8-4 P 2. = 12 kw. AIR T = const. Therefore, Q &

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1 Air i compreed teadily by a compreor. e air temperature i mataed contant by eat rejection to te urroundg. e rate o entropy cange o air i to be determed. Aumption i i a teady-low proce ce tere i no cange wit time. Ketic and potential energy cange are negligible. Air i an ideal ga. 4 e proce volve no ternal irreveribilitie uc a riction, and tu it i an iotermal, ternally reverible proce. Propertie Notg tat () or ideal gae, we ave ce 5. Analyi We take te compreor a te ytem. Notg tat te entalpy o air rema contant, te energy balance or ti teady-low ytem can be expreed te rate orm a (teady) Δytem Rate o net energy traner Rate o cange ternal, ketic, by eat, work, and ma potential, etc.energie ereore, Q W kw Notg tat te proce i aumed to be an iotermal and ternally reverible proce, te rate o entropy cange o air i determed to be,air kw ΔS air kw/k 98 K y Q P AIR cont. P kw

2 An ulated cylder i itially illed wit aturated R-4a vapor at a peciied preure. e rerigerant expand a reverible manner until te preure drop to a peciied value. e al temperature te cylder and te work done by te rerigerant are to be determed. Aumption e ketic and potential energy cange are negligible. e cylder i well-ulated and tu eat traner i negligible. e termal energy tored te cylder itel i negligible. 4 e proce i tated to be reverible. Analyi (a) i i a reverible adiabatic (i.e., ientropic) proce, and tu. From te rerigerant table (able A- troug A-), Alo, v v g P 0.8 MPa u u at. MPa g@0.8 MPa g@0.8 MPa m /kg kj/kg kj/kg K and V 0.05 m m.95 kg v m /kg P 0.4 MPa x u u g + x u g ( )( 7.45).9 kj/kg R-4a 0.8 MPa 0.05 m at@0.4 MPa 8.9 (b) We take te content o te cylder a te ytem. i i a cloed ytem ce no ma enter or leave. e energy balance or ti adiabatic cloed ytem can be expreed a 44 Net energy traner by eat, work, and ma W W b, b, ange ternal, ketic, potential, etc.energie ΔU m( u u ) Δytem 44 Subtitutg, te work done durg ti ientropic proce i determed to be W ( ) (.95 kg)( ) 7.09 kj m u kj/kg b, u PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

3 Saturated Rerigerant-4a vapor at 60 i compreed teadily by an adiabatic compreor. e mimum power put to te compreor i to be determed. Aumption i i a teady-low proce ce tere i no cange wit time. Ketic and potential energy cange are negligible. e device i adiabatic and tu eat traner i negligible. Analyi e power put to an adiabatic compreor will be a mimum wen te compreion proce i reverible. For te reverible adiabatic proce we ave. From te rerigerant table (able A- troug A-), Alo, v v g P 60 at. vapor P 900 V m g@60 g@ 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 ere i only one let and one exit, and tu. We take te compreor a te ytem, wic i a control volume ce ma croe te boundary. e energy balance or ti teady-low ytem can be expreed te rate orm a 44 (teady) Δytem 0 Rate o net energy traner by eat, work, and ma Rate o cange ternal, ketic, potential, etc.energie m m (ce Q Δke Δpe 0) ( ) Subtitutg, te mimum power upplied to te compreor i determed to be W ( 0.7 kg/)( ) 9.7 kw kj/kg PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

4 Steam i expanded an ientropic turbe. e work produced i to be determed. Aumption i i a teady-low proce ce tere i no cange wit time. e proce i ientropic (i.e., reverible-adiabatic). Analyi ere i one let and two exit. We take te turbe a te ytem, wic i a control volume ce ma croe te boundary. e energy balance or ti teady-low ytem can be expreed te rate orm a 44 (teady) Δytem 0 Rate o net energy traner by eat, work, and ma From a ma balance, Rate o cange ternal, ketic, potential, etc.energie (0.05)(5 kg/) 0.5 kg/ (0.95)(5 kg/) 4.75 kg/ Notg tat te expanion proce i ientropic, te entalpie at tree tate are determed a ollow: P kj/kg kj/kg K (able A - 6) 4 MPa 5 kg/ MPa 0.7 MPa 50 Steam turbe P 4 MPa kj/kg K 979. kj/kg (able A - 6) P Subtitutg, W kj/kg K 68 kw 09. kj/kg (able A - 6) (5 kg/)(979. kj/kg) (0.5 kg/)(09. kj/kg) (4.75 kg/)(68.4 kj/kg) PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

5 An adiabatic pump i ued to compre aturated liquid water a reverible manner. e work put i to be determed by dierent approace. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Heat traner to or rom te luid i negligible. Analyi e propertie o water at te let and exit o te pump are (able A-4 troug A-6) 9.8 kj/kg P kj/kg x 0 v m /kg P 5 MPa v kj/kg m (a) Ug te entropy data rom te compreed liquid water table w P /kg kj/kg (b) Ug let peciic volume and preure value w v ( P P ) ( m /kg)(5,000 0) 5.4 kj/kg P rror 0.% (b) Ug average peciic volume and preure value [ / ( ) m /kg](5,000 0) 5.0 kj/kg w v ( P P ) P avg rror 0% 0 5 MPa pump Dicuion e reult ow tat any o te metod may be ued to calculate reverible pump work. PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

6 Nitro i compreed an adiabatic compreor. e mimum work put i to be determed. Aumption i i a teady-low proce ce tere i no cange wit time. e proce i adiabatic, and tu tere i no eat traner. Nitro i an ideal ga wit contant peciic eat. Propertie e propertie o nitro at an anticipated average temperature o 400 K are c p.044 kj/kg K and k.97 (able A-b). Analyi ere i only one let and one exit, and tu m. We take te compreor a te ytem, wic i a control volume ce ma croe te boundary. e energy balance or ti teadylow ytem can be expreed te rate orm a 44 (teady) Δytem 0 Rate o net energy traner by eat, work, and ma m + Rate o cange ternal, ketic, potential, etc.energie m ( ) For te mimum work put to te compreor, te proce mut be reverible a well a adiabatic (i.e., ientropic). i beg te cae, te exit temperature will be 600 Nitro compreor ( k ) / k 0.97 /.97 P 600 (0 K) P K 0 Subtitutg to te energy balance equation give w p c ( ) (.044 kj/kg K)(479 0)K 84 kj/kg PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

7 Steam i expanded an adiabatic turbe wit an ientropic eiciency o 0.9. e power put o te turbe i to be determed. Aumption i i a teady-low proce ce tere i no cange wit time. Ketic and potential energy cange are negligible. e device i adiabatic and tu eat traner i negligible. Analyi ere i only one let and one exit, and tu m. We take te actual turbe a te ytem, wic i a control volume ce ma croe te boundary. e energy balance or ti teadylow ytem can be expreed te rate orm a 44 (teady) Δytem 0 Rate o net energy traner by eat, work, and ma a, Rate o cange ternal, ketic, potential, etc.energie m a, ( + m From te team table (able A-4 troug A-6), P MPa 400 P 0.7 kj/kg x 6.95 kj/kg K g + x ) (ce Δke Δpe 0) (0.876)(5.) 5.7 kj/kg g e actual power put may be determed by multiplyg te ientropic power put wit te ientropic eiciency. en, a, η η, ( (0.9)( kg/)(.7 5.7)kJ/kg 649 kw ) P MPa 400 Steam turbe η 9% P 0 PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

8 Steam enter an adiabatic turbe at a peciied tate, and leave at a peciied tate. e ma low rate o te team and te ientropic eiciency are to be determed. Aumption i i a teady-low proce ce tere i no cange wit time. Potential energy cange are negligible. e device i adiabatic and tu eat traner i negligible. Analyi (a) From te team table (able A-4 and A-6), P 7 MPa 600 P kj/kg kj/kg K a 780. kj/kg ere i only one let and one exit, and tu. We take te actual turbe a te ytem, wic i a control volume ce ma croe te boundary. e energy balance or ti teady-low ytem can be expreed te rate orm a 44 (teady) Δytem 0 Rate o net energy traner by eat, work, and ma ( + V Rate o cange ternal, ketic, potential, etc.energie / ) a, 4444 a, + ( + V V + /) V (ce Δpe 0) Subtitutg, te ma low rate o te team i determed to be (40 m/) 6000 kj/ kg/ (80 m/) kj/kg 000 m / (b) e ientropic exit entalpy o te team and te power put o te ientropic turbe are and P 50,, x 0.98 g x g ( + {( V V )/ } ) ( 6.95 kg/) 874 kw ( 0.98)( 04.7) 467. kj/kg (40 m/) (80 m/) en te ientropic eiciency o te turbe become a 6000 kw η % 874 kw kj/kg 000 m / H O 6 MW PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

9 D S Rerigerant-4a enter an adiabatic compreor wit an ientropic eiciency o 0.80 at a peciied tate wit a peciied volume low rate, and leave at a peciied preure. e compreor exit temperature and power put to te compreor are to be determed. Aumption i i a teady-low proce ce tere i no cange wit time. Ketic and potential energy cange are negligible. e device i adiabatic and tu eat traner i negligible. Analyi (a) From te rerigerant table (able A- troug A-), P 0 g at. vapor v v P MPa g@0 8. kj/kg From te ientropic eiciency relation, u, η P a a a a MPa 9.6 kj/kg a 6.97 kj/kg kj/kg K m /kg (b) e ma low rate o te rerigerant i determed rom V m v ( )/η ( ) 0./60 m / kg/ 0.6 m /kg / kj/kg ere i only one let and one exit, and tu. We take te actual compreor a te ytem, wic i a control volume ce ma croe te boundary. e energy balance or ti teady-low ytem can be expreed a 44 (teady) Δytem 0 Rate o net energy traner by eat, work, and ma a, a, Rate o cange ternal, ketic, potential, etc.energie + m m ( 4444 (ce Δke Δpe 0) ) Subtitutg, te power put to te compreor become, W a, ( kg/)( ).70 kw kj/kg R-4a η 80% 0. m /m PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

10 old water i eated by ot water a eat excanger. e rate o eat traner and te rate o entropy eration wit te eat excanger are to be determed. Aumption Steady operatg condition exit. e eat excanger i well-ulated o tat eat lo to te urroundg i negligible and tu eat traner rom te ot luid i equal to te eat traner to te cold luid. ange te ketic and potential energie o luid tream are negligible. 4 Fluid propertie are contant. Propertie e peciic eat o cold and ot water are given to be 4.8 and 4.9 kj/kg., repectively. Analyi We take te cold water tube a te ytem, wic i a control volume. e energy balance or ti teady-low ytem can be expreed te rate orm a 44 Rate o net energy traner by eat, work, and ma + m Rate o cange ternal, ketic, potential, etc.energie m mc ( 0 (teady) Δytem 4444 p (ce Δke Δpe 0) ) 0 en te rate o eat traner to te cold water ti eat excanger become [ mc ( )] cold water (0.5 kg/)(4.8 kj/kg. )(45 5 ).5 kw p Notg tat eat ga by te cold water i equal to te eat lo by te ot water, te let temperature o te ot water i determed to be.5 kw [ mc p( )] ot water mc ( kg/)(4.9 kj/kg. ) (b) e rate o entropy eration wit te eat excanger i determed by applyg te rate orm o te entropy balance on te entire eat excanger: 0 (teady) S S + S ΔS 44 ytem { 4444 cold Rate o net entropy traner by eat and ma + ot cold Rate o entropy eration + + S 4 ot + S 4 S 0 0 p Rate o cange o entropy (ce Q 0) cold ( ) + ot ( 4 ) Notg tat bot luid tream are liquid (compreible ubtance), te rate o entropy eration i determed to be S cold cp ln + ot 4 cp ln Hot water 00 kg/ (0.5 kg/)(4.8 kj/kg.k)ln + ( kg/)(4.9 kj/kg.k)ln kw/k old water kg/ PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

11 In an ice-makg plant, water i rozen by evaporatg aturated R-4a liquid. e rate o entropy eration i to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi We take te control volume ormed by te R-4a evaporator wit a gle let and gle exit a te ytem. e rate o entropy eration wit ti evaporator durg ti proce can be determed by applyg te rate orm o te entropy balance on te ytem. e entropy balance or ti teady-low ytem can be expreed a S S 44 Rate o net entropy traner by eat and ma + + w S { Rate o entropy eration + S S S 0 (teady) S Δ ytem Rate o cange o entropy R ( ) w R g e propertie o te rerigerant are (able A-) kj/kg kj/kg K 0 w e rate o tat mut be removed rom te water order to reeze it at a rate o 4000 kg/ i Q w (4000 / 600 kg/)(.7 kj/kg) 70.8 kw i were te eat o uion o water at atm i.7 kj/kg. e ma low rate o R-4a i 70.8 kj/ R.800 kg/ kj/kg g R-4a 0 Q 0 at. vapor Subtitutg, S R g w 70.8 kw (.800 kg/)(0.786 kj/kg K) kw/k 7 K PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

12 Steam expand a turbe rom a peciied tate to anoter peciied tate. e rate o entropy eration durg ti proce i to be determed. Aumption i i a teady-low proce ce tere i no cange wit time. Ketic and potential energy cange are negligible. Propertie From te team table (able A-4 troug 6) P 6 MPa 450 P 0 at. vapor 0.9 kj/kg 6.79 kj/kg K kj/kg kj/kg K Analyi ere i only one let and one exit, and tu. We take te turbe a te ytem, wic i a control volume ce ma croe te boundary. e energy balance or ti teady-low ytem can be expreed te rate orm a Subtitutg, 44 (teady) Δytem 0 Rate o net energy traner by eat, work, and ma m Rate o cange ternal, ketic, potential, etc.energie m ( ) Q (5,000/600 kg/)( )kJ/kg 4000 kj/ 89. kj/ e rate o total entropy eration durg ti proce i determed by applyg te entropy balance on an extended ytem tat clude te turbe and it immediate urroundg o tat te boundary temperature o te extended ytem i 5 at all time. It give 0 S S + S ΔS ytem 0 44 { 44 Rate o net entropy traner by eat and ma m m Rate o entropy eration b,urr + S Rate o cange o entropy 0 P 6 MPa 450 SAM URBIN P 0 at. vapor 4 MW Subtitutg, te rate o entropy eration durg ti proce i determed to be S ( ) + ( 5,000/600 kg/)( ) b,urr 89. kw kj/kg K + 98 K.0 kw/k PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

13 Liquid water i eated a camber by mixg it wit upereated team. For a peciied mixg temperature, te ma low rate o te team and te rate o entropy eration are to be determed. Aumption i i a teady-low proce ce tere i no cange wit time. Ketic and potential energy cange are negligible. ere are no work teraction. Propertie Notg tat < 00 0., te cold water and te exit mixture tream exit a a compreed liquid, wic can be approximated a a aturated liquid at te given temperature. From able A-4 troug A-6, 00 kj/m P kj/kg 0 P P kj/kg 7.80 kj/kg kj/kg K o 5.8 kj/kg 0.8 kj/kg K Analyi (a) We take te mixg camber a te ytem, wic i a control volume. e ma and energy balance or ti teady-low ytem can be expreed te rate orm a (teady) Ma balance: m Δ ytem 0 + nergy balance: 44 (teady) Δytem 0 Rate o net energy traner by eat, work, and ma + Rate o cange ternal, ketic, potential, etc.energie ombg te two relation give + ( + ) ( ) + ( ) Solvg or m and ubtitutg, te ma low rate o te upereated team i determed to be Alo, ( ) (00/60kJ/) (.5 kg/)( ) m kg/ ( )kJ/kg kj/kg 0.66 kg/ (b) e rate o total entropy eration durg ti proce i determed by applyg te entropy balance on an extended ytem tat clude te mixg camber and it immediate urroundg o tat te boundary temperature o te extended ytem i 5 at all time. It give 0 S S + S ΔS ytem 0 44 { 44 Rate o net entropy traner by eat and ma + Rate o entropy eration b,urr + S Rate o cange o entropy 0 Subtitutg, te rate o entropy eration durg ti proce i determed to be S + 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 0.5 kg/ 50 MIXING HAMBR PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

14 An ulated rigid tank i connected to a piton-cylder device wit zero clearance tat i mataed at contant preure. A valve i opened, and ome team te tank i allowed to low to te cylder. e al temperature te tank and te cylder are to be determed. Aumption Bot te tank and cylder are well-ulated and tu eat traner i negligible. e water tat rema te tank underwent a reverible adiabatic proce. e termal energy tored te tank and cylder temelve i negligible. 4 e ytem i tationary and tu ketic and potential energy cange are negligible. Analyi (a) e team tank A undergoe a reverible, adiabatic proce, and tu. From te team table (able A-4 troug A-6), v v g P 500 u u at. vapor P 50 v ( at. mixture), A g@500 v u, g@500 + x u m /kg kj/kg kj/kg K, A x v + x, A g, A e itial and te al mae tank A are u, m m, A, B V A v m, A, A 0.4 m.067 kg m /kg m, A, A, A kg (b) e boundary work done durg ti proce i at@ (0.905)( ).0789 m u g g ( V, B ) PB m, B B W b, PdV PB 0 v, akg te content o bot te tank and te cylder to be te ytem, te energy balance or ti cloed ytem can be expreed a or, u, 44 Net energy traner by eat, work, and ma P m B, B v W, B Δytem 44 ange ternal, ketic, potential, etc.energie b, ΔU ( ΔU ) A + ( ΔU ) B Wb, + ( ΔU ) A + ( ΔU ) B 0 ( mu mu ) A + ( mu ) B 0 m + ( m u m u ) 0 +, B, B A (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, 467. and g 69. kj/kg. u at te al tate, te cylder will conta a aturated liquid-vapor mixture ce < < g. ereore,.5, B at@50 /kg Sat. vapor m 50 PROPRIARY MARIAL. 008 e McGraw-Hill ompanie, Inc. Limited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it wit permiion.

1 = The rate at which the entropy of the high temperature reservoir changes, according to the definition of the entropy, is

1 = The rate at which the entropy of the high temperature reservoir changes, according to the definition of the entropy, is 8-7 8-9 A reverible eat um wit eciied reervoir temerature i conidered. e entroy cange o two reervoir i to be calculated and it i to be determed i ti eat um atiie te creae entroy rcile. Aumtion e eat um