Ea). Analyi From the entropy change relation of an ideal ga, Δ air c p ln R ln (50 460)R 00 pia (0.4 Btu/lbm R)ln ( Btu/lbm R)ln ( )R 00 pia 0.06Btu/lbm R 7-84 he fal temperature of air when it i expanded ientropically i to be determed. Aumption Air i an ideal ga with contant pecific heat. ropertie he pecific heat ratio of air at an anticipated average temperature of 550 K i k.8 (able A-b). Analyi From the ientropic relation of an ideal ga under contant pecific heat aumption, ( k ) / k 0.8/ ka (477 7 K) 000 ka 97 K Dicuion he average air temperature i ( )/57.7 K, which i ufficiently cloe to the aumed average temperature of 550 K. 7-85E he fal temperature of air when it i expanded ientropically i to be determed. Aumption Air i an ideal ga with contant pecific heat. ropertie he pecific heat ratio of air at an anticipated average temperature of 00 F i k.94 (able A-Eb). Analyi From the ientropic relation of an ideal ga under contant pecific heat aumption, ( k ) / k 0.94 / pia ( R) 00 pia 609 R Dicuion he average air temperature i (960609)/785 R5 F, which i ufficiently cloe to the aumed average temperature of 00 F.

47 he fal temperature of helium and nitro when they are compreed ientropically are to be compared. Aumption Helium and nitro are ideal gae with contant pecific heat. ropertie he pecific heat ratio of helium and nitro at room temperature are k.667 and k.4, repectively (able A-a). Analyi From the ientropic relation of an ideal ga under contant pecific heat aumption,,he ( k ) / k / ka (98 K) 00 ka 749 K,N ( k ) / k 0.4 / ka (98 K) 00 ka 575 K Hence, the helium produce the greater temperature when it i compreed he fal temperature of neon and air when they are expanded ientropically are to be compared. Aumption Neon and air are ideal gae with contant pecific heat. ropertie he pecific heat ratio of neon and air at room temperature are k.667 and k.4, repectively (able A-a). Analyi From the ientropic relation of an ideal ga under contant pecific heat aumption,,ne ( k ) / k / ka (77 K) 000 ka 08 K,air ( k ) / k 0.4 / ka (77 K) 000 ka 400 K Hence, the neon produce the maller temperature when it i expanded.

48 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 entropy change of air durg thi proce i to be determed for the cae of contant and variable pecific heat. Aumption At pecified condition, air can be treated a an ideal ga. ropertie he ga contant of air i R 0.87 kj/kg.k (able A-). Analyi he ma of the air and the electrical work done durg thi proce are V m R W W& e, e, ( 0 ka)( 0. m ) ( 0.87 ka m /kg K)( 90 K) Δt ( 0. kj/)( 5 60 ) 80 kj 0.45 kg he energy balance for thi tationary cloed ytem can be expreed a E 44 Net energy tranfer by heat, work, and ma W E e, W b, ΔEytem 44 Change ternal, ketic, potential, etc.energie ΔU W e, m( h h ) c ( ) ce ΔU W b ΔH durg a contant preure quai-equilibrium proce. (a) Ug a contant c p value at the anticipated average temperature of 450 K, the fal temperature become hu, W 80 kj e, 90 K mc p hen the entropy change become ΔS y m ( ) m c ( 0.45 kg)(.0 kj/kg K) p,avg ln 0 R ln mc 698 K 90 K p 698 K p,avg ln ( 0.45 kg)(.00 kj/kg K) ln 0.87 kj/k (b) Aumg variable pecific heat, W W e, ( h ) h h 90.6 kj/kg kj/kg m h 80 kj 0.45 kg e, m From the air table (able A-7, we read o.568 kj/kg K correpondg to thi h value. hen, o o ( ) ( 0.45 kg)( ) kj/kg K 0.87 kj/k 0 o o ΔSy m Rln m W e AIR 0. m 0 ka 7 C

49 A cylder conta N ga at a pecified preure and temperature. A ga i compreed polytropically until the volume i reduced by half. he entropy change of nitro durg thi proce i to be determed. Aumption At pecified condition, N can be treated a an ideal ga. Nitro ha contant pecific heat at room temperature. ropertie he ga contant of nitro i R 0.97 kj/kg.k (able A-). he contant volume pecific heat of nitro at room temperature i c v 0.74 kj/kg.k (able A-). Analyi From the polytropic relation, n n v v v v hen the entropy change of nitro become Δ m c ln V Rln S N v,avg V. ( 00 K)( ) 69. K 69. K 00 K (. kg) ( 0.74 kj/kg K) ln ( 0.97 kj/kg K) ln( 0.5) kj/k N V. C

50 EES roblem 7-89 i reconidered. he effect of varyg the polytropic exponent from to.4 on the entropy change of the nitro i to be vetigated, and the procee are to be hown on a common -v diagram. Analyi he problem i olved ug EES, and the reult are tabulated and plotted below. Function BoundWork([],V[],[],V[],n) "hi function return the Boundary Work for the polytropic proce. hi function i required ce the expreion for boundary work depen on whether n or n<>" If n<> then BoundWork:([]*V[]-[]*V[])/(-n)"Ue Equation - when n" ele BoundWork: []*V[]*ln(V[]/V[]) "Ue Equation -0 when n" endif end n [] 0 [ka] [] 7 [C] m. [kg] V[]V[]/ Ga$'N' MMmolarma(Ga$) RR_u/MM R_u8.4 [kj/kmol-k] "Sytem: he ga encloed the piton-cylder device." "roce: olytropic expanion or compreion, *V^n C" []*V[]m*R*([]7) []*V[]^n[]*V[]^n W_b BoundWork([],V[],[],V[],n) "Fd the temperature at tate from the preure and pecific volume." []temperature(ga$,[],vv[]/m) "he entropy at tate and i:" []entropy(ga$,[],vv[]/m) []entropy(ga$,[],vv[]/m) DELASm*([] - []) "Remove the {} to erate the -v plot data" {Ntep 0 V[]V[] [][] Duplicate i,ntep V[i]V[]-i*(V[]-V[])/Ntep [i][]*(v[]/v[i])^n END } ΔS [kj/kg] n W b [kj]

51 n.4 [i] V[i] Δ S 0 kj/k ΔS [kj/k] n W b [kj] n

52 E A fixed ma of helium undergoe a proce from one pecified tate to another pecified tate. he entropy change of helium i to be determed for the cae of reverible and irreverible procee. Aumption At pecified condition, helium can be treated a an ideal ga. Helium ha contant pecific heat at room temperature. ropertie he ga contant of helium i R Btu/lbm.R (able A-E). he contant volume pecific heat of helium i c v 0.75 Btu/lbm.R (able A-E). Analyi From the ideal-ga entropy change relation, ΔS He v m cv,ave ln Rln v 660 R (5 lbm) (0.75 Btu/lbm R) ln 540 R 9.7 Btu/R he entropy change will be the ame for both cae. ( Btu/lbm R) He 540 R 660 R 0 ft /lbm ln 50 ft /lbm 7-9 One ide of a partitioned ulated rigid tank conta an ideal 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 total entropy change durg thi proce i to be determed. Aumption he ga the tank i given to be an ideal ga, and thu ideal ga relation apply. Analyi akg the entire rigid tank a the ytem, the energy balance can be expreed a E E 44 Net energy tranfer by heat, work, and ma u 0 ΔU m( u Change ternal, ketic, potential, etc.energie u ΔEytem 44 u ) ce u u() for an ideal ga. hen the entropy change of the ga become ΔS N c v,avg ln ( 5 kmol)( 8.4 kj/kmol K) ln( ) 8.8 kj/k 0 V R u ln NR V u V ln V hi alo repreent the total entropy change ce the tank doe not conta anythg ele, and there are no teraction with the urroundg. IDEAL GAS 5 kmol 40 C

53 Air i compreed a piton-cylder device a reverible and adiabatic manner. he fal temperature and the work are to be determed for the cae of contant and variable pecific heat. Aumption At pecified condition, air can be treated a an ideal ga. he proce i given to be reverible and adiabatic, and thu ientropic. herefore, ientropic relation of ideal gae apply. ropertie he ga contant of air i R 0.87 kj/kg.k (able A-). he pecific heat ratio of air at low to moderately high temperature i k.4 (able A-). Analyi (a) Aumg contant pecific heat, the ideal ga ientropic relation give hen, ( ) k k ka 00 ka ( 90 K) 55. K ( ) / K c 0.77kJ/kg K avg v, avg We take the air the cylder a the ytem. he energy balance for thi tationary cloed ytem can be expreed a hu, E E 44 Net energy tranfer by heat, work, and ma w W ΔEytem 44 Change ternal, ketic, potential, etc. energie ΔU m( u u) mcv ( ) ( ) ( 0.77 kj/kg K)( ) K 7. kj/kg cv,avg AIR Reverible (b) Aumg variable pecific heat, the fal temperature can be determed ug the relative preure data (able A-7), and 90 K r r u r 800 ka 00 ka hen the work put become w kj/kg (.) ( ) kj/kg 69.5 kj/kg u u u 5.4 K 76.6 kj/kg

54 EES roblem 7-9 i reconidered. he work done and fal temperature durg the compreion proce are to be calculated and plotted a function of the fal preure for the two cae a the fal preure varie from 00 ka to 800 ka. Analyi he problem i olved ug EES, and the reult are tabulated and plotted below. rocedure ContropSol(_,_,_,Ga$:Work Controp,_Controp) C_SECHEA(Ga$,7) MMMOLARMASS(Ga$) R_u8.4 [kj/kmol-k] RR_u/MM C_V C_ - R k C_/C_V (_7)*(_/_)^((k-)/k) _Controp-7 "[C]" DELAu C_v*(-(_7)) Work Controp DELAu End "Known:" _ 00 [ka] _ 7 [C] _ 800 [ka] "Analyi: " " reat the piton-cylder a a cloed ytem, with no heat tranfer, neglect change KE and E of the air. he proce i reverible and adiabatic thu ientropic." "he ientropic work i determed from:" e_ - e_ DELAe_y e_ 0 [kj/kg] e_ Work_ DELAE_y (u_ - u_) u_ INENERGY(air,_) v_ volume(air,_,_) _ entropy(air,_,_) " he proce i reverible and adiabatic or ientropic. hen _ and _ pecify tate." u_ INENERGY(air,_,_) ientemperature(air,_,_) Ga$ 'air' Call ContropSol(_,_,_,Ga$: Work Controp,_Controp) Work [kj/kg] [ka] [ka] Work [kj/kg] Work,Controp [kj/kg]

55 An ulated rigid tank conta argon ga at a pecified preure and temperature. A valve i opened, and argon ecape until the preure drop to a pecified value. he fal ma the tank i to be determed. Aumption At pecified condition, argon can be treated a an ideal ga. he proce i given to be reverible and adiabatic, and thu ientropic. herefore, ientropic relation of ideal gae apply. ropertie he pecific heat ratio of argon i k.667 (able A-). Analyi From the ideal ga ientropic relation, ( ) k k ka 450 ka ( 0 K) 9.0 K he fal ma the tank i determed from the ideal ga relation, ( 00 ka)( 0 K) ( )( ) ( 4 ) 450 ka 9 K.46 kg V mr m m V m R kg ARGON 4 kg 450 ka 0 C

56 EES roblem 7-95 i reconidered. he effect of the fal preure on the fal ma the tank i to be vetigated a the preure varie from 450 ka to 50 ka, and the reult are to be plotted. Analyi he problem i olved ug EES, and the reult are tabulated and plotted below. "Known:" C_ 0.50"[kJ/kg-K ]" C_V 0. "[kj/kg-k ]" R0.08 "[ka-m^/kg-k]" _ 450"[ka]" _ 0"[C]" m_ 4"[kg]" _ 50"[ka]" "Analyi: We aume the ma that tay the tank undergoe an ientropic expanion proce. hi allow u to determe the fal temperature of that ga at the fal preure the tank by ug the ientropic relation:" k C_/C_V _ ((_7)*(_/_)^((k-)/k)-7)"[C]" V_ V *V_m_*R*(_7) _*V_m_*R*(_7) m [kg] [ka] m [kg] [ka]

57 E Air i accelerated an adiabatic nozzle. Diregardg irreveribilitie, the exit velocity of air i to be determed. Aumption Air i an ideal ga with variable pecific heat. he proce i given to be reverible and adiabatic, and thu ientropic. herefore, ientropic relation of ideal gae apply. he nozzle operate teadily. Analyi Aumg variable pecific heat, the let and exit propertie are determed to be and 000 R r r pia 60 pia r (.0).0 h Btu/lbm.46 h 65.9 R 5. Btu/lbm We take the nozzle a the ytem, which i a control volume. he energy balance for thi teady-flow ytem can be expreed the rate form a herefore, E E & 44 & Rate of net energy tranfer by heat, work, and ma m& ( h V h h V E& / ) m& ( h V Rate of change ternal, ketic, potential, etc.energie E& 0 0 (teady) ΔEytem & V /) 0 AIR V ( h h ) ( ) Btu/lbm ( 00 ft/) V 9 ft/ 5,07 ft / Btu/lbm

58 E Air i expanded an ientropic turbe. he exit temperature of the air and the power produced are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. he proce i ientropic (i.e., reverible-adiabatic). Air i an ideal ga with contant pecific heat. ropertie he propertie of air at an anticipated average temperature of 600 F are c p 0.50 Btu/lbm R and k.77 (able A-Eb). he ga contant of air i R pia ft /lbm R (able A-E). Analyi here i only one let and one exit, and thu m & m& m&. We take the turbe a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& V m& h W& Rate of change ternal, ketic, potential, etc.energie E& m& h m& c & V m& h h p ( V W& V V ) V he exit temperature of the air for thi ientropic proce i ( k ) / k 0.77 / pia ( R) 50 pia 74 R he pecific volume of air at the let and the ma flow rate are v m& R ( pia ft /lbm R)( R).58 ft 50 pia AV v (0.5 ft )(500 ft/) lbm/.58 ft /lbm Subtitutg to the energy balance equation give /lbm 50 pia 900 F 500 ft/ urbe 5 pia 00 ft/ 50 pia 5 pia W& m& c p ( (500 ft/) (74.45 lbm/) (0.50 Btu/lbm R)(60 74)R,94 Btu/ V ) V hp Btu/ 7,50 hp (00 ft/) Btu/lbm 5,07 ft /

59 Nitro i compreed an adiabatic compreor. he mimum work put i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. he proce i adiabatic, and thu there i no heat tranfer. Nitro i an ideal ga with contant pecific heat. ropertie he propertie of nitro at an anticipated average temperature of 400 K are c p.044 kj/kg K and k.97 (able A-b). Analyi here i only one let and one exit, and thu m & m& m&. We take the compreor a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teadyflow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& mh & W& W& Rate of change ternal, ketic, potential, etc.energie E& mh & & m& ( h h ) For the mimum work put to the compreor, the proce mut be reverible a well a adiabatic (i.e., ientropic). hi beg the cae, the exit temperature will be 600 ka Nitro compreor 0 ka 0 C 600 ka ( k ) / k 0.97 / ka (0 K) 0 ka 479 K 0 ka Subtitutg to the energy balance equation give w h h c ( ) (.044 kj/kg K)(479 0)K 84 kj/kg p

60 Oxy i expanded an adiabatic nozzle. he maximum velocity at the exit i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. he proce i adiabatic, and thu there i no heat tranfer. Oxy i an ideal ga with contant pecific heat. ropertie he propertie of oxy at room temperature are c p 0.98 kj/kg K and k.95 (able A- a). Analyi For the maximum velocity at the exit, the proce mut be reverible a well a adiabatic (i.e., ientropic). hi beg the cae, the exit temperature will be ( k ) / k 0.95 /.95 0 ka (6 K) 00 ka 80.0 K here i only one let and one exit, and thu m & m& m&. We take nozzle a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& Rate of change ternal, ketic, potential, etc.energie E& & ka 90 C m/ O 0 ka V m& h m& h V h h V V ) 00 ka Solvg for the exit velocity, V 0.5 [ V ( h h )] [ V c ( )] p ka 000 m / ( m/) (0.98 kj/kg K)(6 80)K kj/kg 90 m/ 0.5

61 Air i expanded an adiabatic nozzle by a polytropic proce. he temperature and velocity at the exit are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. here i no heat tranfer or haft work aociated with the proce. Air i an ideal ga with contant pecific heat. ropertie he propertie of air at room temperature are c p.005 kj/kg K and k.4 (able A-a). Analyi For the polytropic proce of an ideal ga, ( n ) / n 0. /. 00 ka (7 K) 700 ka n v Contant, and the exit temperature i given by 79 K here i only one let and one exit, and thu m & m& m&. We take nozzle a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& V h Rate of change ternal, ketic, potential, etc.energie E& h V m& h m& h Solvg for the exit velocity, V 0.5 [ V ( h h )] [ V c ( )] p (0 m/) 46 m/ & V 0.5 V ) 000 m / (.005 kj/kg K)(7 79)K kj/kg 700 ka 00 C 0 m/ 0.5 Air 00 ka

62 Air i expanded an adiabatic nozzle by a polytropic proce. he temperature and velocity at the exit are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. here i no heat tranfer or haft work aociated with the proce. Air i an ideal ga with contant pecific heat. ropertie he propertie of air at room temperature are c p.005 kj/kg K and k.4 (able A-a). Analyi For the polytropic proce of an ideal ga, ( n ) / n 0. /. 00 ka (7 K) 700 ka n v Contant, and the exit temperature i given by 0 K here i only one let and one exit, and thu m & m& m&. We take nozzle a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& V h Rate of change ternal, ketic, potential, etc.energie E& h V m& h m& h Solvg for the exit velocity, V 0.5 [ V ( h h )] [ V c ( )] p (0 m/) 76 m/ & V 0.5 V ) 000 m / (.005 kj/kg K)(7 0)K kj/kg 700 ka 00 C 0 m/ 0.5 Air 00 ka

63 Air i charged to an itially evacuated contaer from a upply le. he mimum temperature of the air the contaer after it i filled i to be determed. Aumption hi i an unteady proce ce the condition with the device are changg durg the proce, but it can be analyzed a a uniform-flow proce ce the tate of fluid at the let rema contant. Air i an ideal ga with contant pecific heat. Ketic and potential energie are negligible. 4 here are no work teraction volved. 5 he tank i well-ulated, and thu there i no heat tranfer. ropertie he pecific heat of air at room temperature i c p 0.40 Btu/lbm R (able A-Ea). Analyi We take the tank a the ytem, which i a control volume ce ma croe the boundary. Notg that the microcopic energie of flowg and nonflowg fluid are repreented by enthalpy h and ternal energy u, repectively, the ma and entropy balance for thi uniform-flow ytem can be expreed a Ma balance: m m Entropy balance: m Δm m m i m m i m m ytem m m Combg the two balance, m m i i e 0 0 e m i m i i i 0 0 he mimum temperature will reult when the equal ign applie. Notg that i, we have hen, i c p ln R ln 0 c p ln 0 i 00 F i i i Air 00 pia, 00 F Evacuated

64 A contaer i filled with liquid water i placed a room and heat tranfer take place between the contaer and the air the room until the thermal equilibrium i etablihed. he fal temperature, the amount of heat tranfer between the water and the air, and the entropy eration are to be determed. Aumption Ketic and potential energy change are negligible. Air i an ideal ga with contant pecific heat. he room i well-ealed and there i no heat tranfer from the room to the urroundg. 4 Sea level atmopheric preure i aumed. 0. ka. ropertie he propertie of air at room temperature are R 0.87 ka.m /kg.k, c p.005 kj/kg.k, c v 0.78 kj/kg.k. he pecific heat of water at room temperature i c w 4.8 kj/kg.k (able A-, A-). Analyi (a) he ma of the air the room i m a V (0. ka)(90 m ).5 kg R (0.87 ka m /kg K)( 7 K) a An energy balance on the ytem that conit of the water the contaer and the air the room give the fal equilibrium temperature 0 m c w w ( w ) m c 0 (45 kg)(4.8 kj/kg.k)( (b) he heat tranfer to the air i a v ( a ) 95) (.5 kg)(0.78 kj/kg.k)( Q m c ( ) (.5 kg)(0.78 kj/kg.k)(70. ) 4660 kj a v a ) 70. C (c) he entropy eration aociated with thi heat tranfer proce may be obtaed by calculatg total entropy change, which i the um of the entropy change of water and the air. ΔS w m c w w ln w (70. 7) K (45 kg)(4.8 kj/kg.k)ln (95 7) K mar ΔS S a V m a c (.5 kg)(0.87 ka m /kg K)(70. 7 K) (90 m ) p ln a R ln. kj/k ka (70. 7) K ka (.5 kg) (.005 kj/kg.k)ln (0.87 kj/kg.k)ln 4.88 kj/k ( 7) K 0. ka ΔS ΔS w ΔS kj/k total a Water 45 kg 95 C Room 90 m C

65 Air i accelerated an ientropic nozzle. he maximum velocity at the exit i to be determed. Aumption Air i an ideal ga with contant pecific heat. he nozzle operate teadily. ropertie he propertie of air at room temperature are c p.005 kj/kg.k, k.4 (able A-a). Analyi he exit temperature i determed from ideal ga ientropic relation to be, ( k ) / k 0.4/.4 00 ka 800 ka ( K) 7.5 K We take the nozzle a the ytem, which i a control volume. he energy balance for thi teady-flow ytem can be expreed the rate form a herefore, E E & 44 & Rate of net energy tranfer by heat, work, and ma m& ( h V E& / ) m& ( h 0 h 0 c Rate of change ternal, ketic, potential, etc.energie E& 0 (teady) ΔEytem & ( V ) /) V 0 h p V 0 AIR V c ( p ) 000 m / (.005 kj/kg.k)(67-7.5)k kj/kg m/

66 An ideal ga i compreed an ientropic compreor. 0% of ga i compreed to 400 ka and 90% i compreed to 600 ka. he compreion proce i to be ketched, and the exit temperature at the two exit, and the ma flow rate to the compreor are to be determed. Aumption he compreor operate teadily. he proce i reverible-adiabatic (ientropic) ropertie he propertie of ideal ga are given to be c p. kj/kg.k and c v 0.8 kj/kg.k. Analyi (b) he pecific heat ratio of the ga i c k p c v he exit temperature are determed from ideal ga ientropic relation to be, 600 ka ( k ) / k 0.75/ ka 00 ka ( 7 7 K) 47.8 K ( k ) / k 0.75/ ka 00 ka ( 7 7 K) K (c) A ma balance on the control volume give where m & & & m& m& m m 0.m& 0.9m& COMRESSOR 00 ka 00 K kw 400 ka We take the compreor a the ytem, which i a control volume. he energy balance for thi teady-flow ytem can be expreed the rate form a E E & 44 & Rate of net energy tranfer by heat, work, and ma E& m& h W& m& c W& p Rate of change ternal, ketic, potential, etc.energie E& m& h m& h 0 (teady) Eytem & Δ m& c p Solvg for the let ma flow rate, we obta m& c [.( ) 0.9( )] p 0 (. kj/kg K) 0.58 kg/ W& kw 0.9m& c p 0 [ 0.( ) 0.9( ) ]

67 Air contaed a contant-volume tank cooled to ambient temperature. he entropy change of the air and the univere due to thi proce are to be determed and the proce i to be ketched on a - diagram. Aumption Air i an ideal ga with contant pecific heat. ropertie he pecific heat of air at room temperature i c v 0.78 kj/kg.k (able A-a). Analyi (a) he entropy change of air i determed from ΔS air mcv ln (7 7) K (5 kg)(0.78 kj/kg.k)ln (7 7) K.488 kj/k (b) An energy balance on the ytem give Q mc ( ) v (5 kg)(0.78 kj/kg.k)(7 7) 077 kj he entropy change of the urroundg i Δ Q 077 kj 00 K urr urr.59 kj/k he entropy change of univere due to thi proce i S ΔS ΔS ΔS kj/k total air urr 7ºC 7ºC air Air 5 kg 7 C 00 ka urr

68 7-68 Reverible Steady-Flow Work 7-08C he work aociated with teady-flow device i proportional to the pecific volume of the ga. Coolg a ga durg compreion will reduce it pecific volume, and thu the power conumed by the compreor. 7-09C Coolg the team a it expand a turbe will reduce it pecific volume, and thu the work put of the turbe. herefore, thi i not a good propoal. 7-0C We would not upport thi propoal ce the teady-flow work put to the pump i proportional to the pecific volume of the liquid, and coolg will not affect the pecific volume of a liquid ignificantly. 7- Air i compreed iothermally a reverible teady-flow device. he work required i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. here i no heat tranfer aociated with the proce. Ketic and potential energy change are negligible. 4 Air i an ideal ga with contant pecific heat. ropertie he ga contant of air i R Btu/lbm R (able A-E). Analyi Subtitutg the ideal ga equation of tate to the reverible teady-flow work expreion give w vd R d R ln 0 pia ( Btu/lbm R)( K)ln 6 pia 7.9 Btu/lbm 0 pia 75 F Compreor Air 6 pia 75 F

69 Saturated water vapor i compreed a reverible teady-flow device. he work required i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. here i no heat tranfer aociated with the proce. Ketic and potential energy change are negligible. Analyi he propertie of water at the let tate are 50 C x ka v m /kg (able A - 4) Notg that the pecific volume rema contant, the reverible teadyflow work expreion give w vd v ( ) kj (0.948 m /kg)( )ka ka m 05.6 kj/kg Ma Compreor Water 50 C at. vap. 7- he work produced for the proce - hown the figure i to be determed. Aumption Ketic and potential energy change are negligible. Analyi he work tegral repreent the area to the left of the reverible proce le. hen, (ka) w,- vd vd v v ( (0.5.0)m 0 kj/kg ) v ( ) /kg (00 500)ka (.0 m /kg)(400-00)ka v (m /kg)

70 he work produced for the proce - hown the figure i to be determed. Aumption Ketic and potential energy change are negligible. Analyi he work tegral repreent the area to the left of the reverible proce le. hen, w,- vd v v ( ) (0..7)ft /lbm Btu (500 00)pia pia ft 66.6 Btu/lbm (pia) v (ft /lbm) 7-5 Liquid water i to be pumped by a 5-kW pump at a pecified rate. he highet preure the water can be pumped to i to be determed. Aumption Liquid water i an compreible ubtance. Ketic and potential energy change are negligible. he proce i aumed to be reverible ce we will determe the limitg cae. ropertie he pecific volume of liquid water i given to be v 0.00 m /kg. Analyi he highet preure the liquid can have at the pump exit can be determed from the reverible teady-flow work relation for a liquid, hu, It yield W& m& v d Δke 0 Δpe 5 kj/ (5 kg/)(0.00 m /kg)( 500 ka 0 m& v ( ) kj 00)k a ka m UM 00 ka 5 kw

71 A team power plant operate between the preure limit of 0 Ma and 0 ka. he ratio of the turbe work to the pump work i to be determed. Aumption Liquid water i an compreible ubtance. Ketic and potential energy change are negligible. he proce i reverible. 4 he pump and the turbe are adiabatic. ropertie he pecific volume of aturated liquid water at 0 ka i v v 0 ka m /kg (able A-5). Analyi Both the compreion and expanion procee are reverible and adiabatic, and thu ientropic, and 4. hen the propertie of the team are 4 0 ka h4 h at. vapor 4 g ka kj/kg kj/kg K 0 Ma h kj/kg Alo, v v 0 ka m /kg. he work put to thi ientropic turbe i determed from the teady-flow energy balance to be Subtitutg, E E & 44 & Rate of net energy tranfer by heat, work, and ma E& mh & W& Rate of change ternal, ketic, potential, etc.energie E& mh & W& 4 m& ( h 0 (teady) ΔEytem & h ) wturb, h h kj/kg H O H O 4 he pump work put i determed from the teady-flow work relation to be w pump, 0 0 ( ) v d Δke Δpe v kj ( m /kg)(0,000 0)ka ka m 0.5 kj/kg hu, w w turb, pump,

72 EES roblem 7-6 i reconidered. he effect of the quality of the team at the turbe exit on the net work put i to be vetigated a the quality i varied from 0.5 to.0, and the net work put u to be plotted a a function of thi quality. Analyi he problem i olved ug EES, and the reult are tabulated and plotted below. "Sytem: control volume for the pump and turbe" "roperty relation: Steam function" "roce: For ump and urbe: Steady tate, teady flow, adiabatic, reverible or ientropic" "Sce we don't know the ma, we write the conervation of energy per unit ma." "Conervation of ma: m_dot[] m_dot[]" "Known:" WorkFluid$ 'Steam_IAWS' [] 0 [ka] x[] 0 [] 0000 [ka] x[4].0 "ump Analyi:" []temperature(workfluid$,[],x0) v[]volume(workfluid$,[],x0) h[]enthalpy(workfluid$,[],x0) []entropy(workfluid$,[],x0) [] [] h[]enthalpy(workfluid$,[],[]) []temperature(workfluid$,[],[]) "he Volume function ha the ame form for an ideal ga a for a real fluid." v[]volume(workfluid$,[],p[]) "Conervation of Energy - SSSF energy balance for pump" " -- neglect the change potential energy, no heat tranfer:" h[]w_pump h[] "Alo the work of pump can be obtaed from the compreible fluid, teady-flow reult:" W_pump_comp v[]*([] - []) "Conervation of Energy - SSSF energy balance for turbe -- neglectg the change potential energy, no heat tranfer:" [4] [] [] [] h[4]enthalpy(workfluid$,[4],xx[4]) [4]entropy(WorkFluid$,[4],xx[4]) [4]temperature(WorkFluid$,[4],xx[4]) [] [4] h[]enthalpy(workfluid$,[],[]) []temperature(workfluid$,[],[]) h[] h[4] W_turb W_net_ W_turb - W_pump

73 7-7 W net, W pump W pump,comp W turb [kj/kg] [kj/kg] [kj/kg] [kj/kg] x 4 [ C] , x Steam 0000 ka 0 ka [kj/kg-k] W net, [kj/kg] x[4]

74 Liquid water i pumped by a 70-kW pump to a pecified preure at a pecified level. he highet poible ma flow rate of water i to be determed. Aumption Liquid water i an compreible ubtance. Ketic energy change are negligible, but potential energy change may be ignificant. he proce i aumed to be reverible ce we will determe the limitg cae. ropertie he pecific volume of liquid water i given to be v 0.00 m /kg. Analyi he highet ma flow rate will be realized when the entire proce i reverible. hu it i determed from the reverible teadyflow work relation for a liquid, hu, It yield W& m& v d Δke 0 Δpe m& { v ( ) g( z z )} kj 7 kj/ m& (0.00 m /kg)(5000 0)ka (9.8 m/ ka m m&.4 kg/ 5 Ma UM kj/kg )(0 m) 000 m / Water 0 ka

75 E Helium ga i compreed from a pecified tate to a pecified preure at a pecified rate. he power put to the compreor i to be determed for the cae of ientropic, polytropic, iothermal, and two-tage compreion. Aumption Helium i an ideal ga with contant pecific heat. he proce i reverible. Ketic and potential energy change are negligible. ropertie he ga contant of helium i R.6805 pia.ft /lbm.r Btu/lbm.R. he pecific heat ratio of helium i k.667 (able A-E). Analyi he ma flow rate of helium i V m& & R ( 4 pia)( 5 ft /) (.6805 pia ft /lbm R)( 50 R) (a) Ientropic compreion with k.667: W & comp, ( k ) / k kr m& k Btu/lbm R ( lbm/) Btu/ 6.4 hp (b) olytropic compreion with n.: W & comp, ( ) / nr m& n lbm/ lbm/ ( )( )( 50 R) ce hp Btu/ ( ) ( )( Btu/lbm R)( 50 R).47 Btu/ 47. hp (c) Iothermal compreion: W & mr & ln n n. ce hp Btu/ 0 pia 4 pia 0 pia 4 pia 0 pia 4 pia 0./ /.667 ( lbm/)( Btu/lbm R)( 50 R) ln 7.8 Btu/ 9.4 hp comp, (d) Ideal two-tage compreion with tercoolg (n.): In thi cae, the preure ratio acro each tage i the ame, and it value i determed from x ( 4 pia)( 0 pia) 4.0 pia he compreor work acro each tage i alo the ame, thu total compreor work i twice the compreion work for a gle tage: W & comp, ( n ) / n nr comp,i x mw & m& n Btu/lbm R ( lbm/). 0.5 Btu/ 4. hp ( )( )( 50 R) ce hp Btu/ 4 pia 4 pia 0./. He 5 ft / W

76 E EES roblem 7-9E i reconidered. he work of compreion and entropy change of the helium i to be evaluated and plotted a function of the polytropic exponent a it varie from to.667. Analyi he problem i olved ug EES, and the reult are tabulated and plotted below. rocedure Funcoly(m_dot,k, R,,,,n:W_dot_comp_polytropic,W_dot_comp_tageoly,Q_dot_Out_polytropic,Q_dot_Out _tageoly) If n then W_dot_comp_polytropic m_dot*r*(460)*ln(/)*convert(btu/,hp) "[hp]" W_dot_comp_tageoly W_dot_comp_polytropic "[hp]" Q_dot_Out_polytropicW_dot_comp_polytropic*convert(hp,Btu/) "[Btu/]" Q_dot_Out_tageoly Q_dot_Out_polytropic*convert(hp,Btu/) "[Btu/]" Ele C_ k*r/(k-) "[Btu/lbm-R]" (460)*((/)^((n)/n)-460)"[F]" W_dot_comp_polytropic m_dot*n*r*(460)/(n-)*((/)^((n-)/n) - )*convert(btu/,hp)"[hp]" Q_dot_Out_polytropicW_dot_comp_polytropic*convert(hp,Btu/)m_dot*C_*(-)"[Btu/]" x(*)^0.5 x(460)*((x/)^((n)/n)-460)"[f]" W_dot_comp_tageoly *m_dot*n*r*(460)/(n-)*((x/)^((n-)/n) - )*convert(btu/,hp)"[hp]" Q_dot_Out_tageolyW_dot_comp_tageoly*convert(hp,Btu/)*m_dot*C_*(- x)"[btu/]" endif END R0.496[Btu/lbm-R] k.667 n. 4 [pia] 70 [F] 0 [pia] V_dot 5 [ft^/] *V_dotm_dot*R*(460)*convert(Btu,pia-ft^) W_dot_comp_ientropic m_dot*k*r*(460)/(k-)*((/)^((k-)/k) - )*convert(btu/,hp)"[hp]" Q_dot_Out_ientropic 0"[Btu/]" Call Funcoly(m_dot,k, R,,,,n:W_dot_comp_polytropic,W_dot_comp_tageoly,Q_dot_Out_polytropic,Q_dot_Out _tageoly) W_dot_comp_iothermal m_dot*r*(460)*ln(/)*convert(btu/,hp)"[hp]" Q_dot_Out_iothermal W_dot_comp_iothermal*convert(hp,Btu/)"[Btu/]"

77 7-77 n W compstageoly [hp] W compientropic [hp] W compiothermal [hp] W comppolytropic [hp] W comp,polytropic [hp] olytropic Iothermal Ientropic Stageoly n

78 Water mit i to be prayed to the air tream the compreor to cool the air a the water evaporate and to reduce the compreion power. he reduction the exit temperature of the compreed air and the compreor power aved are to be determed. Aumption Air i an ideal ga with variable pecific heat. he proce i reverible. Ketic and potential energy change are negligible. Air i compreed ientropically. 4 Water vaporize completely before leavg the compreor. 4 Air propertie can be ued for the air-vapor mixture. ropertie he ga contant of air i R 0.87 kj/kg.k (able A-). he pecific heat ratio of air i k.4. he let enthalpie of water and air are (able A-4 and A-7) h w h f@0 C 8.9 kj/kg, h fg@0 C 45.9 kj/kg and h a K 00.9 kj/kg Analyi In the cae of ientropic operation (thu no coolg or water pray), the exit temperature and the power put to the compreor are W & ( k ) / k comp, kr m& k (. kg/) 00 ka (00 K) 00 ka ( ) ( k { ) / k } (.4 ) / K 0.4/.4 { } 654. kw (.4)( 0.87 kj/kg K)( 00 K) ( 00 ka/00 ka ).4 When water i prayed, we firt need to check the accuracy of the aumption that the water vaporize completely the compreor. In the limitg cae, the compreion will be iothermal at the compreor let temperature, and the water will be a aturated vapor. o avoid the complexity of dealg with two fluid tream and a ga mixture, we diregard water the air tream (other than the ma flow rate), and aume air i cooled by an amount equal to the enthalpy change of water. he rate of heat aborption of water a it evaporate at the let temperature completely i Q & & coolg, max m w h 0 C he mimum power put to the compreor i (0. kg/)(45.9 kj/kg) kw 00 ka W & comp,,m mr & ln (. kg/)(0.87 kj/kg K)(00 K) ln 449. kw 00 ka hi correpond to maximum coolg from the air ce, at contant temperature, Δh 0 and thu Q & W& 449. kw, which i cloe to kw. herefore, the aumption that all the water vaporize i approximately valid. hen the reduction required power put due to water pray become ΔW & W& W& kw comp, comp, ientropic comp, iothermal Water 0 C Dicuion (can be ignored): At contant temperature, Δh 0 and thu Q & W& 449. kw correpond to maximum coolg from the air, which i le than kw. herefore, the aumption that all the water vaporize i only roughly valid. A an alternative, we can aume the compreion proce to be polytropic and the water to be a aturated vapor at the compreor exit temperature, and diregard the remag liquid. But thi cae there i not a unique olution, and we will have to elect either the amount of water or the exit temperature or the polytropic exponent to obta a olution. Of coure we can alo tabulate the reult for different cae, and then make a election. 00 ka He 00 ka 00 K W

79 7-79 Sample Analyi: We take the compreor exit temperature to be 00 C 47 K. hen, hen, W& h w h g@00 C 79.0 kj/kg and h a K 475. kj/kg comp, Energy balance: W & comp, ( n ) / n nr m& n (. kg/) Q& 47 K 00 ka 00 K 00 ka ( ) ( n { ) / n } (.4)( 0.87 kj/kg K).4 nr m& ( n ( n ) / n ) n.4 (47 00)K 570 kw m& ( h h ) Q& W& comp, m& ( h h ) kw (. kg/)( ) 0.0 kw Notg that thi heat i aborbed by water, the rate at which water evaporate the compreor become Q& & 0.0 kj/ ( ) kj/kg,water, air Q,water m& w( hw hw ) m& w hw hw hen the reduction the exit temperature and compreor power put become Δ, ientropic, water cooled C ΔW& W& W& kw comp, comp, ientropic comp, water cooled Note that electg a different compreor exit temperature will reult different value. Q& kg/ 7- A water-jected compreor i ued a ga turbe power plant. It i claimed that the power put of a ga turbe will creae when water i jected to the compreor becaue of the creae the ma flow rate of the ga (air water vapor) through the turbe. hi, however, i not necearily right ce the compreed air thi cae enter the combutor at a low temperature, and thu it aborb much more heat. In fact, the coolg effect will mot likely domate and caue the cyclic efficiency to drop.

80 7-80 Ientropic Efficiencie of Steady-Flow Device 7-C he ideal proce for all three device i the reverible adiabatic (i.e., ientropic) proce. he adiabatic efficiencie of thee device are defed a η actual work put, entropic work put η C entropic work put, and η N actual work put actual exit keticenergy entropic exit ketic energy 7-4C No, becaue the ientropic proce i not the model or ideal proce for compreor that are cooled tentionally. 7-5C Ye. Becaue the entropy of the fluid mut creae durg an actual adiabatic proce a a reult of irreveribilitie. herefore, the actual exit tate ha to be on the right-hand ide of the ientropic exit tate 7-6 Saturated team i compreed an adiabatic proce with an ientropic efficiency of he work required i to be determed. Aumption Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. Analyi We take the team a the ytem. hi i a cloed ytem ce no ma enter or leave. he energy balance for thi tationary cloed ytem can be expreed a E E 44 Net energy tranfer by heat, work, and ma W ΔEytem 44 Change ternal, ketic, potential, etc.energie ΔU m( u u ) From the team table (able A-5 and A-6), 00 ka u at. vapor Ma u u g@ 00 ka g@ 00 ka 90.0 kj/kg he work put durg the ientropic proce i W kj/kg kj/kg K m( u u) (00 kg)( )kJ/kg, he actual work put i then W a, W η, C 9,740 kj ,60 kj 9,740 kj

81 E R-4a i expanded an adiabatic proce with an ientropic efficiency of he fal volume i to be determed. Aumption Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. Analyi We take the R-4a a the ytem. hi i a cloed ytem ce no ma enter or leave. he energy balance for thi tationary cloed ytem can be expreed a E E 44 Net energy tranfer by heat, work, and ma W ΔEytem 44 Change ternal, ketic, potential, etc.energie ΔU m( u u ) From the R-4a table (able A-E through A-E), 0 pia u 00 F 0 pia x u he actual work put i Btu/lbm 0.6 Btu/lbm R u f fg x f u.40 (0.9897)(8.898) Btu/lbm fg w, η w, η ( u u ) (0.95)( )Btu/lbm 4.8 Btu/lbm a he actual ternal energy at the end of the expanion proce i w ( u u ) u u w, a, a a a he pecific volume at the fal tate i (able A-E) u a 94.0 Btu/lbm ua u f pia x u fg Btu/lbm v v x v 0.08 (0.9988)( ).745 ft /lbm he fal volume i then V m (0 lbm)(.745 ft /lbm).75 ft v f fg 0 pia 0 pia a

82 Steam i expanded an adiabatic turbe with an ientropic efficiency of 0.9. he power put of the turbe i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. Analyi here i only one let and one exit, and thu m & m& m&. We take the actual turbe a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teadyflow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma W& E& a, Rate of change ternal, ketic, potential, etc.energie E& & mh & W& a, m& ( h mh & h From the team table (able A-4 through A-6), Ma 400 C 0 ka h.7 kj/kg x h 6.95 kj/kg K h f fg x f ) (ce Q& Δke Δpe 0) h 89.7 (0.876)(5.) 5.7 kj/kg fg he actual power put may be determed by multiplyg the ientropic power put with the ientropic efficiency. hen, W& a, η W&, η m& ( h h ) (0.9)( kg/)(.7 5.7)kJ/kg 649 kw Ma 400 C Steam turbe η 9% 0 ka

83 Steam i expanded an adiabatic turbe with an ientropic efficiency of he power put of the turbe i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. Analyi here i only one let and one exit, and thu m & m& m&. We take the actual turbe a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teadyflow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma W& E& a, Rate of change ternal, ketic, potential, etc.energie E& & mh & W& a, m& ( h mh & h From the team table (able A-4 through A-6), Ma 400 C 0 ka h.7 kj/kg x h 6.95 kj/kg K h f fg x f ) (ce Q& Δke Δpe 0) h 89.7 (0.876)(5.) 5.7 kj/kg fg he actual power put may be determed by multiplyg the ientropic power put with the ientropic efficiency. hen, W& a, η W&, η m& ( h h ) (0.90)( kg/)(.7 5.7)kJ/kg 6 kw Ma 400 C Steam turbe η 90% 0 ka

84 Argon ga i compreed by an adiabatic compreor. he ientropic efficiency of the compreor i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. 4 Argon i an ideal ga with contant pecific heat. ropertie he pecific heat ratio of argon i k.667 (able A-). Analyi he ientropic exit temperature i Ma 550 C ( k ) / k 0.667/.667 From the ientropic efficiency relation, η C w w a h h a h h 000 ka (00 K) 00 ka c c ( ( a ) ) % 8 00 p p a 75.8 K Argon compreor 00 ka 7 C 7- R-4a i compreed by an adiabatic compreor. he ientropic efficiency of the compreor i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. Analyi From the R-4a table (able A- through A-), 0 C h kj/kg x (at. vap.) 0.99 kj/kg K 600 ka ha 90.8 kj/kg 50 C 600 ka h 65.5 kj/kg 0.99 kj/kg K From the ientropic efficiency relation, η C w h h % w h h a a R-4a compreor 0 C at. vapor 600 ka 50 C

85 Steam enter an adiabatic turbe at a pecified tate, and leave at a pecified tate. he ma flow rate of the team and the ientropic efficiency are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. otential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. Analyi (a) From the team table (able A-4 and A-6), 7 Ma 600 C 50 ka h 50 C h kj/kg kj/kg K a 780. kj/kg here i only one let and one exit, and thu m& m& m&. We take the actual turbe a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma m& ( h V W& E& Rate of change ternal, ketic, potential, etc.energie E& / ) W& a, & a, m& h h m& ( h V V /) V (ce Q& Δpe 0) Subtitutg, the ma flow rate of the team i determed to be (40 m/) 6000 kj/ m& m& 6.95 kg/ (80 m/) kj/kg 000 m / (b) he ientropic exit enthalpy of the team and the power put of the ientropic turbe are and W& W& 50 ka,, m& h h h f f x 0.98 fg x h fg ( h {( V V )/ } ) ( 6.95 kg/) 874 kw ( 0.98)( 04.7) 467. kj/kg (40 m/) (80 m/) hen the ientropic efficiency of the turbe become W& a 6000 kw η % W& 874 kw kj/kg 000 m / H O 6 MW

86 Argon enter an adiabatic turbe at a pecified tate with a pecified ma flow rate, and leave at a pecified preure. he ientropic efficiency of the turbe i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. 4 Argon i an ideal ga with contant pecific heat. ropertie he pecific heat ratio of argon i k.667. he contant preure pecific heat of argon i c p 0.50 kj/kg.k (able A-). Analyi here i only one let and one exit, and thu m& m& m&. We take the ientropic turbe a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teadyflow ytem can be expreed the rate form a W& E& E& mh & W&,, m& ( h mh & h From the ientropic relation, ( ) ) (ce Q& Δke Δpe 0) k / k 0.667/ ka 500 ka ( 07 K) 479 K hen the power put of the ientropic turbe become W & & ( ) ( 80/60 kg/m)( 0.50 kj/kg K)( ) 4 kw, mcp. hen the ientropic efficiency of the turbe i determed from W& a 70 kw η % W& 4. kw Ar η 70 kw

87 E Combution gae enter an adiabatic ga turbe with an ientropic efficiency of 8% at a pecified tate, and leave at a pecified preure. he work put of the turbe i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. 4 Combution gae can be treated a air that i an ideal ga with variable pecific heat. Analyi From the air table and ientropic relation, r 000 R h Btu /lbm r pia r 0 pia h ( 74.0) Btu/lbm AIR η 8% here i only one let and one exit, and thu m& m& m&. We take the actual turbe a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed a W& E& E& mh & W& a, a, m& ( h mh & h ) (ce Q& Δke Δpe 0) Notg that w a η w, the work put of the turbe per unit ma i determed from w a ( 0.8)( ) 7.7 Btu/lbm Btu/lbm

88 [Alo olved by EES on encloed CD] Refrigerant-4a enter an adiabatic compreor with an ientropic efficiency of 0.80 at a pecified tate with a pecified volume flow rate, and leave at a pecified preure. he compreor exit temperature and power put to the compreor are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. Analyi (a) From the refrigerant table (able A-E through A-E), h h 0 ka g at. vapor v v Ma h g@0 ka g@0 ka 8. kj/kg From the ientropic efficiency relation, hu, h η C h h a a a h h h a Ma 9.6 kj/kg a h 6.97 kj/kg kj/kg K 58.9 C 0.6 m /kg (b) he ma flow rate of the refrigerant i determed from &m v V & ( h h )/η 6.97 ( ) 0./60 m / kg/ 0.6 m /kg C / kj/kg here i only one let and one exit, and thu m& m& m&. We take the actual compreor a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma W& a, E& W& a, Rate of change ternal, ketic, potential, etc.energie E& mh & mh & m& ( h & (ce Q& Δke Δpe 0) h ) Subtitutg, the power put to the compreor become, R-4a η C 80% 0. m /m W & a, ( kg/)( ).70 kw kj/kg

89 EES roblem 7-5 i reconidered. he problem i to be olved by coniderg the ketic energy and by aumg an let-to-exit area ratio of.5 for the compreor when the compreor exit pipe ide diameter i cm. Analyi he problem i olved ug EES, and the olution i given below. "Input Data from diagram wdow" {[] 0 "ka" [] 000 "ka" Vol_dot_ 0. "m^/m" Eta_c 0.80 "Compreor adiabatic efficiency" A_ratio.5 d_ /00 "m"} "Sytem: Control volume contag the compreor, ee the diagram wdow. roperty Relation: Ue the real fluid propertie for R4a. roce: Steady-tate, teady-flow, adiabatic proce." Fluid$'R4a' "roperty Data for tate " []temperature(fluid$,[],x)"real fluid equ. at the at. vapor tate" h[]enthalpy(fluid$, [], x)"real fluid equ. at the at. vapor tate" []entropy(fluid$, [], x)"real fluid equ. at the at. vapor tate" v[]volume(fluid$, [], x)"real fluid equ. at the at. vapor tate" "roperty Data for tate " _[][]; _[][] "needed for plot" _[][] "for the ideal, ientropic proce acro the compreor" h_[]enhaly(fluid$, [], _[])"Enthalpy at the ientropic tate and preure []" _[]emperature(fluid$, [], _[])"emperature of ideal tate - needed only for plot." "Steady-tate, teady-flow conervation of ma" m_dot_ m_dot_ m_dot_ Vol_dot_/(v[]*60) Vol_dot_/v[]Vol_dot_/v[] Vel[]Vol_dot_/(A[]*60) A[] pi*(d_)^/4 A_ratio*Vel[]/v[] Vel[]/v[] "Ma flow rate: A*Vel/v, A_ratio A[]/A[]" A_ratioA[]/A[] "Steady-tate, teady-flow conervation of energy, adiabatic compreor, ee diagram wdow" m_dot_*(h[](vel[])^/(*000)) W_dot_c m_dot_*(h[](vel[])^/(*000)) "Defition of the compreor adiabatic efficiency, Eta_cW_ien/W_act" Eta_c (h_[]-h[])/(h[]-h[]) "Knowg h[], the other propertie at tate can be found." v[]volume(fluid$, [], hh[])"v[] i found at the actual tate, knowg and h." []temperature(fluid$, [],hh[])"real fluid equ. for at the known let h and." []entropy(fluid$, [], hh[]) "Real fluid equ. at the known let h and." _exit[] "Neglectg the ketic energie, the work i:" m_dot_*h[] W_dot_c_noke m_dot_*h[]

90 7-90 SOLUION A[] [m^] A[] [m^] A_ratio.5 d_0.0 [m] Eta_c0.8 Fluid$'R4a' h[]7 [kj/kg] h[]9. [kj/kg] h_[]8. [kj/kg] m_dot_ [kg/] m_dot_ [kg/] []0.0 [ka] []000.0 [ka] [] [kj/kg-k] []0.986 [kj/kg-k] _[] [kj/kg-k] _[] [kj/kg-k] []-. [C] []58.94 [C] _exit58.94 [C] _[]-. [C] _[]48.58 [C] Vol_dot_0. [m^ /m] Vol_dot_ [m^ /m] v[]0.6 [m^/kg] v[]0.094 [m^/kg] Vel[]0.6 [m/] Vel[].5 [m/] W_dot_c.704 [kw] W_dot_c_noke.706 [kw] R4a - diagram for real and ideal compreor Ideal Compreor Real Compreor emperature [C] ka -5 0 ka Entropy [kj/kg-k]

91 Air enter an adiabatic compreor with an ientropic efficiency of 84% at a pecified tate, and leave at a pecified temperature. he exit preure of air and the power put to the compreor are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. 4 Air i an ideal ga with variable pecific heat. ropertie he ga contant of air i R 0.87 ka.m /kg.k (able A-) Analyi (a) From the air table (able A-7), 90 K 50 K h 90.6 kj/kg, h a From the ientropic efficiency relation h h η C 90.6 ( h h ) a hen from the ientropic relation, 5.98 kj/kg h r a. η, C h h h ( 0.84)( ) kj/kg r r 7.95 r. r ( 00 ka) 646 ka (b) here i only one let and one exit, and thu m& m& m&. We take the actual compreor a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teadyflow ytem can be expreed a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma W& a, W& E& a, Rate of change ternal, ketic, potential, etc.energie E& mh & mh & m& ( h & (ce Q& Δke Δpe 0) h ) r AIR η C 84%.4 m / where V m& & R (00 ka)(.4 m /).884 kg/ (0.87 ka m /kg K)(90 K) hen the power put to the compreor i determed to be W & a, (.884 kg/)( ) kj/kg 70 kw

92 Air i compreed by an adiabatic compreor from a pecified tate to another pecified tate. he ientropic efficiency of the compreor and the exit temperature of air for the ientropic cae are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. 4 Air i an ideal ga with variable pecific heat. Analyi (a) From the air table (able A-7), 00 K h 00.9 kj / kg, K h kj / kg a From the ientropic relation, r 600 ka 95 ka (.86) h kj/kg r hen the ientropic efficiency become h h η C h h % a (b) If the proce were ientropic, the exit temperature would be h kj / kg K r AIR

93 E Argon enter an adiabatic compreor with an ientropic efficiency of 80% at a pecified tate, and leave at a pecified preure. he exit temperature of argon and the work put to the compreor are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. otential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. 4 Argon i an ideal ga with contant pecific heat. ropertie he pecific heat ratio of argon i k.667. he contant preure pecific heat of argon i c p 0.5 Btu/lbm.R (able A-E). Analyi (a) he ientropic exit temperature i determed from ( ) k / k 0.667/ pia 0 pia ( 550 R) 8.9 R he actual ketic energy change durg thi proce i ( 40 ft/) ( 60 ft/) V V Btu/lbm Δke a.08 Btu/lbm 5,07 ft / he effect of ketic energy on ientropic efficiency i very mall. herefore, we can take the ketic energy change for the actual and ientropic cae to be ame efficiency calculation. From the ientropic efficiency relation, cludg the effect of ketic energy, It yield η C w w a ( h ( h a 59 R a h ) Δke c h ) Δke c p p ( ) ( ) a Δke Δke a ( 550) ( 550). 08 (b) here i only one let and one exit, and thu m& m& m&. We take the actual compreor a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teadyflow ytem can be expreed a W& E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma a, m& ( h V W& E& Rate of change ternal, ketic, potential, etc.energie E& / ) m& ( h a, & V m& h h /) (ce Q& Δpe 0) V V Subtitutg, the work put to the compreor i determed to be w w a, h h Δke ( 0.5 Btu/lbm R)( ) R.08 Btu/lbm.6 Btu/lbm a, Ar η C 80% a.08

94 E Air i accelerated a 90% efficient adiabatic nozzle from low velocity to a pecified velocity. he exit temperature and preure of the air are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. otential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. 4 Air i an ideal ga with variable pecific heat. Analyi From the air table (able A-7E), 480 R h 6.89 Btu / lbm, r here i only one let and one exit, and thu m& m& m&. We take the nozzle a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma m& ( h E& Rate of change ternal, ketic, potential, etc.energie E& & V / ) m& ( h V /) (ce W& Q& Δpe 0) h V h V 0 Subtitutg, the exit temperature of air i determed to be ( 800 ft/) 0 Btu/lbm h 6.89 kj/kg 5. Btu/lbm 5,07 ft / From the air table we read a 4. R From the ientropic efficiency relation h η N h h a h h ( h h )/ η 6.89 ( ) /( 0.90) Btu/lbm h a r N hen the exit preure i determed from the ientropic relation to be AIR η N 90% r r pia r 5.04 r ( 60 ) 5. pia

95 E EES roblem 7-40E i reconidered. he effect of varyg the nozzle ientropic efficiency from 0.8 to.0 on the exit temperature and preure of the air i to be vetigated, and the reult are to be plotted. Analyi he problem i olved ug EES, and the reult are tabulated and plotted below. "Known:" WorkFluid$ 'Air' [] 60 [pia] [] 00 [F] Vel[] 800 [ft/] Vel[] 0 [ft/] eta_nozzle 0.9 "Conervation of Energy - SSSF energy balance for turbe -- neglectg the change potential energy, no heat tranfer:" h[]enthalpy(workfluid$,[]) []entropy(workfluid$,[],[]) _[] [] [] [] _[] [] h_[]enthalpy(workfluid$,_[]) _[]temperature(workfluid$,[],_[]) eta_nozzle ke[]/ke_[] ke[] Vel[]^/ ke[]vel[]^/ h[]ke[]*convert(ft^/^,btu/lbm) h[] ke[]*convert(ft^/^,btu/lbm) h[] ke[]*convert(ft^/^,btu/lbm) h_[] ke_[]*convert(ft^/^,btu/lbm) []temperature(workfluid$,hh[]) anwer [] anwer [] η nozzle [pia [F, [F] [] 960 [] η nozzle

96 Air i expanded an adiabatic nozzle with an ientropic efficiency of he air velocity at the exit i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. here i no heat tranfer or haft work aociated with the proce. Air i an ideal ga with contant pecific heat. ropertie he propertie of air at room temperature are c p.005 kj/kg K and k.4 (able A-a). Analyi For the ientropic proce of an ideal ga, the exit temperature i determed from ( k ) / k 0.4 /.4 00 ka (80 7 K) 00 ka.0 K here i only one let and one exit, and thu m & m& m&. We take nozzle a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma V m& h E& V h h h c ( p Rate of change ternal, ketic, potential, etc. energie E& h V V ) m& h & V V V V Δke he ketic energy change for the ientropic cae i Δke c ( p ) (.005 kj/kg K)(45 )K he ketic energy change for the actual proce i Δke Δke (0.96)(.6 kj/kg) 7.7 kj/kg a η N 00 ka 80 C 0 m/.6 kj/kg Subtitutg to the energy balance and olvg for the exit velocity give Air 00 ka V Δke ) ( a m / (7.7 kj/kg) kj/kg m/

97 E Air i decelerated an adiabatic diffuer with an ientropic efficiency of 0.8. he air velocity at the exit i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. here i no heat tranfer or haft work aociated with the proce. Air i an ideal ga with contant pecific heat. ropertie he propertie of air at room temperature are c p 0.40 Btu/lbm R and k.4 (able A-Ea). Analyi For the ientropic proce of an ideal ga, the exit temperature i determed from ( k ) / k 0.4 /.4 0 pia (0 460 R) pia 554. R here i only one let and one exit, and thu m & m& m&. We take nozzle a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma V m& h E& V h h h c ( p Rate of change ternal, ketic, potential, etc. energie E& h V V ) m& h & V V V V Δke he ketic energy change for the ientropic cae i Δke c ( ) (0.40 Btu/lbm R)( )R p he ketic energy change for the actual proce i Δke Δke (0.8)(5.4 Btu/lbm).6 Btu/lbm a η N pia 0 F 000 ft/ Subtitutg to the energy balance and olvg for the exit velocity give 5.4 Btu/lbm Air 0 pia V ( V Δke a ) 0.5 (000 ft/) 5,07 ft / (.6 Btu/lbm) Btu/lbm ft/

98 7-98 Entropy Balance 7-44 Heat i lot from Refrigerant-4a a it i throttled. he exit temperature of the refrigerant and the entropy eration are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy change are negligible. Analyi he propertie of the refrigerant at the let of the device are (able A-) 900 ka h 5 C kj/kg 0.75 kj/kg he enthalpy of the refrigerant at the exit of the device i h h q kj/kg R-4a 900 ka 5 C Now, the propertie at the exit tate may be obtaed from the R-4a table 00 ka 00 ka h kj/kg 0.09 C kj/kg.k he entropy eration aociated with thi proce may be obtaed by addg the entropy change of R- 4a a it flow the device and the entropy change of the urroundg. ΔR -4a kj/kg.k Δ q 0.8 kj/kg (5 7) K urr urr kj/kg.k Δ Δ Δ kj/kg.k total R 4a urr

99 Liquid water i withdrawn from a rigid tank that itially conta aturated water mixture until no liquid i left the tank. he quality of team the tank at the itial tate, the amount of ma that ha ecaped, and the entropy eration durg thi proce are to be determed. Aumption Ketic and potential energy change are zero. here are no work teraction. Analyi (a) he propertie of the team the tank at the fal tate and the propertie of exitg team are (able A-4 through A-6) u 55. kj/kg 400 ka v m /kg x (at. vap.) kj/kg.k e 400 ka he xe 0 (at. liq.) e kj/kg.7765 kj/kg.k he relation for the volume of the tank and the fal ma the tank are V m v (7.5 kg) v m V (7.5 kg) v 6.9v v m /kg he ma, energy, and entropy balance may be written a m e Q Q Subtitutg, m m m h ource e e m e m u e S m u m m m v () e 5 ( v v u () )(604.66) 6.9 (55.) ( v )(.7765) S 6.9v (6.8955) 7. 5 () Eq. () may be olved by a trial-error approach by tryg different qualitie at the let tate. Or, we can ue EES to olve the equation to fd x Other propertie at the itial tate are u 9. kj/kg 400 ka v m /kg x kj/kg.k Subtitutg to Eq () and (), (b) (c) m e ( ) kg [ ( ) ] (.7765) S 6.9( )(6.8955) 7.5(6.9) S kj/k Water mixture 7.5 kg 400 ka Q

100 Each member of a family of four take a 5-m hower every day. he amount of entropy erated by thi family per year i to be determed. Aumption Steady operatg condition exit. he ketic and potential energie are negligible. Heat loe from the pipe and the mixg ection are negligible and thu Q & 0. 4 Shower operate at maximum flow condition durg the entire hower. 5 Each member of the houehold take a 5-m hower every day. 6 Water i an compreible ubtance with contant propertie at room temperature. 7 he efficiency of the electric water heater i 00%. ropertie he denity and pecific heat of water at room temperature are ρ kg/l 000 kg/ and c 4.8 kj/kg. C (able A-). Analyi he ma flow rate of water at the hower head i m& ρv & ( kg/l)( L/m) kg/m he ma balance for the mixg chamber can be expreed the rate form a m& m& m& Δm& m& 0 (teady) ytem 0 m& m& m& where the ubcript denote the cold water tream, the hot water tream, and the mixture. he rate of entropy eration durg thi proce can be determed by applyg the rate form of the entropy balance on a ytem that clude the electric water heater and the mixg chamber (the - elbow). Notg that there i no entropy tranfer aociated with work tranfer (electricity) and there i no heat tranfer, the entropy balance for thi teady-flow ytem can be expreed a S S & 44 & Rate of net entropy tranfer by heat and ma S& { Rate of entropy eration m& m& m& S& S& 0 (teady) S& Δ ytem Rate of change of entropy (ce Q 0 and work i entropy free) m& m& m& Notg from ma balance that m& m& m& and ce hot water enter the ytem at the ame temperature a the cold water, the rate of entropy eration i determed to be S& m& ( m& m& ) m& ( ) m& c ln 4 7 ( kg/m)(4.8 kj/kg.k)ln kj/m.k 5 7 Notg that 4 people take a 5-m hower every day, the amount of entropy erated per year i S ( S& ) Δt(No. of (4.495 kj/m.k)(5 m/peron day)(4 peron)(65 day/year),84 kj/k people)(no. of (per year) day) p Cold water Mixture Hot water Dicuion he value above repreent the entropy erated with the water heater and the -elbow the abence of any heat loe. It doe not clude the entropy erated a the hower water at 4 C i dicarded or cooled to the door temperature. Alo, an entropy balance on the mixg chamber alone (hot water enterg at 55 C tead of 5 C) will exclude the entropy erated with the water heater.

101 Steam i condened by coolg water the condener of a power plant. he rate of condenation of team and the rate of entropy eration are to be determed. Aumption Steady operatg condition exit. he heat exchanger i well-ulated o that heat lo to the urroundg i negligible and thu heat tranfer from the hot fluid i equal to the heat tranfer to the cold fluid. Change the ketic and potential energie of fluid tream are negligible. 4 Fluid propertie are contant. ropertie he enthalpy and entropy of vaporization of water at 60 C are h fg 57.7 kj/kg and fg kj/kg.k (able A-4). he pecific heat of water at room temperature i c p 4.8 kj/kg. C (able A-). Analyi (a) We take the cold water tube a the ytem, which i a control volume. he energy balance for thi teady-flow ytem can be expreed the rate form a E E & 44 & Rate of net energy tranfer by heat, work, and ma Q& E& mh & Q& Rate of change ternal, ketic, potential, etc.energie E& mh & mc & ( 0 (teady) ΔEytem & p (ce Δke Δpe 0) ) 0 hen the heat tranfer rate to the coolg water the condener become Q& [ mc & p( )] coolg water (75 kg/)(4.8 kj/kg. C)(7 C 8 C) 8 kj/ Steam 60 C 60 C 7 C 8 C Water he rate of condenation of team i determed to be Q& ( mh & fg ) team m& team Q& h fg 8 kj/ 57.7 kj/kg.0 kg/ (b) he rate of entropy eration with the condener durg thi proce can be determed by applyg the rate form of the entropy balance on the entire condener. Notg that the condener i well-ulated and thu heat tranfer i negligible, the entropy balance for thi teady-flow ytem can be expreed a m& water m& S S & 44 & Rate of net entropy tranfer by heat and ma team m& water m& 4 4 team 4 S& { Rate of entropy eration m& m& m& m& S& S& S& 0 (teady) ΔS& ytem m& Rate of change of entropy (ce Q 0) water ( ) m& team ( 4 ) Notg that water i an compreible ubtance and team change from aturated vapor to aturated liquid, the rate of entropy eration i determed to be S & m& water cp ln m& team ( f g ) m& water cp ln m& team 7 7 (75 kg/)(4.8 kj/kg.k)ln (.0 kg/)( kj/kg.k) kw/k fg

102 Cold water i heated by hot water a heat exchanger. he rate of heat tranfer and the rate of entropy eration with the heat exchanger are to be determed. Aumption Steady operatg condition exit. he heat exchanger i well-ulated o that heat lo to the urroundg i negligible and thu heat tranfer from the hot fluid i equal to the heat tranfer to the cold fluid. Change the ketic and potential energie of fluid tream are negligible. 4 Fluid propertie are contant. ropertie he pecific heat of cold and hot water are given to be 4.8 and 4.9 kj/kg. C, repectively. Analyi We take the cold water tube a the ytem, which i a control volume. he energy balance for thi teady-flow ytem can be expreed the rate form a E E & 44 & Rate of net energy tranfer by heat, work, and ma Q& E& mh & Q& Rate of change ternal, ketic, potential, etc.energie E& mh & mc & ( 0 (teady) ΔEytem & p (ce Δke Δpe 0) ) 0 hen the rate of heat tranfer to the cold water thi heat exchanger become Q& [ mc & ( )] cold water (0.5 kg/)(4.8 kj/kg. C)(45 C 5 C).5 kw p Notg that heat ga by the cold water i equal to the heat lo by the hot water, the let temperature of the hot water i determed to be Q& Q& [ mc & p( )] hot water mc &.5 kw 00 C 97.5 C ( kg/)(4.9 kj/kg. C) p (b) he rate of entropy eration with the heat exchanger i determed by applyg the rate form of the entropy balance on the entire heat exchanger: m& cold S S & 44 & Rate of net entropy tranfer by heat and ma m& hot m& cold m& 4 hot S& { Rate of entropy eration m& m& m& m& S& S& 4 S& 0 (teady) ΔS& ytem m& Rate of change of entropy (ce Q 0) cold ( ) m& hot ( 4 ) Notg that both fluid tream are liquid (compreible ubtance), the rate of entropy eration i determed to be S& m& cold cp ln m& hot 4 cp ln Hot water 00 C kg/ 45 C (0.5 kg/)(4.8 kj/kg.k)ln ( kg/)(4.9 kj/kg.k)ln kw/k Cold water 5 C 0.5 kg/

103 Air i preheated by hot exhaut gae a cro-flow heat exchanger. he rate of heat tranfer, the let temperature of the air, and the rate of entropy eration are to be determed. Aumption Steady operatg condition exit. he heat exchanger i well-ulated o that heat lo to the urroundg i negligible and thu heat tranfer from the hot fluid i equal to the heat tranfer to the cold fluid. Change the ketic and potential energie of fluid tream are negligible. 4 Fluid propertie are contant. ropertie he pecific heat of air and combution gae are given to be.005 and.0 kj/kg. C, repectively. he ga contant of air i R 0.87 kj/kg.k (able A-). Analyi We take the exhaut pipe a the ytem, which i a control volume. he energy balance for thi teadyflow ytem can be expreed the rate form a E E & 44 & Rate of net energy tranfer by heat, work, and ma E& mh & Q& Rate of change ternal, ketic, potential, etc.energie E& Q& mh & mc & ( 0 (teady) ΔEytem & p ) 0 (ce Δke Δpe 0) hen the rate of heat tranfer from the exhaut gae become Q& [ mc & p( )] ga. he ma flow rate of air i (. kg/)(.kj/kg. C)(80 C 95 C) 05.7 kw V (95 ka)(.6 m /) m& &.808 kg/ R (0.87 ka.m /kg.k) (9 K) Notg that heat lo by the exhaut gae i equal to the heat ga by the air, the let temperature of the air become Q& Q 05.7 kw [ mc & )] 0 C. C p( air & mc & p (.808 kg/)(.005 kj/kg. C) he rate of entropy eration with the heat exchanger i determed by applyg the rate form of the entropy balance on the entire heat exchanger: m& exhaut S S & 44 & Rate of net entropy tranfer by heat and ma m& air m& exhaut m& 4 air S& { Rate of entropy eration m& m& m& m& S& S& hen the rate of entropy eration i determed to be S& m& exhaut cp ln m& air 4 cp ln 4 S& 0 (teady) ΔS& ytem m& Rate of change of entropy (ce Q 0) exhaut Air 95 ka 0 C.6 m / ( ) m& air ( 4 ) (. kg/)(.kj/kg.k)ln (.808 kg/)(.005 kj/kg.k)ln kw/k Exhaut gae. kg/, 95 C

104 Water i heated by hot oil a heat exchanger. he let temperature of the oil and the rate of entropy eration with the heat exchanger are to be determed. Aumption Steady operatg condition exit. he heat exchanger i well-ulated o that heat lo to the urroundg i negligible and thu heat tranfer from the hot fluid i equal to the heat tranfer to the cold fluid. Change the ketic and potential energie of fluid tream are negligible. 4 Fluid propertie are contant. ropertie he pecific heat of water and oil are given to be 4.8 and. kj/kg. C, repectively. Analyi (a) We take the cold water tube a the ytem, which i a control volume. he energy balance for thi teady-flow ytem can be expreed the rate form a E E & 44 & Rate of net energy tranfer by heat, work, and ma Q& E& mh & Q& Rate of change ternal, ketic, potential, etc.energie E& mh & mc & ( 0 (teady) ΔEytem & p (ce Δke Δpe 0) ) 0 hen the rate of heat tranfer to the cold water thi heat exchanger become Q& [ mc & ( )] water p (4.5 kg/)(4.8 kj/kg. C)(70 C 0 C) kw. Notg that heat ga by the water i equal to the heat lo by the oil, the let temperature of the hot oil i determed from Q& [ mc & ( )] oil p Q& mc & p 70 C kw (0 kg/)(. kj/kg. 9. C C) (b) he rate of entropy eration with the heat exchanger i determed by applyg the rate form of the entropy balance on the entire heat exchanger: m& water S S & 44 & Rate of net entropy tranfer by heat and ma m& oil m& water m& 4 oil 4 S& { Rate of entropy eration m& m& m& m& S& S& S& 0 (teady) ΔS& ytem m& Rate of change of entropy (ce Q 0) water ( ) m& oil ( 4 ) Notg that both fluid tream are liquid (compreible ubtance), the rate of entropy eration i determed to be S& m& water cp ln m& oil 4 cp ln 70 C Water 0 C 4.5 kg/ (4.5 kg/)(4.8 kj/kg.k)ln (0 kg/)(. kj/kg.k)ln kw/k Oil 70 C 0 kg/

105 E Refrigerant-4a i expanded adiabatically from a pecified tate to another. he entropy eration i to be determed. Aumption Steady operatg condition exit. Ketic and potential energy change are negligible. Analyi he rate of entropy eration with the expanion device durg thi proce can be determed by applyg the rate form of the entropy balance on the ytem. Notg that the ytem i adiabatic and thu there i no heat tranfer, the entropy balance for thi teady-flow ytem can be expreed a S S & 44 & Rate of net entropy tranfer by heat and ma m& m& S& { Rate of entropy eration S& S& 0 (teady) ΔS& ytem m& ( Rate of change of entropy ) R-4a 00 pia 00 F he propertie of the refrigerant at the let and exit tate are (able A-E through A-E) 0 pia at. vapor 00 pia 00 F Btu/lbm R Subtitutg, 0 pia x Btu/lbm R Btu/lbm R

106 In an ice-makg plant, water i frozen by evaporatg aturated R-4a liquid. he rate of entropy eration i to be determed. Aumption Steady operatg condition exit. Ketic and potential energy change are negligible. Analyi We take the control volume formed by the R-4a evaporator with a gle let and gle exit a the ytem. he rate of entropy eration with thi evaporator durg thi proce can be determed by applyg the rate form of the entropy balance on the ytem. he entropy balance for thi teady-flow ytem can be expreed a S S & 44 & Rate of net entropy tranfer by heat and ma m& m& Q& w S& { Rate of entropy eration S& S& S& 0 (teady) S& Δ ytem Rate of change of entropy Q& m& R ( ) w Q& m& R fg he propertie of the refrigerant are (able A-) h 0 C 0 C kj/kg kj/kg K w he rate of that mut be removed from the water order to freeze it at a rate of 4000 kg/h i Q & m& w h if (4000 / 600 kg/)(.7 kj/kg) 70.8 kw where the heat of fuion of water at atm i.7 kj/kg. he ma flow rate of R-4a i m& R Q& h fg 70.8 kj/ kj/kg.800 kg/ R-4a 0 C Q 0 C at. vapor Subtitutg, S& m& R fg Q& w 70.8 kw (.800 kg/)(0.786 kj/kg K) kw/k 7 K

107 Air i heated by team a heat exchanger. he rate of entropy eration aociated with thi proce i to be determed. Aumption Steady operatg condition exit. he heat exchanger i well-ulated o that heat lo to the urroundg i negligible and thu heat tranfer from the hot fluid i equal to the heat tranfer to the cold fluid. Change the ketic and potential energie of fluid tream are negligible. 4 Air i an ideal ga with contant pecific heat. ropertie he pecific heat of air at room temperature i c p.005 kj/kg C (able A-). Analyi he rate of entropy eration with the heat exchanger i determed by applyg the rate form of the entropy balance on the entire heat exchanger: m& water m& S S & 44 & Rate of net entropy tranfer by heat and ma air m& water m& air S& { Rate of entropy eration 4 S& S& 0 (teady) ΔS& ytem m& he propertie of the team at the let and exit tate are Rate of change of entropy water ( C Steam 5 C at. vap. 0,000 kg/h ) m& air ( 4 Air 0 C 0 C ) 5 C x h kj/kg 8.57 kj/kg K (able A-4) x C 0 h 4.0 kj/kg (able A-4) kj/kg K From an energy balance, the heat given up by team i equal to the heat picked up by the air. hen, Q & m& water ( h h ) (0,000 / 600 kg/)( ) kj/kg 675 kw m& Q& 675 kw ( ) (.005 kj/kg C)(0 0) C air c p 4 Subtitutg to the entropy balance relation, S& m& m& water water ( ( (0,000 / kw/k ) m& ) m& air air ( c p 4 ) ln 600 kg/)( ) kj/kg kg/ K (67.7 kg/)(.005 kj/kg K)ln 0 K 9 K Note that the preure of air rema unchanged a it flow the heat exchanger. hi i why the preure term i not cluded the entropy change expreion of air.

108 Oxy i cooled a it flow an ulated pipe. he rate of entropy eration the pipe i to be determed. Aumption Steady operatg condition exit. he pipe i well-ulated o that heat lo to the urroundg i negligible. Change the ketic and potential energie are negligible. 4 Oxy i an ideal ga with contant pecific heat. ropertie he propertie of oxy at room temperature are R kj/kg K, c p 0.98 kj/kg K (able A-a). Analyi he rate of entropy eration the pipe i determed by applyg the rate form of the entropy balance on the pipe: S S & 44 & Rate of net entropy tranfer by heat and ma m& m& S& { Rate of entropy eration S& S& 0 (teady) ΔS& ytem m& ( Rate of change of entropy (ce Q 0) he pecific volume of oxy at the let and the ma flow rate are v R ( ka m /kg K)(9 K) 0.7 m 40 ka ) Oxy 40 ka 0 C 70 m/ /kg 00 ka 8 C m& A V v π D V 4v π (0. m) (70 m/).496 kg/ 4(0.7 m /kg) Subtitutg to the entropy balance relation, S& m& ( m& c ) p ln R ln (.496 kg/) (0.98 kj/kg K)ln 0.05 kw/k 9K 9 K 00 ka (0.598 kj/kg K)ln 40 ka

109 Nitro i compreed by an adiabatic compreor. he entropy eration for thi proce i to be determed. Aumption Steady operatg condition exit. he compreor i well-ulated o that heat lo to the urroundg i negligible. Change the ketic and potential energie are negligible. 4 Nitro i an ideal ga with contant pecific heat. ropertie he pecific heat of nitro at the average temperature of (77)/ C 95 K i c p.044 kj/kg K (able A-b). Analyi he rate of entropy eration the pipe i determed by applyg the rate form of the entropy balance on the compreor: S S & 44 & Rate of net entropy tranfer by heat and ma m& m& S& { Rate of entropy eration S& S& 0 (teady) ΔS& ytem m& ( Rate of change of entropy (ce Q 0) ) Compreor 600 ka 7 C Subtitutg per unit ma of the oxy, c p ln R ln (7 7) K 600 ka (.044 kj/kg K)ln (0.968 kj/kg K)ln (7 7) K 00 ka kj/kg K Air 00 ka 7 C

110 E Steam i condened by coolg water a condener. he rate of heat tranfer and the rate of entropy eration with the heat exchanger are to be determed. Aumption Steady operatg condition exit. he heat exchanger i well-ulated o that heat lo to the urroundg i negligible and thu heat tranfer from the hot fluid i equal to the heat tranfer to the cold fluid. Change the ketic and potential energie of fluid tream are negligible. 4 Fluid propertie are contant. ropertie he pecific heat of water i.0 Btu/lbm. F (able A-E). he enthalpy and entropy of vaporization of water at 0 F are 05. Btu/lbm and fg.7686 Btu/lbm.R (able A-4E). Analyi We take the tube-ide of the heat exchanger where cold water i flowg a the ytem, which i a control volume. he energy balance for thi teady-flow ytem can be expreed the rate form a E E & 44 & Rate of net energy tranfer by heat, work, and ma Q& E& mh & Q& Rate of change ternal, ketic, potential, etc.energie E& mh & mc & ( 0 (teady) ΔEytem & p (ce Δke Δpe 0) ) 0 Steam 0 F 0 7 F 60 F Water hen the rate of heat tranfer to the cold water thi heat exchanger become Q& [ mc & p( )] water (9 lbm/)(.0 Btu/lbm. F)(7 F 60 F) 96 Btu/ Notg that heat ga by the water i equal to the heat lo by the condeng team, the rate of condenation of the team the heat exchanger i determed from Q& Q& ( mh & fg ) m& team h 96 Btu/ 05. Btu/lbm team fg.67 lbm/ (b) he rate of entropy eration with the heat exchanger i determed by applyg the rate form of the entropy balance on the entire heat exchanger: m& water m& S S & 44 & Rate of net entropy tranfer by heat and ma team m& water m& 4 4 team 4 S& { Rate of entropy eration m& m& m& m& S& S& S& 0 (teady) ΔS& ytem m& Rate of change of entropy (ce Q 0) water ( ) m& team ( 4 ) Notg that water i an compreible ubtance and team change from aturated vapor to aturated liquid, the rate of entropy eration i determed to be S & m& water cp ln m& team ( f g ) m& water cp ln m& team (9 lbm/)(.0 Btu/lbm.R) ln (.67 lbm/)(7686 Btu/lbm.R) Btu/.R fg

111 A reerator i conidered to ave heat durg the coolg of milk a dairy plant. he amount of fuel and money uch a erator will ave per year and the annual reduction the rate of entropy eration are to be determed. Aumption Steady operatg condition exit. he propertie of the milk are contant. Hot milk ropertie he average denity and pecific heat of 7 C milk can be taken to be ρ milk kg/l and ρ water c p, milk.79 kj/kg. C (able A-). Analyi he ma flow rate of the milk i m& ρv & milk milk ( kg/l)( L/) kg/ 4,00 kg/h akg the pateurizg ection a the ytem, the energy balance for thi teady-flow ytem can be expreed the rate form a 0 (teady) E E ΔEytem 0 & 44 & & Rate of net energy tranfer by heat, work, and ma Q& mh & Q& Rate of change ternal, ketic, potential, etc. energie mh & m& milk (ce Δke Δpe 0) c ( p ) herefore, to heat the milk from 4 to 7 C a beg done currently, heat mut be tranferred to the milk at a rate of Q & mc & ( )] ( kg/)(.79 kj/kg. C)(7 4) C 09 kj/ E& E& current [ p paturization refrigeration milk he propoed reerator ha an effectivene of ε 0.8, and thu it will ave 8 percent of thi energy. herefore, Q & & aved εqcurrent ( 0. 8 )( 09 kj / ) 56 kj / Notg that the boiler ha an efficiency of η boiler 0.8, the energy avg above correpond to fuel avg of (56 kj / ) Fuel Saved &Q aved (therm) 0.09therm / η (0.8) (05,500 kj) boiler Notg that year h and unit cot of natural ga i $0.5/therm, the annual fuel and money avg will be Fuel Saved (0.09 therm/)( ) 94,450 therm/yr Money aved (Fuel aved)(unit cot of fuel) (94,450 therm/yr)($.04/therm) $96,400/yr he rate of entropy eration durg thi proce i determed by applyg the rate form of the entropy balance on an extended ytem that clude the reerator and the immediate urroundg o that the boundary temperature i the urroundg temperature, which we take to be the cold water temperature of 8 C.: 0 (teady) S S S& S& ytem S& S& S& & 44 & Δ { Rate of net entropy tranfer by heat and ma Rate of entropy eration Rate of change of entropy Diregardg entropy tranfer aociated with fuel flow, the only ignificant difference between the two cae i the reduction i the entropy tranfer to water due to the reduction heat tranfer to water, and i determed to be Q&,reduction Q& aved 56 kj/ S&, reduction S&, reduction 8.75 kw/k 8 7 S, reduction urr S& Δt (8.75 kj/.k)( /year).75 0, reduction urr Q & 8 4 C Cold milk kj/k (per year)

112 Stale teel ball bearg leavg the oven at a uniform temperature of 900 C at a rate of 400 /m are expoed to air and are cooled to 850 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 entropy eration 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 ropertie he denity and pecific heat of the ball bearg are given to be ρ 8085 kg/m and c p kj/kg. C. Analyi (a) We take a gle bearg ball a the ytem. he energy balance for thi cloed ytem can be expreed a E E 44 Net energy tranfer by heat, work, and ma Q Q Change ternal, ketic, potential, etc. energie ΔU ball mc( ΔEytem 44 m( u ) u ) he total amount of heat tranfer from a ball i πd π (0.0 m) m ρv ρ (8085 kg/m ) kg 6 6 Q mc( ) ( kg)(0.480 kj/kg. C)( ) C kj/ball hen the rate of heat tranfer from the ball to the air become Q & total n& Q (400 ball/m) (0.756 kj/ball) ball (per ball) herefore, heat i lot to the air at a rate of 4.0 kw kj/m 4.0 kw (b) We aga take a gle bearg ball a the ytem. he entropy erated durg thi proce can be determed by applyg an entropy balance on an extended ytem that clude the ball and it immediate urroundg o that the boundary temperature of the extended ytem i at 0 C at all time: where ΔS S S 44 Net entropy tranfer by heat and ma ytem Subtitutg, m( Q b S { Entropy eration S ) mc avg ΔSytem 44 Change entropy ΔS ln ytem S Q b ΔS ytem ( kg)(0.480 kj/kg.k)ln kj/k Q kj S ΔSytem kj/k kj/k 0 K b hen the rate of entropy eration become S & S n& ball Furnace Steel ball, 900 C (per ball) ( kj/k ball)(400 ball/m) kj/m.k kw/k

113 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 entropy eration aociated with thi heat tranfer proce are to be determed. Aumption he egg i pherical hape with a radiu of r 0.75 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. ropertie he denity and pecific heat of the egg are given to be ρ 00 kg/m and c p. kj/kg. C. Analyi We take the egg a the ytem. hi i a cloe ytem ce no ma enter or leave the egg. he energy balance for thi cloed ytem can be expreed a E E 44 Net energy tranfer by heat, work, and ma Q Change ternal, ketic, potential, etc. energie ΔU egg ΔEytem 44 m( u u) mc( ) Boilg Water hen the ma of the egg and the amount of heat tranfer become πd π (0.055 m) m ρv ρ (00 kg/m ) kg 6 6 Q mc ( ) ( kg)(. kj/kg. C)(70 8) C 8. p kj Egg 8 C We aga take a gle egg a the ytem he entropy erated durg thi proce can be determed by applyg an entropy balance on an extended ytem that clude the egg and it immediate urroundg o that the boundary temperature of the extended ytem i at 97 C at all time: S S 44 Net entropy tranfer by heat and ma Q b S { Entropy eration S ΔSytem 44 Change entropy ΔS ytem S Q b ΔS ytem where Subtitutg, 70 7 ΔSytem m( ) mcavg ln ( kg)(. kj/kg.k) ln kj/k 8 7 S Q ΔS b ytem 8. kj kj/k kj/k (per egg) 70 K

114 Long cyldrical teel rod are heat-treated an oven. he rate of heat tranfer to the rod the oven and the rate of entropy eration aociated with thi heat tranfer proce are to be determed. Aumption he thermal propertie of the rod are contant. he change ketic and potential energie are negligible. ropertie he denity and pecific heat of the teel rod are given to be ρ 78 kg/m and c p kj/kg. C. Analyi (a) Notg that the rod enter the oven at a velocity of m/m and exit at the ame velocity, we can ay that a -m long ection of the rod i heated the oven m. hen the ma of the rod heated mute i m ρv ρla ρl( πd / 4) (78 kg/m )( m)[ π (0. m) / 4] 84.6 kg We take the -m ection of the rod the oven a the ytem. he energy balance for thi cloed ytem can be expreed a Subtitutg, E E 44 Net energy tranfer by heat, work, and ma Q Change ternal, ketic, potential, etc. energie ΔU rod ΔEytem 44 m( u u) mc( ) Q mc( ) (84.6 kg)(0.465 kj/kg. C)(700 0) C 57,5 kj Notg that thi much heat i tranferred m, the rate of heat tranfer to the rod become Q & Q / Δt (57,5 kj)/(m) 57,5 kj/m kw (b) We aga take the -m long ection of the rod a the ytem. he entropy erated durg thi proce can be determed by applyg an entropy balance on an extended ytem that clude the rod and it immediate urroundg o that the boundary temperature of the extended ytem i at 900 C at all time: where S Subtitutg, S 44 Net entropy tranfer by heat and ma Q b S { Entropy eration S ΔSytem 44 Change entropy ΔS ytem S Q b ΔS ytem ΔSytem m( ) mcavg ln (84.6 kg)(0.465 kj/kg.k)ln 00.kJ/K 0 7 Q 57,5 kj S ΔSytem 00. kj/k 5. kj/k K b Notg that thi much entropy i erated m, the rate of entropy eration become S & S 5. kj/k m Δt 5. kj/m.k 0.85 kw/k Oven, 900 C Steel rod, 0 C

115 he ner and er urface of a brick wall are mataed at pecified temperature. he rate of entropy eration with the wall i to be determed. Aumption Steady operatg condition exit ce the urface temperature of the wall rema contant at the pecified value. Analyi We take the wall to be the ytem, which i a cloed ytem. Under teady condition, the rate form of the entropy balance for the wall implifie to S S & 44 & Rate of net entropy tranfer by heat and ma Q& b, Q& b, S& { Rate of entropy eration S& 890 W 890 W S& 9 K 78 K S&,wall,wall,wall 0 ΔS& ytem Rate of change of entropy 0.48 W/K herefore, the rate of entropy eration the wall i 0.48 W/K. Brick Wall 0 cm 0 C 5 C 7-6 A peron i tandg a room at a pecified temperature. he rate of entropy tranfer from the body with heat i to be determed. Aumption Steady operatg condition exit. Analyi Notg that Q/ repreent entropy tranfer with heat, the rate of entropy tranfer from the body of the peron accompanyg heat tranfer i S& tranfer Q& 6 W.094 W/K 07 K Q & 4 C

116 A 000-W iron i left on the iron board with it bae expoed to the air at 0 C. he rate of entropy eration i to be determed teady operation. Aumption Steady operatg condition exit. Analyi We take the iron to be the ytem, which i a cloed ytem. Coniderg that the iron experience no change it propertie teady operation, cludg it entropy, the rate form of the entropy balance for the iron implifie to S S & 44 & Rate of net entropy tranfer by heat and ma Q& b, S& { Rate of entropy eration S&,iron 0 ΔS& ytem 0 44 Rate of change of entropy 0 Iron 000 W herefore, S&,iron Q& b, 000 W 67 K.486 W/K he rate of total entropy eration durg thi proce i determed by applyg the entropy balance on an extended ytem that clude the iron and it immediate urroundg o that the boundary temperature of the extended ytem i at 0 C at all time. It give S&,total Q& b, Q& urr 000 W 9 K.4 W/K Dicuion Note that only ab one-third of the entropy eration occur with the iron. he ret occur the air urroundg the iron a the temperature drop from 400 C to 0 C with ervg any ueful purpoe.

117 E A cylder conta aturated liquid water at a pecified preure. Heat i tranferred to liquid from a ource and ome liquid evaporate. he total entropy eration durg thi proce i to be determed. Aumption No heat lo occur from the water to the urroundg durg the proce. he preure ide the cylder and thu the water temperature rema contant durg the proce. No irreveribilitie occur with the cylder durg the proce. Analyi he preure of the team i mataed contant. herefore, the temperature of the team rema contant alo at 40.0 F 700 R (able A-5E) pia akg the content of the cylder a the ytem and notg that the temperature of water rema contant, the entropy change of the ytem durg thi iothermal, ternally reverible proce become ΔS Q 400 Btu 700 R y, ytem y 0.57 Btu/R H O 5 pia 400Btu Source 900 F Similarly, the entropy change of the heat ource i determed from ΔS ource Q ource, ource 400 Btu 0.94 Btu/R R Now conider a combed ytem that clude the cylder and the ource. Notg that no heat or ma croe the boundarie of thi combed ytem, the entropy balance for it can be expreed a S S 44 Net entropy tranfer by heat and ma S { Entropy eration,total ΔSytem 44 Change entropy 0 S ΔS ΔS water ource herefore, the total entropy erated durg thi proce i S, total ΔS ΔS Btu/R water ource Dicuion he entropy eration thi cae i entirely due to the irreverible heat tranfer through a fite temperature difference. We could alo determe the total entropy eration by writg an energy balance on an extended ytem that clude the ytem and it immediate urroundg o that part of the boundary of the extended ytem, where heat tranfer occur, i at the ource temperature.

118 E Steam i decelerated a diffuer from a velocity of 900 ft/ to 00 ft/. he ma flow rate of team and the rate of entropy eration are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. otential energy change are negligible. here are no work teraction. ropertie he propertie of team at the let and the exit of the diffuer are (able A-4E through A-6E) 0 pia h 6. Btu/lbm 40 F.7406 Btu/lbm R h 60.5 Btu/lbm 40 F.74 Btu/lbm R at. vapor v 6.6 ft /lbm Analyi (a) he ma flow rate of the team can be determed from it defition to be m& AV ft/ v 6.6 ft /lbm ( ft )( 00 ) 6.9 lbm/ (b) We take diffuer a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma m& ( h V E& / ) Q& Q& Rate of change ternal, ketic, potential, etc.energie E& & m& ( h V m& h h /) V (ce W& Δpe 0) V Subtitutg, the rate of heat lo from the diffuer i determed to be Q & ( 6.9 lbm/) ( 00 ft/) ( 900 ft/) Btu/lbm 5,07 ft / 08.4 Btu/ he rate of total entropy eration durg thi proce i determed by applyg the entropy balance on an extended ytem that clude the diffuer and it immediate urroundg o that the boundary temperature of the extended ytem i 77 F at all time. It give S S & 44 & Rate of net entropy tranfer by heat and ma m & m & Q& b,urr S& { Rate of entropy eration S& 0 ΔS& ytem 0 44 Rate of change of entropy 0 Subtitutg, the total rate of entropy eration durg thi proce become S& m& 08.4 Btu/ 57 R ( ) ( 6.9 lbm/)( ) Btu/lbm R Btu/ R Q& b,urr 0 pia 40 F V 900 ft/ Q Steam 40 F Sat. vapor V 00 ft/ A ft

119 Steam expand a turbe from a pecified tate to another pecified tate. he rate of entropy eration durg thi proce i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. ropertie From the team table (able A-4 through 6) 6 Ma 450 C 0 ka at. vapor h 0.9 kj/kg 6.79 kj/kg K h kj/kg kj/kg K Analyi here i only one let and one exit, and thu m& m& m&. We take the turbe a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a Subtitutg, E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& mh & Q& Rate of change ternal, ketic, potential, etc.energie E& & Q& W& mh & m& ( h h ) W& Q & (5,000/600 kg/)( )kJ/kg 4000 kj/ 89. kj/ he rate of total entropy eration durg thi proce i determed by applyg the entropy balance on an extended ytem that clude the turbe and it immediate urroundg o that the boundary temperature of the extended ytem i 5 C at all time. It give S S & 44 & Rate of net entropy tranfer by heat and ma m & m & Q& b,urr S& { Rate of entropy eration S& 0 ΔS& ytem 0 44 Rate of change of entropy 0 Subtitutg, the rate of entropy eration durg thi proce i determed to be S& m& 89. kw 98 K ( ) ( 5,000/600 kg/)( ) kj/kg K.0 kw/k Q& b,urr 6 Ma 450 C SEAM URBINE 0 ka at. vapor 4 MW

120 A hot water tream i mixed with a cold water tream. For a pecified mixture temperature, the ma flow rate of cold water tream and the rate of entropy eration are to be determed. Aumption Steady operatg condition exit. he mixg chamber i well-ulated o that heat lo to the urroundg i negligible. Change the ketic and potential energie of fluid tream are negligible. ropertie Notg that < 00 ka 0. C, the water all three tream exit a a compreed liquid, which can be approximated a a aturated liquid at the given temperature. hu from able A-4, 00 ka h h 70 C f 00 ka h h 4 C f C C 00 ka h h 0 C C o C C o C 9.07 kj/kg kj/kg K o o 8.9 kj/kg kj/kg K kj/kg kj/kg K Analyi (a) We take the mixg chamber a the ytem, which i a control volume. he ma and energy balance for thi teady-flow ytem can be expreed the rate form a 0 (teady) Ma balance: m m E& & & Δ ytem 0 m& m& m& Energy balance: E E & 44 & Rate of net energy tranfer by heat, work, and ma E& mh & m& h Rate of change ternal, ketic, potential, etc.energie E& m& h 0 (teady) ΔEytem & (ce Q& W& Δke Δpe 0) & & & & Combg the two relation give m h m h ( m m ) h Solvg for &m and ubtitutg, the ma flow rate of cold water tream i determed to be Alo, m & h h ( )kJ/kg & (.6 kg/) kg/ h h ( )kJ/kg m m & m& m& kg/ (b) Notg that the mixg chamber i adiabatic and thu there i no heat tranfer to the urroundg, the entropy balance of the teady-flow ytem (the mixg chamber) can be expreed a S S & 44 & Rate of net entropy tranfer by heat and ma m& m& S& { Rate of entropy eration m& S& 0 ΔS& ytem 0 44 Rate of change of entropy 0 Subtitutg, the total rate of entropy eration durg thi proce become S & m& m& m& ( 8.86 kg/)( kj/kg K) ( kg/)( kj/kg K) (.6 kg/)( kj/kg K) kw/k 70 C.6 kg/ 0 C H O 00 ka 4 C

121 Liquid water i heated a chamber by mixg it with uperheated team. For a pecified mixg temperature, the ma flow rate of the team and the rate of entropy eration are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. here are no work teraction. ropertie Notg that < 00 ka 0. C, the cold water and the exit mixture tream exit a a compreed liquid, which can be approximated a a aturated liquid at the given temperature. From able A-4 through A-6, 00 kj/m 00 ka 8.9 kj/kg h h o C 0 C 00 ka 50 C 00 ka h h 60 C f h o C 769. kj/kg 7.80 kj/kg K C C kj/kg K o 5.8 kj/kg 0.8 kj/kg K Analyi (a) We take the mixg chamber a the ytem, which i a control volume. he ma and energy balance for thi teady-flow ytem can be expreed the rate form a 0 (teady) Ma balance: m m E& & & Δ ytem 0 m& m& m& Energy balance: E E & 44 & 0 (teady) ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& m& h m& h Rate of change ternal, ketic, potential, etc.energie E& Q& & m& h Combg the two relation give Q& m& h m& h ( m& m& ) h m& ( h h ) m& ( h h ) Solvg for &m and ubtitutg, the ma flow rate of the uperheated team i determed to be Alo, m& Q& m& h h ( h h ) (00/60kJ/) (.5 kg/)( ) m & m& m& kg/ ( )kJ/kg kj/kg 0.66 kg/ (b) he rate of total entropy eration durg thi proce i determed by applyg the entropy balance on an extended ytem that clude the mixg chamber and it immediate urroundg o that the boundary temperature of the extended ytem i 5 C at all time. It give 0 S S S& ΔS& ytem 0 & 44 & { 44 Rate of net entropy tranfer by heat and ma m& m& m& Q& Rate of entropy eration b,urr S& Rate of change of entropy 0 Subtitutg, the rate of entropy eration durg thi proce i determed to be Q& S& m& m& m& b,urr (.666 kg/)( 0.8 kj/kg K) ( 0.66 kg/)( 7.80 kj/kg K) (00/ 60 kj/) (.5 kg/)( kj/kg K) 98 K 0. kw/k 0 C.5 kg/ 50 C MIXING CHAMBER 00 ka 60 C

122 A rigid tank itially conta aturated liquid water. A valve at the bottom of the tank i opened, and half of ma liquid form i withdrawn from the tank. he temperature the tank i mataed contant. he amount of heat tranfer and the entropy eration durg thi proce are to be determed. Aumption hi i an unteady proce ce the condition with the device are changg durg the proce, but it can be analyzed a a uniform-flow proce ce the tate of fluid leavg the device rema contant. Ketic and potential energie are negligible. here are no work teraction volved. 4 he direction of heat tranfer i to the tank (will be verified). ropertie he propertie of water are (able A-4 through A-6) v v f 50 C u u at. liquid 50 C he h e at. liquid e C C o o C C o o C m /kg 6.66 kj/kg.848 kj/kg K 6.8 kj/kg.848 kj/kg K Analyi (a) We take the tank a the ytem, which i a control volume ce ma croe the boundary. Notg that the microcopic energie of flowg and nonflowg fluid are repreented by enthalpy h and ternal energy u, repectively, the ma and energy balance for thi uniform-flow ytem can be expreed a Ma balance: m m Δm me m m ytem H O 0. m 50 C cont. m e Q Energy balance: E E 44 Net energy tranfer by heat, work, and ma Q Change ternal, ketic, potential, etc.energie m h e e ΔEytem 44 m u m u he itial and the fal mae the tank are (ce W ke pe 0) m m V 0. m 75.0 kg v m /kg m ( 75.0 kg) 7.55 kg me Now we determe the fal ternal energy and entropy, V v m x x v v f v 0. m m 7.75 kg fg C u u f xu f x fg fg /kg ( )( 97.4) 67.0 kj/kg ( )( 4.995).8557 kj/kg K he heat tranfer durg thi proce i determed by ubtitutg thee value to the energy balance equation,

123 7- Q mehe mu 80 kj m u ( 7.55 kg)( 6.8 kj/kg) ( 7.55 kg)( 67.0 kj/kg) ( 75.0 kg)( 6.66 kj/kg) (b) he total entropy eration i determed by coniderg a combed ytem that clude the tank and the heat ource. Notg that no heat croe the boundarie of thi combed ytem and no ma enter, the entropy balance for it can be expreed a S S 44 Net entropy tranfer by heat and ma S { Entropy eration ΔSytem mee S 44 Change entropy herefore, the total entropy erated durg thi proce i S m e e ΔS tank ΔS tank ΔS ( 7.55 kg)(.848 kj/kg K) ( 7.55 kg)(.8557 kj/kg K) 80 kj ( 75.0 kg)(.848 kj/kg K) 0.0 kj/k ΔS ource m e e ( m 4 K Q m ) ource, ource ource

124 E An unknown ma of iron i dropped to water an ulated tank while beg tirred by a 00- W paddle wheel. hermal equilibrium i etablihed after 0 m. he ma of the iron block and the entropy erated 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 ytem i tationary and thu the ketic and potential energy change are zero. he ytem i well-ulated and thu there i no heat tranfer. ropertie he pecific heat of water and the iron block at room temperature are c p, water.00 Btu/lbm. F and c p, iron 0.07 Btu/lbm. F (able A-E). he denity of water at room temperature i 6. lbm/ft³. Analyi (a) We take the entire content of the tank, water iron block, a the ytem. hi i a cloed ytem ce no ma croe the ytem boundary durg the proce. he energy balance on the ytem can be expreed a E E 44 Net energy tranfer by heat, work, and ma W pw, ΔU ΔEytem 44 Change ternal, ketic, potential, etc.energie or, W ΔU Δ U where W m pw, iron water ( )] iron [ mc( ) water pw, [ mc ] water W pw ρv W& pw ( 6. lbm/ft )( 0.8 ft ) 49.7 lbm Btu Δt (0. kj/)(0 60 ).7 Btu.055 kj Ug pecific heat value for iron and liquid water and ubtitutg,.7 Btu m m iron iron.4 (0.07 Btu/lbm F)(75 85) F lbm o o ( 49.7 ) lbm (.00 Btu/lbm F)(75 70) F (b) Aga we take the iron water the tank to be the ytem. Notg that no heat or ma croe the boundarie of thi combed ytem, the entropy balance for it can be expreed a where S S 44 Net entropy tranfer by heat and ma ΔS ΔS iron water mc S { Entropy eration,total ΔSytem 44 Change entropy 0 S ΔS ΔS avg mc ln avg ln iron water (.4 lbm)( 0.07 Btu/lbm R) herefore, the total entropy erated durg thi proce i 00 W 55 R ln 0.8 Btu/R 645 R 55 R 50 R ( 49.6 lbm)(.0 Btu/lbm R) ln Btu/R ΔStotal S,total ΔSiron ΔSwater Btu/R WAER 70 F o Iron 85 F o

125 E Air i compreed teadily by a compreor. he ma flow rate of air through the compreor and the rate of entropy eration are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. otential energy change are negligible. Air i an ideal ga with variable pecific heat. ropertie he ga contant of air i Btu/lbm.R. he let and exit enthalpie of air are (able A- 7) 50 R 5 pia h 4.7Btu/lbm o 0.597Btu/lbm R 080 R h 60.97Btu/lbm o 50 pia Btu/lbm R Analyi (a) We take the compreor a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a W& E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma m& ( h W& V E& Q& / ) Rate of change ternal, ketic, potential, etc.energie E& Q& m& h & m& ( h h V V V /) Subtitutg, the ma flow rate i determed to be hu, ( hp) It yield (ce Δpe 0) Btu/ 500 Btu 400 m& hp 60 m&.85 lbm/ ( 50 ft/) Btu/lbm 5,07 ft / (b) Aga we take the compreor to be the ytem. Notg that no heat or ma croe the boundarie of thi combed ytem, the entropy balance for it can be expreed a where S S & 44 & Rate of net entropy tranfer by heat and ma ΔS& air Q& m & m & m& ( ) b,urr S& { Rate of entropy eration S& o m& o 0 S& Δ ytem 0 44 Rate of change of entropy 0 S& Rln m& ( ) Q& (.85 lbm/) ( Btu/lbm R) ln 0.07 Btu/ R b,urr 50 pia 5 pia Subtitutg, the rate of entropy eration durg thi proce i determed to be S& m& 500/60 Btu/ 50 R ( ) 0.07 Btu/.R Btu/.R Q& b,urr AIR 400 hp,500 Btu/m

126 Steam i accelerated a nozzle from a velocity of 70 m/ to 0 m/. he exit temperature and the rate of entropy eration are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. otential energy change are negligible. here are no work teraction. 4 he device i adiabatic and thu heat tranfer i negligible. ropertie From the team table (able A-6), h. kj/kg 4 Ma kj/kg K 450 C v m /kg Analyi (a) here i only one let and one exit, and thu m& m& m&. We take nozzle a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a Subtitutg,, or, hu, E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma h m& ( h E& Rate of change ternal, ketic, potential, etc.energie E& 0 h & V / ) m& ( h V /) (ce Q& W& Δpe 0). kj/kg Ma ha 8.4 kj/kg he ma flow rate of team i m& v V h V ( 0 m/) ( 70 m/) 4. C kj/kg K AV m /kg kj/kg 000 m / 8.4 kj/kg 4 ( 7 0 m )( 70 m/) 0.6 kg/ (b) Aga we take the nozzle to be the ytem. Notg that no heat croe the boundarie of thi combed ytem, the entropy balance for it can be expreed a S S & 44 & Rate of net entropy tranfer by heat and ma S& { Rate of entropy eration m & m & S& S& 0 ΔS& ytem 0 44 Rate of change of entropy 0 m& ( ) Subtitutg, the rate of entropy eration durg thi proce i determed to be S & ( ) ( 0.6 kg/)( ) kj/kg 0.06 kw/k m& K 4 Ma 450 C V 70 m/ Steam Ma V 0 m/

127 7-7 Special opic: Reducg the Cot of Compreed Air 7-7 he total talled power of compreed air ytem the US i etimated to be ab 0 million horepower. he amount of energy and money that will be aved per year if the energy conumed by compreor i reduced by 5 percent i to be determed. Aumption he compreor operate at full load durg one-third of the time on average, and are hut down the ret of the time. he average motor efficiency i 85 percent. Analyi he electrical energy conumed by compreor per year i Energy conumed (ower ratg)(load factor)(annual Operatg Hour)/Motor efficiency (0 0 6 hp)(0.746 kw/hp)(/)(65 4 hour/year)/ kwh/year hen the energy and cot avg correpondg to a 5% reduction energy ue for compreed air become Energy Savg (Energy conumed)(fraction aved) ( kwh)(0.05) kwh/year Cot Savg (Energy avg)(unit cot of energy) ( kwh/year)($0.07/kwh) $ /year Air Compreor herefore, reducg the energy uage of compreor by 5% will ave $79 million a year. W0 0 6 hp 7-74 he total energy ued to compre air the US i etimated to be kj per year. Ab 0% of the compreed air i etimated to be lot by air leak. he amount and cot of electricity wated per year due to air leak i to be determed. Aumption Ab 0% of the compreed air i lot by air leak. Analyi he electrical energy and money wated by air leak are Energy wated (Energy conumed)(fraction wated) ( kj)( kwh/600 kj)(0.0) kwh/year Money wated (Energy wated)(unit cot of energy) ( kwh/year)($0.07/kwh) $ /year Air Compreor herefore, air leak are cotg almot $ billion a year electricity cot. he environment alo uffer from thi becaue of the pollution aociated with the eration of thi much electricity. W kj

128 he compreed air requirement of a plant i beg met by a 5 hp compreor that compree air from 0. ka to 900 ka. he amount of energy and money aved by reducg the preure ettg of compreed air to 750 ka i to be determed. Aumption Air i an ideal ga with contant pecific heat. Ketic and potential energy change are negligible. he load factor of the compreor i given to be he preure given are abolute preure rather than gage preure. ropertie he pecific heat ratio of air i k.4 (able A-). Analyi he electrical energy conumed by thi compreor per year i Energy conumed (ower ratg)(load factor)(annual Operatg Hour)/Motor efficiency (5 hp)(0.746 kw/hp)(0.75)(500 hour/year)/ ,60 kwh/year he fraction of energy aved a a reult of reducg the preure ettg of the compreor i ( ower Reduction Factor (750/0.) (900/0.) 0.09 ( k ) / k,reduced / ) ( k ) / k ( / ) (.4 ) /,4 (.4 ) /,4 hat i, reducg the preure ettg will reult ab percent avg from the energy conumed by the compreor and the aociated cot. herefore, the energy and cot avg thi cae become Energy Savg (Energy conumed)(ower reduction factor) (78,60 kwh/year)(0.09) 0,40 kwh/year Cot Savg (Energy avg)(unit cot of energy) (0,40 kwh/year)($0.085/kwh) $585/year herefore, reducg the preure ettg by 50 ka will reult annual avg of 0.40 kwh that i worth $585 thi cae. Dicuion Some application require very low preure compreed air. In uch cae the need can be met by a blower tead of a compreor. Coniderable energy can be aved thi manner, ce a blower require a mall fraction of the power needed by a compreor for a pecified ma flow rate. 900 ka Air Compreor 0 ka 5 C W5 hp

129 A 50 hp compreor an dutrial facility i houed ide the production area where the average temperature durg operatg hour i 5 C. he amount of energy and money aved a a reult of drawg cooler ide air to the compreor tead of ug the ide air are to be determed. Aumption Air i an ideal ga with contant pecific heat. Ketic and potential energy change are negligible. Analyi he electrical energy conumed by thi compreor per year i Energy conumed (ower ratg)(load factor)(annual Operatg Hour)/Motor efficiency Alo, Cot of Energy (50 hp)(0.746 kw/hp)(0.85)(4500 hour/year)/ ,84 kwh/year (Energy conumed)(unit cot of energy) (475,84 kwh/year)($0.07/kwh) $,77/year he fraction of energy aved a a reult of drawg cooler ide air i ide 0 7 ower Reduction Factor ide hat i, drawg air which i 5 C cooler will reult 5.0 percent avg from the energy conumed by the compreor and the aociated cot. herefore, the energy and cot avg thi cae become Energy Savg (Energy conumed)(ower reduction factor) Cot Savg (475,84 kwh/year)(0.050),99 kwh/year (Energy avg)(unit cot of energy) (,99 kwh/year)($0.07/kwh) $675/year 0 0 C Air Compreor 0 ka 5 C herefore, drawg air from the ide will reult annual avg of,99 kwh, which i worth $675 thi cae. Dicuion he price of a typical 50 hp compreor i much lower than $50,000. herefore, it i teretg to note that the cot of energy a compreor ue a year may be more than the cot of the compreor itelf. he implementation of thi meaure require the tallation of an ordary heet metal or VC duct from the compreor take to the ide. he tallation cot aociated with thi meaure i relatively low, and the preure drop the duct mot cae i negligible. Ab half of the manufacturg facilitie we have viited, epecially the newer one, have the duct from the compreor take to the ide place, and they are already takg advantage of the avg aociated with thi meaure. W50 hp

130 he compreed air requirement of the facility durg 60 percent of the time can be met by a 5 hp reciprocatg compreor tead of the exitg 00 hp compreor. he amount of energy and money aved a a reult of witchg to the 5 hp compreor durg 60 percent of the time are to be determed. Analyi Notg that hp kw, the electrical energy conumed by each compreor per year i determed from (Energy conumed) Large (ower)(hour)[(lfxf/η motor ) Unloaded (LFxF/η motor ) Loaded ] (00 hp)(0.746 kw/hp)(800 hour/year)[ / /0.9] 85,990 kwh/year (Energy conumed) Small (ower)(hour)[(lfxf/η motor ) Unloaded (LFxF/η motor ) Loaded ] (5 hp)(0.746 kw/hp)(800 hour/year)[ ]/ ,0 kwh/year herefore, the energy and cot avg thi cae become Energy Savg Cot Savg (Energy conumed) Large - (Energy conumed) Small 85,990-65,0 kwh/year 0,959 kwh/year (Energy avg)(unit cot of energy) (0,959 kwh/year)($0.075/kwh) $9,07/year Air Compreor Dicuion Note that utilizg a mall compreor durg the time of reduced compreed air requirement and huttg down the large compreor will reult annual avg of 0,959 kwh, which i worth $9,07 thi cae. W00 hp

131 A facility top production for one hour every day, cludg weekend, for lunch break, but the 5 hp compreor i kept operatg. If the compreor conume 5 percent of the rated power when idlg, the amount of energy and money aved per year a a reult of turng the compreor off durg lunch break are to be determed. Analyi It eem like the compreor thi facility i kept on unnecearily for one hour a day and thu 65 hour a year, and the idle factor i 0.5. hen the energy and cot avg aociated with turng the compreor off durg lunch break are determed to be Energy Savg (ower Ratg)(urned Off Hour)(Idle Factor)/η motor (5 hp)(0.746 kw/hp)(65 hour/year)(0.5)/0.84 4,8 kwh/year Cot Savg (Energy avg)(unit cot of energy) (4,8 kwh/year)($0.09/kwh) $,76/year Dicuion Note that the imple practice of turng the compreor off durg lunch break will ave thi facility $,76 a year energy cot. here are alo ide benefit uch a extendg the life of the motor and the compreor, and reducg the matenance cot. Air Compreor W5 hp

132 It i determed that 40 percent of the energy put to the compreor i removed from the compreed air a heat the aftercooler with a refrigeration unit whoe CO i.5. he amount of the energy and money aved per year a a reult of coolg the compreed air before it enter the refrigerated dryer are to be determed. Aumption he compreor operate at full load when operatg. Analyi Notg that 40 percent of the energy put to the compreor i removed by the aftercooler, the rate of heat removal from the compreed air the aftercooler under full load condition i Q & aftercooli (Rated ower of Compreor)(Load Factor)(Aftercoolg Fraction) ng (50 hp)(0.746 kw/hp)(.0)(0.4) kw he compreor i aid to operate at full load for 600 hour a year, and the CO of the refrigeration unit i.5. hen the energy and cot avg aociated with thi meaure become Energy Savg ( & Q aftercoolg )(Annual Operatg Hour)/CO Aftercooler Q aftercoolg Cot Savg (44.76 kw)(600 hour/year)/.5 0,46 kwh/year (Energy avg)(unit cot of energy aved) (0,46 kwh/year)($0.06/kwh) $7/year Air Compreor W50 hp Dicuion Note that the aftercooler will ave thi facility 0,46 kwh of electrical energy worth $7 per year. he actual avg will be le than dicated above ce we have not conidered the power conumed by the fan and/or pump of the aftercooler. However, if the heat removed by the aftercooler i utilized for ome ueful purpoe uch a pace heatg or proce heatg, then the actual avg will be much more.

133 he motor of a 50 hp compreor i burned and i to be replaced by either a 9% efficient tandard motor or a 96.% efficient high efficiency motor. It i to be determed if the avg from the high efficiency motor jutify the price differential. Aumption he compreor operate at full load when operatg. he life of the motor i 0 year. here are no rebate volved. 4 he price of electricity rema contant. Analyi he energy and cot avg aociated with the tallation of the high efficiency motor thi cae are determed to be Energy Savg (ower Ratg)(Operatg Hour)(Load Factor)(/η tandard - /η efficient ) Cot Savg (50 hp)(0.746 kw/hp)(4,68 hour/year)(.0)(/ /0.96) 7,48 kwh/year (Energy avg)(unit cot of energy) (7,48 kwh/year)($0.075/kwh) $/year he additional cot of the energy efficient motor i Cot Differential $0,94 - $9,0 $,9 Dicuion he money aved by the high efficiency motor will pay for thi cot difference $,9/$.5 year, and will contue avg the facility money for the ret of the 0 year of it lifetime. herefore, the ue of the high efficiency motor i recommended thi cae even the abence of any centive from the local utility company. Air Compreor 50 hp

134 he compreor of a facility i beg cooled by air a heat-exchanger. hi air i to be ued to heat the facility wter. he amount of money that will be aved by divertg the compreor wate heat to the facility durg the heatg eaon i to be determed. Aumption he compreor operate at full load when operatg. Analyi Aumg operation at ea level and takg the denity of air to be. kg/m, the ma flow rate of air through the liquid-to-air heat exchanger i determed to be Ma flow rate of air (Denity of air)(average velocity)(flow area) (. kg/m )( m/)(.0 m ).6 kg/,960 kg/h Notg that the temperature rie of air i C, the rate at which heat can be recovered (or the rate at which heat i tranferred to air) i Rate of Heat Recovery (Ma flow rate of air)(specific heat of air)(emperature rie) (,960 kg/h)(.0 kj/kg. C)( C) 44,70 kj/h he number of operatg hour of thi compreor durg the heatg eaon i Operatg hour (0 hour/day)(5 day/week)(6 week/year) 600 hour/year hen the annual energy and cot avg become Energy Savg (Rate of Heat Recovery)(Annual Operatg Hour)/Efficiency (44,70 kj/h)(600 hour/year)/0.8,47,840,000 kj/year,776 therm/year Cot Savg (Energy avg)(unit cot of energy aved) (,776 therm/year)($.0/therm) $,776/year Air 0 C m/ Hot Compreed air herefore, utilizg the wate heat from the compreor will ave $,776 per year from the heatg cot. Dicuion he implementation of thi meaure require the tallation of an ordary heet metal duct from the let of the heat exchanger to the buildg. he tallation cot aociated with thi meaure i relatively low. A few of the manufacturg facilitie we have viited already have thi conervation ytem place. A damper i ued to direct the air to the buildg wter and to the ambient ummer. Combed compreor/heat-recovery ytem are available the market for both air-cooled (greater than 50 hp) and water cooled (greater than 5 hp) ytem. 5 C

135 he compreed air le a facility are mataed at a gage preure of 850 ka at a location where the atmopheric preure i 85.6 ka. here i a 5-mm diameter hole on the compreed air le. he energy and money aved per year by ealg the hole on the compreed air le. Aumption Air i an ideal ga with contant pecific heat. Ketic and potential energy change are negligible. ropertie he ga contant of air i R 0.87 kj/kg.k. he pecific heat ratio of air i k.4 (able A-). Analyi Diregardg any preure loe and notg that the abolute preure i the um of the gage preure and the atmopheric preure, the work needed to compre a unit ma of air at 5 C from the atmopheric preure of 85.6 ka to ka i determed to be w comp, η kr ( k ) comp ( k ) / k (.4)(0.87 kj/kg.k)(88 K) 95.6 ka (0.8)(.4 ) 85.6 ka 54.5 kj/kg he cro-ectional area of the 5-mm diameter hole i 6 A πd / 4 π ( 5 0 m) / m Notg that the le condition are 0 98 K and ka, the ma flow rate of the air leakg through the hole i determed to be m& air C lo k /( k ) (0.65).4 /(.4 ) (0.87 ka.m 000 m / (.4)(0.87 kj/kg.k) kj/kg kg/ 0 R 0 A kr k 95.6 ka 0 (.4 ) /.4 / kg.k)(98 K) (98 K).4 hen the power wated by the leakg compreed air become (9.6 0 ower wated m& w ( kg / )(54.5 kj /kg) 9. 9 kw air comp, Notg that the compreor operate 400 hour a year and the motor efficiency i 0.9, the annual energy and cot avg reultg from repairg thi leak are determed to be Energy Savg (ower wated)(annual operatg hour)/motor efficiency (9.9 kw)(400 hour/year)/0.9 44,755 kwh/year Cot Savg (Energy avg)(unit cot of energy) (44,755 kwh/year)($0.07/kwh) $/year atm 85.6 ka, 5 C Compreed air le 850 ka, 5 C herefore, the facility will ave 44,755 kwh of electricity that i worth $ a year when thi air leak i ealed. 6 m ) Air leak

136 7-6 Review roblem 7-8E he ource and k temperature and the thermal efficiency of a heat enge are given. he entropy change of the two reervoir i to be calculated and it i to be determed if thi enge atifie the creae of entropy prciple. Aumption he heat enge operate teadily. Analyi Accordg to the firt law and the defition of the thermal efficiency, H Q L ( η) Q ( 0.4)(Btu) 0.6 Btu H Q H when the thermal efficiency i 40%. he entropy change of everythg volved thi proce i then ΔS total ΔS Q H H H ΔS Q L L L Btu 0.6 Btu 00 R 500 R Btu/R Q L HE L W net Sce the entropy of everythg ha creaed, thi enge i poible. When the thermal efficiency of the enge i 70%, Q L ( η) Q ( 0.7)(Btu) 0. Btu H he total entropy change i then ΔS total ΔS Q H H H ΔS Q L L L Btu 0. Btu 00 R 500 R Btu/R which i a decreae the entropy of everythg volved with thi enge. herefore, thi enge i now impoible.

137 he ource and k temperature and the CO of a refrigerator are given. he total entropy change of the two reervoir i to be calculated and it i to be determed if thi refrigerator atifie the econd law. Aumption he refrigerator operate teadily. Analyi Combg the firt law and the defition of the coefficient of performance produce Q H Q L CO R (kj).5 kj 4 when CO 4. he entropy change of everythg i then ΔS total ΔS Q H H H ΔS Q L L L.5 kj kj kj/k 0 K 5 K Sce the entropy creae, a refrigerator with CO 4 i poible. When the coefficient of performance i creaed to 6, Q H Q L CO and the net entropy change i ΔS total ΔS Q H H H Q R ΔS L L L (kj).67 kj 6 and the refrigerator can no longer be poible..67 kj kj kJ/K 0 K 5 K Q H kj 0 C R 0 C W net

138 he operatg condition and thermal reervoir temperature of a heat pump are given. It i to be determed if the creae of entropy prciple i atified. Aumption he heat pump operate teadily. Analyi Applyg the firt law to the cyclic heat pump give Q& L Q& W& H net, 5 kw 5 kw 0 kw Accordg to the defition of the entropy, the rate at which the entropy of the high-temperature reervoir creae i ΔS& H Q& H H 5 kw 0.08 kw/k 00 K Similarly, the rate at which the entropy of the low-temperature reervoir decreae i ΔS& L Q& L L 0 kw kw/k 60 K he rate at which the entropy of everythg change i then ΔS & total ΔS& H ΔS& L kw/k which i poitive and therefore it atifie the creae entropy prciple. Q & H Q & L 00 K H 60 K W & net, 7-86 Steam i expanded adiabatically a cloed ytem. he mimum ternal energy that can be achieved durg thi proce i to be determed. Analyi he entropy at the itial tate i 500 ka 0 C kj/kg K (from able A - 6 or from EES) he ternal energy will be mimum if the proce i ientropic. hen, 00 ka kj/kg K x u u fg x f f u (0.9400)(088.) 80. kj/kg fg

139 E Water i expanded an iothermal, reverible proce. It i to be determed if the proce i poible. Analyi he entropie at the itial and fal tate are (able A-5E and A-6E) 0 pia x pia 50. F 50. F f x fg 0.68 (0.70)(.).00 Btu/lbm R.877 Btu/lbm R he heat tranfer durg thi iothermal, reverible proce i the area under the proce le: q ( ) ( K)( ) Btu/lbm R 74.6 Btu/lbm he total entropy change (i.e., entropy eration) i the um of the entropy change of water and the reervoir: Δ total Δ water Δ R q R 74.6 Btu/lbm ( ) Btu/lbm R (00 460) R 0.047Btu/lbm R Note that the ign of heat tranfer i with repect to the reervoir.

140 E Air i compreed adiabatically a cloed ytem. It i to be determed if thi proce i poible. Aumption Change the ketic and potential energie are negligible. 4 Air i an ideal ga with contant pecific heat. ropertie he propertie of air at room temperature are R pia ft /lbm R, c p 0.40 Btu/lbm R (able A-Ea). Analyi he pecific volume of air at the itial tate i v R ( pia ft /lbm R)(560 R).96 ft 6 pia he volume at the fal tate will be mimum if the proce i ientropic. he pecific volume for thi cae i determed from the ientropic relation of an ideal ga to be / k /.4 /lbm 6 pia v,m v (.96 ft /lbm).500 ft 00 pia and the mimum volume i V m ( lbm)(.500 ft /lbm) 7.00 ft v which i greater than the propoed volume 4 ft /lbm. Hence, it i not poible to compre thi air to 4 ft /lbm. /lbm 7-89 Oxy i expanded adiabatically a piton-cylder device. he maximum volume i to be determed. Aumption Change the ketic and potential energie are negligible. 4 Oxy i an ideal ga with contant pecific heat. ropertie he ga contant of oxy i R ka m /kg K. he pecific heat ratio at the room temperature i k.95 (able A-a). Analyi he volume of oxy at the itial tate i V mr ( kg)(0.598 ka m /kg K)(7 7 K) m 950 ka he volume at the fal tate will be maximum if the proce i ientropic. he volume for thi cae i determed from the ientropic relation of an ideal ga to be V,max V / k (0.500 m 950 ka ) 00 ka / m

141 E A olid block i heated with aturated water vapor. he fal temperature of the block and water, and the entropy change of the block, water, and the entire ytem are to be determed. Aumption he ytem i tationary and thu the ketic and potential energy change are zero. here are no work teraction volved. here i no heat tranfer between the ytem and the urroundg. Analyi (a) A the block i heated, ome of the water vapor will be condened. We will aume (will be checked later) that the water i a mixture of liquid and vapor at the end of the proce. Baed upon thi aumption, the fal temperature of the water and olid block i F (he aturation temperature at 4.7 pia). he heat picked up by the block i Qblock mc( ) (00 lbm)(0.5 Btu/lbm R)( 70)R 700 Btu he water propertie at the itial tate are 4.7 pia x F h 50. Btu/lbm.7566 Btu/lbm R (able A-5E) he heat releaed by the water i equal to the heat picked up by the block. Alo notg that the preure of water rema contant, the enthalpy of water at the end of the heat exchange proce i determed from h Q 700 Btu 50. Btu/lbm 0 lbm water h m w 440. Btu/lbm he tate of water at the fal tate i aturated mixture. hu, our itial aumption wa correct. he propertie of water at the fal tate are h 4.7 pia 440. Btu/lbm x h f h h fg x f (0.68)(.4444) Btu/lbm R fg he entropy change of the water i then ΔS water m (b) he entropy change of the block i ΔS block w ( ) (0 lbm)( ) Btu/lbm 0.57 Btu/R mc ln (c) he total entropy change i ( 460)R (00 lbm)(0.5 Btu/lbm R)ln.87 Btu/R (70 460)R ΔS S ΔS ΔS Btu/R total water block he poitive reult for the total entropy change (i.e., entropy eration) dicate that thi proce i poible.

142 Air i compreed a piton-cylder device. It i to be determed if thi proce i poible. Aumption Change the ketic and potential energie are negligible. 4 Air i an ideal ga with contant pecific heat. he compreion proce i reverible. ropertie he propertie of air at room temperature are R 0.87 ka m /kg K, c p.005 kj/kg K (able A-a). Analyi We take the content of the cylder a the ytem. hi i a cloed ytem ce no ma enter or leave. he energy balance for thi tationary cloed ytem can be expreed a E 44 Net energy tranfer by heat, work, and ma W W W E b, b, b, Q Q Q Q Change ternal, ketic, potential, etc.energie ΔU m( u mc 0 W p b, ΔEytem 44 ( ) (ce u ) ) he work put for thi iothermal, reverible proce i hat i, 50 ka w R ln (0.87 kj/kg K)(00 K)ln kj/kg 00 ka q w kj/kg he entropy change of air durg thi iothermal proce i Δ air c p ln R ln he entropy change of the reervoir i Δ R q R R R ln kj/kg 0.60 kj/kg K 00 K 50 ka (0.87 kj/kg K)ln 0.60 kj/kg K 00 ka Note that the ign of heat tranfer i taken with repect to the reervoir. he total entropy change (i.e., entropy eration) i the um of the entropy change of air and the reervoir: Δ Δ Δ kj/kg K total air R Not only thi proce i poible but alo completely reverible. Air 00 ka 7 C Heat

143 A paddle wheel doe work on the water contaed a rigid tank. For a zero entropy change of water, the fal preure the tank, the amount of heat tranfer between the tank and the urroundg, and the entropy eration durg the proce are to be determed. Aumption he tank i tationary and the ketic and potential energy change are negligible. Analyi (a) Ug aturated liquid propertie for the compreed liquid at the itial tate (able A-4) 0 C u x 0 (at.liq.) kj/kg.579 kj/kg.k he entropy change of water i zero, and thu at the fal tate we have 95 C 84.6 ka.579 kj/kg.k u 49.6 kj/kg (b) he heat tranfer can be determed from an energy balance on the tank Q W m( u u ) kj (.5 kg)( ) kj/kg 8.5 kj w, Water 0 C 500 ka W pw (c) Sce the entropy change of water i zero, the entropy eration i only due to the entropy creae of the urroundg, which i determed from S ΔS urr Q urr 8.5 kj 0.4 kj/k (5 7) K

144 A horizontal cylder i eparated to two compartment by a piton, one ide contag nitro and the other ide contag helium. Heat i added to the nitro ide. he fal temperature of the helium, the fal volume of the nitro, the heat tranferred to the nitro, and the entropy eration durg thi proce are to be determed. Aumption Ketic and potential energy change are negligible. Nitro and helium are ideal gae with contant pecific heat at room temperature. he piton i adiabatic and frictionle. ropertie he propertie of nitro at room temperature are R ka.m /kg.k, c p.09 kj/kg.k, c v 0.74 kj/kg.k, k.4. he propertie for helium are R.0769 ka.m /kg.k, c p 5.96 kj/kg.k, c v.56 kj/kg.k, k.667 (able A-). Analyi (a) Helium undergoe an ientropic compreion proce, and thu the fal helium temperature i determed from He,.7 K ( k ) / k (.667 ) / ka (0 7)K 95 ka (b) he itial and fal volume of the helium are Q N 0. m He 0. kg V He, mr (0. kg)(.0769 ka m /kg K)(0 7 K) m 95 ka V He, mr hen, the fal volume of nitro become V (0. kg)(.0769 ka m /kg K)(.7 K) m 0 ka V V m N, N, He, V He, (c) he ma and fal temperature of nitro are m V (95 ka)(0. m ) N R (0.968 ka m /kg K)(0 7 K) V N, mr (0 ka)(0.88 m ) (0.85 kg)(0.968 ka m /kg K) 0.85 kg 55. K he heat tranferred to the nitro i determed from an energy balance Q ΔU ΔU N He v ( N v He [ mc )] [ mc ( )] (0.85 kg)(0.74 kj/kg.k)(55. 9) (0. kg)(.56 kj/kg.k)(.7 9) 46.6 kj (d) Notg that helium undergoe an ientropic proce, the entropy eration i determed to be S Q ΔS N ΔSurr mn c p ln R ln R 55. K 0 ka 46.6 kj (0.85 kg) (.09 kj/kg.k)ln (0.968 kj/kg.k)ln 9 K 95 ka (500 7) K kj/k

145 An electric reitance heater i dog work on carbon dioxide contaed an a rigid tank. he fal temperature the tank, the amount of heat tranfer, and the entropy eration are to be determed. Aumption Ketic and potential energy change are negligible. Carbon dioxide i ideal ga with contant pecific heat at room temperature. ropertie he propertie of CO at an anticipated average temperature of 50 K are R ka.m /kg.k, c p kj/kg.k, c v kj/kg.k (able A-b). Analyi (a) he ma and the fal temperature of CO may be determed from ideal ga equation V (00 ka)(0.8 m ) m.694 kg R (0.889 ka m /kg K)(50 K) CO 50 K 00 ka W e V (75 ka)(0.8 m ) 47.5 K mr (.694 kg)(0.889 ka m /kg K) (b) he amount of heat tranfer may be determed from an energy balance on the ytem Q E& e, Δt mc v ( ) (0.5 kw)(40 60 ) - (.694 kg)(0.706 kj/kg.k)( )k (c) he entropy eration aociated with thi proce may be obtaed by calculatg total entropy change, which i the um of the entropy change of CO and the urroundg kj S Q ΔS CO ΔSurr m c p ln R ln urr 47.5 K 75 ka kj (.694 kg) (0.895 kj/kg.k)ln (0.889 kj/kg.k)ln 50 K 00 ka 00 K.9 kj/k

146 Heat i lot from the helium a it i throttled a throttlg valve. he exit preure and temperature of helium and the entropy eration are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy change are negligible. Helium i an ideal ga with contant pecific heat. q ropertie he propertie of helium are R.0769 ka.m /kg.k, c p 5.96 kj/kg.k (able A-a). Analyi (a) he fal temperature of helium may be determed from an energy balance on the control volume q q.5 kj/kg c p ( ) 70 C 4.5 K 69.5 C c 5.96 kj/kg. C he fal preure may be determed from the relation for the entropy change of helium Δ He Rln 4.5 K 0.5 kj/kg.k (5.96 kj/kg.k)ln (.0769 kj/kg.k)ln 4 K 500 ka 44.7 ka cp ln p (b) he entropy eration aociated with thi proce may be obtaed by addg the entropy change of helium a it flow the valve and the entropy change of the urroundg Δ He Δ urr Δ He q urr Helium 500 ka 70 C.5 kj/kg 0.5 kj/kg.k 0.58 kj/kg.k (5 7) K

147 Refrigerant-4a i compreed a compreor. he rate of heat lo from the compreor, the exit temperature of R-4a, and the rate of entropy eration are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy change are negligible. Analyi (a) he propertie of R-4a at the let of the compreor are (able A-) 00 ka m /kg v x kj/kg h kj/kg.k he ma flow rate of the refrigerant i &m v V & 0.0 m / kg/ m /kg Given the entropy creae of the urroundg, the heat lot from the compreor i ΔS & urr Q& urr Q& urr ΔS& urr (b) An energy balance on the compreor give W & Q& 0 kw -.44 kw m& ( h he exit tate i now fixed. hen, 700 ka h kj/kg h ) (0.004 kg/)( h.5 C kj/kg.k (0 7 K)(0.008 kw/k) ) kj/kg h.44 kw kj/kg (c) he entropy eration aociated with thi proce may be obtaed by addg the entropy change of R-4a a it flow the compreor and the entropy change of the urroundg S & ΔS& R ΔS& urr (0.004 kg/)( kj/k m& ( ) ΔS& urr 0.977) kj/kg.k kw/k Q Compreor R-4a 00 ka at. vap. 700 ka

148 Air flow an adiabatic nozzle. he ientropic efficiency, the exit velocity, and the entropy eration are to be determed. ropertie he ga contant of air i R 0.87 kj/kg.k (able A-). Aumption Steady operatg condition exit. otential energy change are negligible. Analyi (a) (b) Ug variable pecific heat, the propertie can be determed from air table a follow 400 K r 50 K r h 0 r h 0 00 ka 500 ka kj/kg.9994 kj/kg.k kj/kg kj/kg.k (.806).86 h 46. kj/kg Energy balance on the control volume for the actual and ientropic procee give (0 m/) kj/kg (0 m/) kj/kg kj/kg 000 m / V V h kj/kg 000 m / 0.95 V V h h V V kj/kg 9.m/ h V.8 m/ he ientropic efficiency i determed from it defition, V η N V (9. m/) (.8 m/) kj/kg 000 m / V kj/kg 46. kj/kg 000 m / (c) Sce the nozzle i adiabatic, the entropy eration i equal to the entropy creae of the air a it flow the nozzle Δ air 0 0 Rln Air 500 ka 400 K 0 m/ 00 ka ( )kJ/kg.K (0.87 kj/kg.k)ln 500 ka 0.08 kj/kg.k 00 ka 50 K

149 It i to be hown that the difference between the teady-flow and boundary work i the flow energy. Analyi he total differential of flow energy v can be expreed a d ( v ) dv v d δ w δ w δ ( w w ) b flow b herefore, the difference between the reverible teady-flow work and the reverible boundary work i the flow energy. flow

150 An ulated rigid tank i connected to a piton-cylder device with zero clearance that i mataed at contant preure. A valve i opened, and ome team the tank i allowed to flow to the cylder. he fal temperature the tank and the cylder are to be determed. Aumption Both the tank and cylder are well-ulated and thu heat tranfer i negligible. he water that rema the tank underwent a reverible adiabatic proce. he thermal energy tored the tank and cylder themelve i negligible. 4 he ytem i tationary and thu ketic and potential energy change are negligible. Analyi (a) he team tank A undergoe a reverible, adiabatic proce, and thu. From the team table (able A-4 through A-6), v v g 500 ka u u at. vapor 50 ka v ( at. mixture), A g@500 ka v u, ka g@500 ka f x u f m /kg kj/kg kj/kg K, A x v x, A fg, A he itial and the fal mae tank A are hu, m m, A, B V A v m, A, A 0.4 m.067 kg m /kg m, A, A, A kg (b) he boundary work done durg thi proce i at@50 ka.5 C (0.905)( ).0789 m u fg fg ( V, B ) B m, B B W b, dv B 0 v, akg the content of both the tank and the cylder to be the ytem, the energy balance for thi cloed ytem can be expreed a or, hu, E E 44 Net energy tranfer by heat, work, and ma m h B, B v W, B ΔEytem 44 Change ternal, ketic, potential, etc.energie b, ΔU ( ΔU ) A ( ΔU ) B Wb, ( ΔU ) A ( ΔU ) B 0 ( mu mu ) A ( mu ) B 0 m h ( m u m u ) 0, B, B A f (0.905)(05. kj/kg) 76.6 kj/kg and m, A V A v ( mu mu ) (.067)( 560.7) ( 0.7)( 76.6), A A, B m, B m 0.7 kg.0789 m /kg kj/kg At 50 ka, h f 467. and h g 69. kj/kg. hu at the fal tate, the cylder will conta a aturated liquid-vapor mixture ce h f < h < h g. herefore,, B at@50 ka.5 C /kg Sat. vapor 500 ka 0.4 m 50 ka

151 Carbon dioxide i compreed a reverible iothermal proce ug a teady-flow device. he work required and the heat tranfer are to be determed. Aumption Steady operatg condition exit. Change the ketic and potential energie are negligible. CO i an ideal ga with contant pecific heat. ropertie he ga contant of CO i R ka m /kg K (able A-a). Analyi here i only one let and one exit, and thu m & m& m&. We take the compreor a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teadyflow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma mh & W& W& E& Q& Q& W& Rate of change ternal, ketic, potential, etc. energie E& mh & m& ( h Q& & h ) mc & (ce p ( ) ) he work put for thi iothermal, reverible proce i w R ln From the energy balance equation, q w (0.889 kj/kg K)(9 K)ln 76.7 kj/kg 400 ka 00 ka 76.7 kj/kg 400 ka 0 C Compreor 00 ka 0 C

152 Carbon dioxide i compreed an ientropic proce ug a teady-flow device. he work required and the heat tranfer are to be determed. Aumption Steady operatg condition exit. Change the ketic and potential energie are negligible. CO i an ideal ga with contant pecific heat. ropertie he ga contant of CO i R ka m /kg K. Other propertie at room temperature are c p kj/kg K and k.89 (able A-a). Analyi here i only one let and one exit, and thu m & m& m&. We take the compreor a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teadyflow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& mh & W& W& Rate of change ternal, ketic, potential, etc.energie E& mh & & m& ( h h ) mc & p ( ) he temperature at the compreor exit for the ientropic proce of an ideal ga i Subtitutg, ( k ) / k 0.89 / ka (9 K) 00 ka w 99.8 K c ( ) (0.846 kj/kg K)(99.8 9)K 90.4 kj p 400 ka Compreor 00 ka 0 C he work put creae from 76.7 kj/kg to 90.4 kj/kg when the proce i executed ientropically tead of iothermally. Sce the proce i ientropic (i.e., reverible, adiabatic), the heat tranfer i zero.

153 R-4a i compreed an ientropic compreor. he work required i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. he proce i ientropic (i.e., reverible-adiabatic). Ketic and potential energy change are negligible. Analyi here i only one let and one exit, and thu m & m& m&. We take the compreor a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teadyflow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& mh & W& W& Rate of change ternal, ketic, potential, etc.energie E& mh & & m& ( h h) he let tate propertie are 0 C x h 44.5 kj/kg kj/kg K For thi ientropic proce, the fal tate enthalpy i 800 ka Subtitutg, kj/kg K w h 7. kj/kg (able A -) (able A -) h h ( ) kj/kg 8.7 kj/kg 800 ka -0 C Compreor -0 C at. vapor 800 ka

154 Refrigerant-4a i expanded adiabatically a capillary tube. he rate of entropy eration i to be determed. Aumption Steady operatg condition exit. Ketic and potential energy change are negligible. Analyi he rate of entropy eration with the expanion device durg thi proce can be determed by applyg the rate form of the entropy balance on the ytem. Notg that the ytem i adiabatic and thu there i no heat tranfer, the entropy balance for thi teady-flow ytem can be expreed a S S & 44 & Rate of net entropy tranfer by heat and ma S& { Rate of entropy eration m& m& S& S& 0 (teady) ΔS& ytem m& ( Rate of change of entropy ) It may be eaily hown with an energy balance that the enthalpy rema contant durg the throttlg proce. he propertie of the refrigerant at the let and exit tate are (able A- through A-) 50 C x h 0 C h h.50 kj/kg K kj/kg K.50 kj/kg K x h f h h fg x f (0.4)( ) kj/kg K fg R-4a 50 C at. liq. Capillary tube C Subtitutg, S & m& ( ) (0. kg/)( ) kj/kg K kw/k

155 Steam i expanded an adiabatic turbe. Six percent of the let team i bled for feedwater heatg. he ientropic efficiencie for two tage of the turbe are given. he power produced by the turbe and the overall efficiency of the turbe are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. he turbe i wellulated, and there i no heat tranfer from the turbe. Analyi here i one let and two exit. We take the turbe a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& w w m& h W& Rate of change ternal, ketic, potential, etc.energie E& m& ( h & h m& m& h m& h h 0.06h h W& m& 0.94h h ) 0.94( h h h he ientropic and actual enthalpie at three tate are determed ug team table a follow: 4 Ma 50 C 800 ka h 09. kj/kg kj/kg K kj/kg K x h ) kj/kg h h η, h h η, ( h h ) 09. (0.97)( ) kj/kg h h h 800 ka kj/kg x kj/kg K 4 Ma 50 C 800 ka urbe 0 ka 4 Ma 0.8 Ma 0 ka 0 ka kj/kg K x h kj/kg Subtitutg, h h η, h h η,( h h ) (0.95)( ) 5.7 kj/kg h h w ( h h ) 0.94( h h ) ( ) 0.94( ) 80.kJ/kg - let he overall ientropic efficiency of the turbe i ( h h ) 0.94( h η ( h h ) 0.94( h h ) ( ) 0.94( ) h ) ( ) 0.94( ) %

156 Air i compreed teadily by a compreor from a pecified tate to a pecified preure. he mimum power put required i to be determed for the cae of adiabatic and iothermal operation. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. Air i an ideal ga with variable pecific heat. 4 he proce i reverible ce the work put to the compreor will be mimum when the compreion proce i reverible. ropertie he ga contant of air i R 0.87 kj/kg.k (able A-). Analyi (a) For the adiabatic cae, the proce will be reverible and adiabatic (i.e., ientropic), thu the ientropic relation are applicable. and 90 K r r r. and h 700 ka (.) ka 90.6 kj/kg he energy balance for the compreor, which i a teady-flow ytem, can be expreed the rate form a E & 44 & Rate of change ternal, ketic, potential, etc.energie 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma W& E& E& & mh & mh & W& m& ( h h) h 50. K kj/kg Subtitutg, the power put to the compreor i determed to be cont. cont. W & (5/60 kg/)( ) kj/kg 8.0 kw (b) In the cae of the reverible iothermal proce, the teady-flow energy balance become 0 E & E& W& mh Q& mh W& Q& & & m& ( h h ) Q& ce h h() for ideal gae, and thu the enthalpy change thi cae i zero. Alo, for a reverible iothermal proce, where Q& m & ( ) m & ( ) o o ka ( ) Rln Rln ( 0.87 kj/kg K) ln kj/kg K Subtitutg, the power put for the reverible iothermal cae become 00 ka W & (5/60 kg/)(90 K)( kj/kg K).5 kw

157 Air i compreed a two-tage ideal compreor with tercoolg. For a pecified ma flow rate of air, the power put to the compreor i to be determed, and it i to be compared to the power put to a gle-tage compreor. Aumption he compreor operate teadily. Ketic and potential energie are negligible. he compreion proce i reverible adiabatic, and thu ientropic. 4 Air i an ideal ga with contant pecific heat at room temperature. ropertie he ga contant of air i R 0.87 ka.m /kg.k (able A-). he pecific heat ratio of air i k.4 (able A-). Analyi he termediate preure between the two tage i x ( 00 ka)( 900 ka) 00 ka 00 ka 7 C 900 ka he compreor work acro each tage i the ame, thu total compreor work i twice the compreion work for a gle tage: w comp, k / k ( ) ( )( ) ( ) ( w ) x comp,,i (.4)( 0.87 kj/kg K)( 00 K). kj/kg kr k.4 00 ka 00 ka W 0.4/.4 Stage I Heat Stage II 7 C and W & & ( 0.0 kg/)(. kj/kg) 4.44 kw mwcomp, he work put to a gle-tage compreor operatg between the ame preure limit would be and ) ( k ( ) / k ) (.4)( 0.87 kj/kg K)( 00 K) 0.4/.4 kr 900 ka wcomp, k.4 00 ka W & & ( 0.0 kg/)( 6. kj/kg) 5.6 kw mwcomp, 6. kj/kg Dicuion Note that the power conumption of the compreor decreae ignificantly by ug -tage compreion with tercoolg.

158 A three-tage compreor with two tage of tercoolg i conidered. he two termediate preure that will mimize the work put are to be determed term of the let and exit preure. Analyi he work put to thi three-tage compreor with termediate preure x and y and two tercooler can be expreed a ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) n n x n n x y n n x n n x n n x y n n x n n x n n x y n n x n nr n nr n nr n nr n nr w w w w / / / / / / / / / comp,iii comp,ii comp,i comp he x and y value that will mimize the work put are obtaed by takg the partial differential of w with repect to x and y, and ettg them equal to zero: n n y n n x y x y n n y x y n n x x n n n n w n n n n w Simplifyg, ( ) ( ) ( ) ( ) n x n y n y n y x n x n n y n x y x n y n x n y x n y x n n n y x y n x which yield ( ) ( ) y y y x x x

159 Steam expand a two-tage adiabatic turbe from a pecified tate to pecified preure. Some team i extracted at the end of the firt tage. he power put of the turbe i to be determed for the cae of 00% and 88% ientropic efficiencie. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he turbe i adiabatic and thu heat tranfer i negligible. ropertie From the team table (able A-4 through 6) 6 Ma h 4. kj/kg 500 C kj/kg K. Ma h 96.8 kj / kg f ka x fg h h x h 5.4 f fg ( 0.855)( 57.5) 67.5 kj/kg Analyi (a) he ma flow rate through the econd tage i ( 0.9)( 5 kg/).5 kg/ m & 0.9m& We take the entire turbe, cludg the connection part between the two tage, a the ytem, which i a control volume ce ma croe the boundary. Notg that one fluid tream enter the turbe and two fluid tream leave, the energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma E& m& h W& Rate of change ternal, ketic, potential, etc.energie E& ( m& m& h ( m& & m& ) h m& ) h m& ( h h ) m& ( h W& m& h m& h h ) Subtitutg, the power put of the turbe i 6 Ma 500 C. Ma SEAM 5 kg/ 0% I 90% SEAM.5 kg/ 0 ka II ( 5 kg/)( ) kj/kg (.5 kg)( ) 6,9 kw W & kj/kg (b) If the turbe ha an adiabatic efficiency of 88%, then the power put become W & a ( 0.88)( 6,9 ) 4,6 kw η W& kw

160 Steam expand an 84% efficient two-tage adiabatic turbe from a pecified tate to a pecified preure. Steam i reheated between the tage. For a given power put, the ma flow rate of team through the turbe i to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he turbe i adiabatic and thu heat tranfer i negligible. ropertie From the team table (able A-4 through 6) 8 Ma h 550 C Ma h Ma h 550 C ka h 5.8 kj/kg kj/kg K kj/kg kj/kg kj/kg K kj/kg Analyi he power put of the actual turbe i given to be 80 MW. hen the power put for the ientropic operation become W&, W& a, / η (80,000 kw)/ ,40 kw We take the entire turbe, excludg the reheat ection, a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem ientropic operation can be expreed the rate form a Subtitutg, which give E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma W& E& mh & mh &, Rate of change ternal, ketic, potential, etc.energie E& mh & & mh & 4 W&, m& [( h h ) ( h h4 [( )kJ/kg ( )kJ/kg] 95,40 kj/ m& m& 85.8 kg/ )] Ma 8 Ma 550 C Stage I Heat Ma 550 C Stage II 00 ka 80 MW

161 Refrigerant-4a i compreed by a 0.7-kW adiabatic compreor from a pecified tate to another pecified tate. he ientropic efficiency, the volume flow rate at the let, and the maximum flow rate at the compreor let are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. ropertie From the R-4a table (able A- through A-) v m /kg 40 ka h 46.6 kj/kg 0 C kj/kg K 700 ka h 50 C 700 ka h 88.5 kj/kg 8.6 kj/kg Analyi (a) he ientropic efficiency i determed from it defition, η C h h % h h a (b) here i only one let and one exit, and thu m& m& m&. We take the actual compreor a the ytem, which i a control volume. he energy balance for thi teady-flow ytem can be expreed a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma W& a, E& W& a, Rate of change ternal, ketic, potential, etc.energie E& mh & mh & m& ( h & (ce Q& Δke Δpe 0) h ) hen the ma and volume flow rate of the refrigerant are determed to be W& a, m& ha h V& & mv ( ) 0.7 kj/ kg/ kj/kg ( kg/)( m /kg) m / 45 L/m (c) he volume flow rate will be a maximum when the proce i ientropic, and it i determed imilarly from the teady-flow energy equation applied to the ientropic proce. It give m& V& max,max W&, h h m& max v 0.7 kj/ ( ) 0.00 kg/ kj/kg ( 0.00 kg/)( m /kg) m / 76 L/m Dicuion Note that the raig the ientropic efficiency of the compreor to 00% would creae the volumetric flow rate by more than 0%. R-4a V 0.7 kw

162 7-6 7-E Helium i accelerated by a 94% efficient nozzle from a low velocity to 000 ft/. he preure and temperature at the nozzle let are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Helium i an ideal ga with contant pecific heat. otential energy change are negligible. 4 he device i adiabatic and thu heat tranfer i negligible. ropertie he pecific heat ratio of helium i k.667. he contant preure pecific heat of helium i.5 Btu/lbm.R (able A-E). Analyi We take nozzle a the ytem, which i a control volume ce ma croe the boundary. he energy balance for thi teady-flow ytem can be expreed the rate form a E & 44 & 0 (teady) E ΔEytem 0 Rate of net energy tranfer by heat, work, and ma m& ( h E& Rate of change ternal, ketic, potential, etc.energie E& 0 h & V / ) m& ( h V /) (ce Q& W& Δpe 0) V h Solvg for and ubtitutg, 0 V 0 c p,avg ( 000 ft/) ( R) ( ) V Btu/lbm V 80 F a 96.0 F 656 R C.5 Btu/lbm 5,07 ft / p From the ientropic efficiency relation, or, ( a ) ( ) ( )/ η 656 ( ) /( 0.94) 69 R a From the ientropic relation, h ηn h k / a N h h c c ( k ) / k ( k ) 656 R 4 pia 69 R.667/0.667 V ( ) 4.9 pia V HELIUM η N 94%

163 [Alo olved by EES on encloed CD] An adiabatic compreor i powered by a direct-coupled team turbe, which alo drive a erator. he net power delivered to the erator and the rate of entropy eration are to be determed. Aumption hi i a teady-flow proce ce there i no change with time. Ketic and potential energy change are negligible. he device are adiabatic and thu heat tranfer i negligible. 4 Air i an ideal ga with variable pecific heat. ropertie he ga contant of air i R 0.87 kj/kg.k (able A-). From the team table (able A-4 through 6) and air table (able A-7), 95 K 60 K 500 C.5 Ma h 4.6 kj/kg kj/kg K ka h4 hf x4hfg x f x4 fg Analyi here i only one let and one exit for either device, and thu m & m& m&. We take either the o h 95.7 kj/kg, o h kj/kg,.6855 kj/kg K.4456 kj/kg K turbe or the compreor a the ytem, which i a control volume ce ma croe the boundary. he energy balance for either teady-flow ytem can be expreed the rate form a 0 (teady) E E Eytem 0 E& E& & 44 & & Δ Rate of net energy tranfer by heat, work, and ma Rate of change ternal, ketic, potential, etc. energie For the turbe and the compreor it become Compreor: W& m& h m& h W& m& h h ) comp, air air comp, ( 0.9)( 9.) 9.5 kj/kg ( 0.9)( ) kj/kg K air ( urbe: m& h W& m& h W& m& h h ) Subtitutg, W& W& herefore, W & team comp, turb, net, turb, team 4 turb, team( 4 ( 0 kg/)( ) kj/kg 9 kw ( 5 kg/)( ) kj/kg,777 kw W& W&, ,448 kw turb, comp, Notg that the ytem i adiabatic, the total rate of entropy change (or eration) durg thi proce i the um of the entropy change of both fluid, S& m& ) m& ( ) where m& m& air team air( team 4 ( ) ( 0 kg/) Rln 000 ka ln kj/kg K 0.9 kw/k 98 ka ( ) ( 5 kg/)( ) kj/kg K 7. kw/k 4 o m& Subtitutg, the total rate of entropy eration i determed to be S & S& S& kw/k, total,comp o,turb Air comp 98 ka 95 K Ma 60 K.5 Ma 500 C Steam turbe 0 ka

164 EES roblem 7- i reconidered. he ientropic efficiencie for the compreor and turbe are to be determed, and then the effect of varyg the compreor efficiency over the range 0.6 to 0.8 and the turbe efficiency over the range 0.7 to 0.95 on the net work for the cycle and the entropy erated for the proce i to be vetigated. he net work i to be plotted a a function of the compreor efficiency for turbe efficiencie of 0.7, 0.8, and 0.9. Analyi he problem i olved ug EES, and the reult are tabulated and plotted below. "Input Data" m_dot_air 0 [kg/] "air compreor (air) data" _air[](95-7) "[C]" "We will put temperature C" _air[]98 [ka] _air[](700-7) "[C]" _air[]000 [ka] m_dot_t5 [kg/] "team turbe (t) data" _t[]500 [C] _t[]500 [ka] _t[]0 [ka] x_t[]0.9 "quality" "Compreor Analyi:" "Conervation of ma for the compreor m_dot_air_ m_dot_air_ m_dot_air" "Conervation of energy for the compreor i:" E_dot_comp_ - E_dot_comp_ DELAE_dot_comp DELAE_dot_comp 0 "Steady flow requirement" E_dot_comp_m_dot_air*(enthalpy(air,_air[])) W_dot_comp_ E_dot_comp_m_dot_air*(enthalpy(air,_air[])) "Compreor adiabatic efficiency:" Eta_compW_dot_comp ien/w_dot_comp_ W_dot_comp ienm_dot_air*(enthalpy(air,_air_ien[])-enthalpy(air,_air[])) _air[]entropy(air,_air[],_air[]) _air[]entropy(air,_air[],_air[]) _air_ien[]entropy(air, _air_ien[],_air[]) _air_ien[]_air[] "urbe Analyi:" "Conervation of ma for the turbe m_dot_t_ m_dot_t_ m_dot_t" "Conervation of energy for the turbe i:" E_dot_turb_ - E_dot_turb_ DELAE_dot_turb DELAE_dot_turb 0 "Steady flow requirement" E_dot_turb_m_dot_t*h_t[] h_t[]enthalpy(team,_t[], _t[]) E_dot_turb_m_dot_t*h_t[]W_dot_turb_ h_t[]enthalpy(team,_t[], xx_t[]) "urbe adiabatic efficiency:" Eta_turbW_dot_turb_/W_dot_turb ien W_dot_turb ienm_dot_t*(h_t[]-h_t_ien[]) _t[]entropy(team,_t[],_t[]) h_t_ien[]enthalpy(team, _t[],_t[]) "Note: When Eta_turb i pecified a an dependent variable the arametric able, the iteration proce may put the team tate the uperheat region, where the quality i undefed. hu, _t[], _t[] are calculated at _t[], h_t[] and not _t[] and x_t[]" _t[]entropy(team,_t[],hh_t[]) _t[]temperature(team,_t[], hh_t[]) _t_ien[]_t[] "Net work done by the proce:" W_dot_netW_dot_turb_-W_dot_comp_

165 7-65 "Entropy eration:" "Sce both the compreor and turbe are adiabatic, and thu there i no heat tranfer to the urroundg, the entropy eration for the two teady flow device become:" S_dot compm_dot_air*( _air[]-_air[]) S_dot turbm_dot_t*(_t[]-_t[]) S_dot totals_dot comps_dot turb "o erate the data for lot Wdow, Comment the le ' _air[](700-7) C' and elect value for Eta_comp the armetric able, then pre F to olve the table. EES then olve for the unknown value of _air[] for each Eta_comp." "o erate the data for lot Wdow, Comment the two le ' x_t[]0.9 quality ' and ' h_t[]enthalpy(team,_t[], xx_t[]) ' and elect value for Eta_turb the armetric able, then pre F to olve the table. EES then olve for the h_t[] for each Eta_turb." W net S total S total η turb η comp W net η turb η comp [kw] [kw/k] [kw] [kw/k] W net [kw] Effect of Compreor Efficiency on Net Work and Entropy Generated η turb η comp b S,total [kw/k] W net [kw] Effect of urbe Efficiency on Net Work and Entropy Generated 0 η 6000 comp S,total [kw/k] η turb b 5

166 he preure a hot water tank rie to Ma, and the tank explode. he exploion energy of the water i to be determed, and expreed term of it N equivalence. Aumption he expanion proce durg exploion i ientropic. Ketic and potential energy change are negligible. Heat tranfer with the urroundg durg exploion i negligible. ropertie he exploion energy of N i 50 kj/kg. From the team table (able A-4 through 6) v v Ma u u at. liquid 00 ka u f f x f fg Ma Ma Ma 47.40,.08, m /kg 906. kj/kg.4467 kj/kg K u fg fg 088. kj/kg kj/kg K Water ank Ma u u f x u fg ( 0.889)( 088.) 8.8 kj/kg Analyi We idealize the water tank a a cloed ytem that undergoe a reverible adiabatic proce with negligible change ketic and potential energie. he work done durg thi idealized proce repreent the exploive energy of the tank, and i determed from the cloed ytem energy balance to be where Subtitutg, E E 44 Net energy tranfer by heat, work, and ma W b, E exp Change ternal, ketic, potential, etc.energie ΔU m( u W b, ΔEytem 44 m u u ) ( u ) V m m kg v m /kg E ( kg)( ) kj/kg 640 kj exp which i equivalent to m N 640 kj.97 kg N 50 kj/kg

167 A 0.5-L canned drk explode at a preure of. Ma. he exploive energy of the drk i to be determed, and expreed term of it N equivalence. Aumption he expanion proce durg exploion i ientropic. Ketic and potential energy change are negligible. Heat tranfer with the urroundg durg exploion i negligible. 4 he drk can be treated a pure water. ropertie he exploion energy of N i 50 kj/kg. From the team table (able A-4 through 6) v v. Ma u u Comp. liquid Ma Ma Ma m /kg kj/kg.59 kj/kg K 00 ka u f f x f fg 47.40,.08, u fg fg 088. kj/kg kj/kg K COLA. Ma u u f x u fg ( 0.508)( 088.) 7.6 kj/kg Analyi We idealize the canned drk a a cloed ytem that undergoe a reverible adiabatic proce with negligible change ketic and potential energie. he work done durg thi idealized proce repreent the exploive energy of the can, and i determed from the cloed ytem energy balance to be E E 44 Net energy tranfer by heat, work, and ma W b, ΔEytem 44 Change ternal, ketic, potential, etc. energie ΔU m( u u ) E exp W b, m u ( u ) where Subtitutg, E exp which i equivalent to V m m kg v m /kg ( kg)( ) 9.9 kj kj/kg m N 9.9 kj 50 kj/kg kg N

168 he validity of the Clauiu equality i to be demontrated ug a reverible and an irreverible heat enge operatg between the ame temperature limit. Analyi Conider two heat enge, one reverible and one irreverible, both operatg between a hightemperature reervoir at H and a low-temperature reervoir at L. Both heat enge receive the ame amount of heat, Q H. he reverible heat enge reject heat the amount of Q L, and the irreverible one the amount of Q L, irrev Q L Q diff, where Q diff i a poitive quantity ce the irreverible heat enge produce le work. Notg that Q H and Q L are tranferred at contant temperature of H and L, repectively, the cyclic tegral of δq/ for the reverible and irreverible heat enge cycle become δ Q rev δ Q H H δ Q L L H δ Q ce (Q H / H ) (Q L / L ) for reverible cycle. Alo, δ Q irrev Q H H Q L,irrev L Q H H Q L L H Q δ Q ce Q diff i a poitive quantity. hu, 0. L diff L δ Q L Q Q diff L H H < 0 Q L L 0 H Rev HE Q H Q L W net, rev Irrev HE Q H W net, irrev Q L, irrev L

169 E R-4a vapor from a torage tank i ued to drive an ientropic turbe. he work produced by the turbe i to be determed. Aumption hi i an unteady-flow proce ce the condition the tank change. Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. Analyi he let and exit enthalpie for the turbe are (able A-E through A-E), 80 F h x (at. vap.) 0 pia x h h.94 Btu/lbm 0.97 Btu/lbm R h he itial ma of R-4a the tank i f g f fg 0.06 x h.56 ( )(95.58) Btu/lbm fg 80 F Sat. vap. R-4a turbe m V 0 ft itial v F 0.04 ft /lbm lbm he amount of ma which pae through the turbe durg thi expanion i then m m itial lbm 74.8 lbm he amount of work produced from the turbe i then W m( h h ) (74.8 lbm)( ) Btu/lbm 790 Btu 0 pia

170 R-4a i expanded an adiabatic proce with an ientropic efficiency of he work produced and fal enthalpy are to be determed. Aumption Ketic and potential energy change are negligible. he device i adiabatic and thu heat tranfer i negligible. Analyi We take the R-4a a the ytem. hi i a cloed ytem ce no ma enter or leave. he energy balance for thi tationary cloed ytem can be expreed a E E 44 Net energy tranfer by heat, work, and ma W ΔEytem 44 Change ternal, ketic, potential, etc.energie ΔU m( u u ) From the R-4a table (able A- through A-), 700 ka u 40 C 60 ka x u he actual work put i w kj/kg K 56.9 kj/kg u fg x f f u.798 (0.9997)(05.) kj/kg fg η w η u u ) (0.80)( ) kj/kg 7.87 kj/kg a,, ( he actual ternal energy at the end of the expanion proce i w, ( u u ) u u w, kj/kg a a a he enthalpy at the fal tate i 700 ka 60 ka u 60 ka h 8.5 kj/kg 8.4 kj/kg (able A-)

171 E A ytem conitg of a compreor, a torage tank, and a turbe a hown the figure i conidered. he total work required to fill the tank and the total heat tranferred from the air the tank a it i beg filled are to be determed. Aumption Change the ketic and potential energie are negligible. 4 Air i an ideal ga with contant pecific heat. ropertie he propertie of air at room temperature are R pia ft /lbm R, c p 0.40 Btu/lbm R, c v 0.7 Btu/lbm R, k.4 (able A-Ea). Analyi he itial ma of air the tank i 6 itialv (4.696 pia)( 0 ft )/lbm R) mitial 74,860 lbm R itial (0.704 pia ft /lbm R)(50 R) and the fal ma the tank i 6 falv (46.96 pia)( 0 ft )/lbm R) mfal 748,600 lbm R fal (0.704 pia ft /lbm R)(50 R) Sce the compreor operate a an ientropic device, ( k ) / k where matche the preure the tank. he conervation of ma applied to the tank give dm m & dt while the firt law give d mu dm Q& ( ) h dt dt Employg the ideal ga equation of tate and ug contant pecific heat, expand thi reult to c d d Q& V V v c p R dt R dt Ug the temperature relation acro the compreor and multiplyg by dt put thi reult the form ( k ) / k V v c Qdt & V d c p d R R When thi tegrated, it yield (i and f tand for itial and fal tate) ( k ) / k Vc k c p f Q v V ( ) f i f i R k R i 6 ( 0 )(0.7).4 (0.4)( 0 (47 4.7) (.4) ) / Btu he negative reult how that heat i tranferred from the tank. Applyg the firt law to the tank and compreor give ( Q & W & ) dt d( mu) hdm which tegrate to Q W m u m u ) h ( m m ) Upon rearrangement, W Q ( c ( f f i i f i p c 7 v ) ( m f m ) i ( )(50)(748,600 74,860) Btu

172 E A ytem conitg of a compreor, a torage tank, and a turbe a hown the figure i conidered. he total work produced by the turbe and the total heat added to the air the tank durg the dicharge are to be determed. Aumption Change the ketic and potential energie are negligible. 4 Air i an ideal ga with contant pecific heat. ropertie he propertie of air at room temperature are R pia ft /lbm R, c p 0.40 Btu/lbm R, c v 0.7 Btu/lbm R, k.4 (able A-Ea). Analyi he itial ma of air the tank i m 6 itialv (46.96 pia)( 0 ft )/lbm R) itial R itial (0.704 pia ft /lbm R)(50 R) and the fal ma the tank i m At any time, and m t 6 falv (4.696 pia)( 0 ft )/lbm R) fal R fal (0.704 pia ft /lbm R)(50 R) dm t dt V R V R d dt Sce the turbe operate a an ientropic device, 4 4 ( k ) / k 748,600 lbm 74,860 lbm where 4 i the contant atmopheric preure and matche the preure the tank. he conervation of ma applied to the tank give dm m& dt while the firt law applied to the turbe i dm W& m& ( h h4 ) mc & p ( 4 ) c p ( 4 ) dt Subtitution of the precedg reult expand thi reult to ( k ) / k W& 4 c p V R d dt Notg that i the preure the tank and that 4 i the contant atmopheric preure, multiplyg of thi reult by dt and tegration from the itial to the fal tate give