4-93 RT RT. He PV n = C = = Then the boundary work for this polytropic process can be determined from. n =

Transcription

1 - A cylder i itially filled it eliu ga at a ecified tate. Heliu i creed lytrically t a ecified teerature and reure. e eat tranfer durg te rce i t be detered. Autin Heliu i an ideal ga it cntant ecific eat. e cylder i tatinary and tu te ketic and tential energy cange are negligible. e teral energy tred te cylder itelf i negligible. e crein r exanin rce i quai-equilibriu. rertie e ga cntant f eliu i R.79 ka. /kg.k (able A-. Al, c v. kj/kg.k (able A-. Analyi e a f eliu and te exnent n are detered t be V R n V V R R V ( ka(. (.79 ka /kg K( 9 K n V V V. kg K ka V V. 9 K ka n.. n. en te bundary rk fr ti lytric rce can be detered fr W b, ( V V R dv n n (. kg(.79 kj/kg K( 9K 7.. kj n. He V n We take te cntent f te cylder a te yte. i i a cled yte ce n a enter r leave. akg te directin f eat tranfer t be t te cylder, te energy balance fr ti tatinary cled yte can be exreed a Subtitutg, E E Net energy tranfer by eat, rk, and a Q + W b, Q ange ternal, ketic, tential, etc.energie U ( u ( u c ( v Eyte u W u b, W Q (. kg(. kj/kg K( - 9K - (7. kj -. kj e negative ign dicate tat eat i lt fr te yte. b, Q -9 RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

2 - A ell-ulated r i eated by a tea radiatr, and te ar air i ditributed by a fan. e average teerature te r after i t be detered. Autin Air i an ideal ga it cntant ecific eat at r teerature. e ketic and tential energy cange are negligible. e air reure te r rea cntant and tu te air exand a it i eated, and e ar air ecae. rertie e ga cntant f air i R.87 ka. /kg.k (able A-. Al, c. kj/kg.k fr air at r teerature (able A-. Analyi We firt take te radiatr a te yte. i i a cled yte ce n a enter r leave. e energy balance fr ti cled yte can be exreed a E E Net energy tranfer by eat, rk, and a Q Q ange ternal, ketic, tential, etc.energie U ( u ( u Eyte u u (cew KE E Ug data fr te tea table (able A- trug A-, e rertie are detered t be ka v.89 /kg u. kj/kg ka v f., ( v v u 7., u 88. kj/kg x u Subtitutg, v v f v u f V..9 kg v.89 /kg f fg + x u v.9 /kg fg g fg kj/kg Q (.9 kg(. 78.7kJ/kg.8 kj e vlue and te a f te air te r are V 8 and V ( ka( 8 (.87 ka /kg K( 8 K air R e aunt f fan rk dne i W fan, W& fan, t (. kj/( kj 98. kg Stea radiatr We n take te air te r a te yte. e energy balance fr ti cled yte i exreed a Q + W fan, Q E E W + W b, fan, E U yte H c ( ce te bundary rk and U cbe t H fr a cntant reure exanin r crein rce. It can al be exreed a Subtitutg, ic yield Q & + W & t c ( ( fan,,avg. (.8 kj + ( kj (98. kg(. kj/kg ( - erefre, te air teerature te r rie fr t.. - RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

3 -9 Water i t be eated teadily fr t by an electrical reitr ide an ulated ie. e er ratg f te reitance eater and te average velcity f te ater are t be detered. Autin i i a teady-fl rce ce tere i n cange it tie at any t it te yte and tu V and EV. Water i an creible ubtance it cntant ecific eat. e ketic and tential energy cange are negligible, ke e. e ie i ulated and tu te eat le are negligible. rertie e denity and ecific eat f ater at r teerature are ρ kg/ and c.8 kj/kg (able A-. Analyi (a We take te ie a te yte. i i a cntrl vlue ce a cre te yte bundary durg te rce. Al, tere i nly ne let and ne exit and tu & & &. e energy balance fr ti teady-fl yte can be exreed te rate fr a erefre, E& E& Rate f net energy tranfer by eat, rk, and a W& e, E& W& e, Rate f cange ternal, ketic, tential, etc.energie E& + & & (teady E& yte & ( (ce Q& & [ c( e a fl rate f ater trug te ie i & ρv & ( kg/ (. / ke e + v kg/ ] c & (b e average velcity f ater trug te ie i detered fr ( ( W & e, c & (/ kg/(.8 kj/kg ( 7. kw V & V& V A πr. /. / π(. WAER L/ D c W e -9 RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

4 -9 e turbcarger f an ternal cbutin enge cnitg f a turbe, a crer, and an aftercler i cnidered. e teerature f te air at te crer let and te iu fl rate f abient air are t be detered. Autin All rcee are teady ce tere i n cange it tie. Ketic and tential energy cange are negligible. Air rertie are ued fr exaut gae. Air i an ideal ga it cntant ecific eat. e ecanical efficiency beteen te turbe and te crer i %. All device are adiabatic. 7 e lcal ateric reure i ka. rertie e cntant reure ecific eat f exaut gae, ar air, and cld abient air are taken t be c.,.8, and. kj/kg K, reectively (able A-b. Analyi (a An energy balance n turbe give W& & c urbe Exaut gae ld air ( (. kg/(. kj/kg K( K. kw ex,ex ex, ex, Air rer Aftercler - i i al te er ut t te crer ce te ecanical efficiency beteen te turbe and te crer i aued t be %. An energy balance n te crer give te air teerature at te crer let W& & a c,a ( a, a,. kw (.8 kg/(.8 kj/kg K( K (b An energy balance n te aftercler give te a fl rate f cld abient air & c a,a ( a, a, & c ca,ca (.8 kg/(.8 kj/kg (8. 8 & ca (. kj/kg ( &.kg/ a, ca e vlu e fl rate ay be detered if e firt calculate ecific vlue f cld abient air at te let f aftercler. at i, v V& R ( ca.87 kj/kg K( + 7 K ka ( ca,.89 /kg a, 8. & (.kg/(.89 /kg.9 /.9 L/ ca v ca ca, RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

5 7- A t ater trea i ixed it a cld ater trea. Fr a ecified ixture teerature, te a fl rate f cld ater trea and te rate f entry eratin are t be detered. Autin Steady eratg cnditin exit. e ixg caber i ell-ulated tat eat l t te urrundg i negligible. ange te ketic and tential energie f fluid trea are negligible. rertie Ntg tat < ka., te ater all tree trea exit a a creed liquid, ic can be arxiated a a aturated liquid at te given teerature. u fr able A-, ka 9.7 kj/kg 7.9 kj/kg K ka @ 8.9 kj/kg.9 kj/kg K 7.9 kj/kg.99 kj/kg K Analyi (a We take te ixg caber a te yte, ic i a cntrl vlue. e a and energy balance fr ti teady-fl yte can be exreed te rate fr a Energy balance: a k f (teady Ma balance: E& & & yte & + & & E E & & Rate f net energy tranfer by eat, rk, and a E & & + & & bg te t relatin give (teady Eyte & Rate f cange ternal, ketic, tential, etc. energie E& ( & & & & + + (ce Q& W& ke e 7. kg/ Slvg fr & and ubtitutg, te a fl rate f cld ater trea i detered t be Al, & ( kJ/kg & (. kg/.8 kg/ ( kJ/kg & & + & kg/ H O ka (b Ntg tat te ixg caber i adiabatic and tu tere i n eat tranfer t te urrundg, te entry balance f te teady-fl yte (te ixg caber can be exreed a S S & & Rate f net entry tranfer by eat and a & + & + S& { Rate f entry eratin & + S& S& yte Subtitutg, te ttal rate f entry eratin durg ti rce bece S & & & & Rate f cange f entry ( 8.8 kg/(.99 kj/kg K (.8 kg/(.9 kj/kg K (. kg/(. kw/k.9 kj/kg K 7-8 RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

6 7-9 Air i exanded by an adiabatic turbe it an ientric efficiency f 8%. e let teerature, te rk rduced, and te entry eratin are t be detered. Autin i i a teady-fl rce ce tere i n cange it tie. Ketic and tential energy cange are negligible. e device i adiabatic and tu eat tranfer i negligible. Air i an ideal ga it cntant ecific eat. rertie e rertie f air at te anticiated average teerature f K are c. kj/kg and k.9 (able A-b. Al, R.87 kj/kg K (able A-a. Analyi We take te turbe a te yte, ic i a cntrl vlue ce a cre te bundary. Ntg tat ne fluid trea enter and leave te turbe, te energy balance fr ti teady-fl yte can be exreed te rate fr a E E & & Rate f net energy tranfer by eat, rk, and a W& E& E& & W& a, Rate f cange ternal, ketic, tential, etc. energie a, & ( e ientric exit teerature i (teady Eyte & + & c & (ce Q& ke e (. Ma Air turbe ka Ma 7- ( k / k.9/.9 ka ( + 7 K ka 9. K. Ma Fr te defitin f te ientric efficiency, η η c (.9(. kj/kg K(7 9.K 7. kj/kg a,, ( e actual exit teerature i ten a, c ( a a a c, a c, 7. kj/kg 7 K 8.8 K. kj/kg K e rate f entry eratin te turbe i detered by alyg te rate fr f te entry balance n te turbe: S S & & Rate f net entry tranfer by eat and a & & S { & Rate f entry eratin en, fr te entry cange relatin f an ideal ga, c + ln + S& S& R ln (teady Syte & & ( Rate f cange f entry (ce Q& 8.8 K (. kj/kg Kln (.87 kj/kg Kln 7 K.9 kj/kg K ka ka RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

7 e feedater f a tea er lant i reeated ug tea extracted fr te turbe. e rati f te a fl rate f te extracted tea t te feedater and entry eratin er unit a f feedater are t be detered. Autin i i a teady-fl rce ce tere i n cange it tie. Ketic and tential energy cange are negligible. Heat l fr te device t te urrundg i negligible. rertie e rertie f tea and feedater are (able A- trug A- Ma 88. kj/kg.9 kj/kg K Ma at. liquid. Ma 7. kj/kg kj/kg. Ma kj/kg K Ma Ma.8 kj/kg 7 K 79.8 kj/kg.7 kj/kg K Stea fr turbe Ma Feedater. Ma Analyi (a We take te eat excanger a te yte, ic i a cntrl vlue. e a and energy balance fr ti teady-fl yte can be exreed te rate fr a fll: Ma balance (fr eac fluid trea: at. liquid (teady yte & & & & & & & & and & & & Energy balance (fr te eat excanger: E & & & (teady E Eyte Rate f net energy tranfer by eat, rk, and a E & Rate f cange ternal, ketic, tential, etc.energie E& & + & & & + bg te t, & ( & ( Dividg by & f and ubtitutg, f (ce Q & W & ke e f & & f ( ( kj/kg.7 kj/kg (b e ttal entry cange (r entry eratin durg ti rce er unit a f feedater can be detered fr an entry balance exreed te rate fr a & & S & & + & & S& { S + Syte Rate f net entry tranfer by eat and a Rate f entry eratin + S& & ( + & f ( + S& & Rate f cange f entry S& & f & & f ( + ( (.7(. 8. kj/k er kg f feedater.9 + (.7.78 RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

8 7- Water i eated fr t by an electric reitance eater laced te ater ie a it fl trug a eread teadily at a rate f L/. e electric er ut t te eater and te rate f entry eratin are t be detered. e reductin er ut and entry eratin a a reult f tallg a % efficient reeratr are al t be detered. Autin i i a teady-fl rce ce tere i n cange it tie at any t it te yte and tu V and EV. Water i an creible ubtance it cntant ecific eat. e ketic and tential energy cange are negligible, ke e. Heat le fr te ie are negligible. rertie e denity f ater i given t be ρ kg/l. e ecific eat f ater at r teerature i c.8 kj/kg (able A-. Analyi ( a We take te ie a te yte. i i a cntrl vlue ce a cre te yte bundary durg te rce. We berve tat tere i nly ne let and ne exit and tu & & &. en te energy balance fr ti teady-fl yte can be exreed te rate fr a ere Subtitutg, & & & (teady E & & E Eyte E E Rate f net energy tranfer by eat, rk, and a W& + & & e, W& e, Rate f cange ternal, ketic, tential, etc. energie & ( c & ( & ρv & kg/l L/ e, (ce ke e ( ( kg/ ( / kg/(.8 kj/kg ( 8.8 kw W & WAER e rate f entry eratin te eatg ectin durg ti rce i detered by alyg te entry balance n te eatg ectin. Ntg tat ti i a teady-fl rce and eat tranfer fr te eatg ectin i negligible, S S & & Rate f net entry tranfer by eat and a + S& { Rate f entry eratin & & + S& S& yte Rate f cange f entry S& & ( Ntg tat ater i an creible ubtance and ubtitutg, S & c & ln (b e energy recvered by te eat excanger i Q & & & ( / kg/(.8 kj/kg K ln. kj/k K 89 K (.( / kg/(.8 kj/kg ( 9 8. kj/ 8. kw aved ε Qax ε ax erefre, 8. kw le energy i needed ti cae, and te required electric er ti cae reduce t akg te cld ater trea te eat excanger a ur cntrl vlue (a teady-fl yte, te teerature at ic te cld ater leave te eat excanger and enter te electric reitance eatg ectin i detered fr Subtitutg, It yield W &, ne W&,ld Q& aved kw Q& c & ( c, 8 kj/ (/ kg/(.8 kj/kg ( c, c, 7-87 RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

9 c, 7..K 7-88 e rate f entry eratin te eatg ectin ti cae i detered iilarly t be S & ( / kg/(.8 kj/kg K ln. kj/k u te reductin te rate f entry eratin it te eatg ectin i S & c & ln reductin...7 kw/k K. K RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

10 8-8- Stea and R-a at te ae tate are cnidered. e fluid it te iger exergy cntent i t be identified. Autin Ketic and tential energy cange are negligible. Analyi e rertie f ater at te given tate and at te dead tate are 8 ka 8 u 9.7 kj/kg v.7 u u f v v f ka e exergy f tea i Fr R-a; Φ /kg.7 kj/kg. (able A - /kg.7 kj/kg K [ u u + ( v v ( ] (able A - (9.7.8kJ/kg + ( ka(.7. (kg (98 K(.7.7kJ/kg K.7 kj 8 ka 8 u 8.99 kj/kg v. u u f v v f ka Φ /kg kj/kg (able A -.88 /kg. kj/kg K [ u u + ( v v ( ] (able A - ( kJ/kg + ( ka(..88 (kg (98 K(.7.kJ/kg K. kj e tea can terefre a re rk tential tan te R-a. Stea kg 8 ka 8 kj /kg ka R-a kg 8 ka 8 kj /kg ka RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

11 8- A cylder i itially filled it R-a at a ecified tate. e refrigerant i cled and cndened at cntant reure. e exergy f te refrigerant at te itial and fal tate, and te exergy detryed durg ti rce are t be detered. Autin e ketic and tential energie are negligible. rertie Fr te refrigerant table (able A- trug A-, v.87 / kg.7 Ma u 7. kj/kg. kj/kg K v v f.7 Ma u 8. kj/kg v.78 / kg. Ma u.8 kj/kg. kj/kg K / kg.98 kj/kg K Analyi (a Fr te cled yte exergy relatin, {( u u ( + ( v } X Φ v ( kg{(7..8 kj/kg (97 K(.. kj/kg K R-a.7 Ma cnt. Q 8-7 and + ( ka( kj kj /kg ka {( u u ( + ( v } X Φ v ( kg{(8..8 kj/kg - (97 K(.98. kj/kg K } + ( ka( kj kj /kg ka (b e reverible rk ut, ic rereent te iu rk ut W rev, ti cae can be detered fr te exergy balance by ettg te exergy detructin equal t zer, X X Net exergy tranfer by eat,rk,anda detryed Exergy detructin (reverible X Xyte W rev, X ange exergy X } kj Ntg tat te rce vlve nly bundary rk, te ueful rk ut durg ti rce i ily te bundary rk exce f te rk dne by te urrundg air, W u, W W urr, ( ( v v W ( V V ( V V ( v v ( kg(7 - ka(.87.8 kj / kg ka. kj Kng bt te actual ueful and reverible rk ut, te exergy detructin r irreveribility tat i te difference beteen te t i detered fr it defitin t be X detryed I W W kj u, rev, RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

12 8- An ulated tank cnta O ga at a ecified reure and vlue. A addle-eel te tank tir te ga, and te reure and teerature f O rie. e actual addle-eel rk and te iu addle-eel rk by ic ti rce can be acclied are t be detered. Autin At ecified cnditin, O can be treated a an ideal ga it cntant ecific eat at te average teerature. e urrundg teerature i 98 K. rertie e ga cntant f O i.889 kj/kg K (able A- Analyi (a e itial and fal teerature f O are V ( ka(. 98. K R (. kg(.889 ka / kg K V R ( ka(. (. kg(.889 ka 7.9 K / kg K.. kg O ka W 8- avg v ( + / ( / 8 K c, avg.8 kj/kg K (able A-b e actual addle-eel rk dne i detered fr te energy balance n te O ga te tank, We take te cntent f te cylder a te yte. i i a cled yte ce n a enter r leave. e energy balance fr ti tatinary cled yte can be exreed a E E Net energy tranfer by eat, rk, and a W, Eyte ange ternal, ketic, tential, etc.energie U c ( v r W, (. kg(.8 kj/kg K( K 87. kj (b e iu addle-eel rk it ic ti rce can be acclied i te reverible rk, ic can be detered fr te exergy balance by ettg te exergy detructin equal t zer, (reverible X Xdetryed Xyte Wrev, X X X Net exergy tranfer by eat,rk,anda Exergy detructin ange exergy Subtitutg te cled yte exergy relatin, te reverible rk ut fr ti rce i detered t be W rev, c 7.7 kj ce [( u u ( + ( v v ] [ ( ( ] v,avg (. kg [(.8 kj/kg K( K (98.(. kj/kg K ] v 7.9 K cv,avg ln + R ln (.8 kj/kg K ln. kj/kg K v 98. K RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

13 8-9 arbn teel ball are t be annealed at a rate f / by eatg te firt and ten allg te t cl lly abient air at a ecified rate. e ttal rate f eat tranfer fr te ball t te abient air and te rate f exergy detructin due t ti eat tranfer are t be detered. Autin e teral rertie f te ball are cntant. ere are n cange ketic and tential energie. e ball are at a unifr teerature at te end f te rce. rertie e denity and ecific eat f te ball are given t be ρ 78 kg/ and c. kj/kg.. Analyi (a We take a gle ball a te yte. e energy balance fr ti cled yte can be exreed a E E Net energy tranfer by eat, rk, and a Q Q ange ternal, ketic, tential, etc. energie U ball c ( Eyte ( u u e aunt f eat tranfer fr a gle ball i πd π (.8 ρv ρ (78 kg/. kg Q c ( (.kg(. kj/kg. (9 78J en te ttal rate f eat tranfer fr te ball t te abient air bece Q & n& Q ( ball/ (.78kJ/ball 9 kj/ W ball.78kj (er ball (b e exergy detructin (r irreveribility can be detered fr it defitin X detryed S. e entry erated durg ti rce can be detered by alyg an entry balance n an extended yte tat clude te ball and it iediate urrundg tat te bundary teerature f te extended yte i at at all tie: ere S Subtitutg, S Net entry tranfer by eat and a Q + b S { Entry eratin + S Syte ange entry S Syte ( c yte ln S Q b + S yte + 7 (. kg(. kj/kg.kln. kj/k Q.78 kj S + Syte. kj/k. kj/k 8 K b en te rate f entry eratin bece S & S n& ball (er ball (. kj/k ball( ball/.7 kj/.k.7 kw/k 8- Fally, X & & detryed S (8 K(.7 kw/ K. kw W RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

14 8- Stea exand a turbe fr a ecified tate t anter ecified tate. e actual er ut f te turbe i given. e reverible er ut and te ecnd-la efficiency are t be detered. Autin i i a teady-fl rce ce tere i n cange it tie. tential energy cange i negligible. e teerature f te urrundg i given t be. rertie Fr te tea table (able A- trug A- Ma ka 8.8 kj/kg 7.9 kj/kg K 8. kj/kg 7.9 kj/kg K Analyi (b ere i nly ne let and ne exit, and tu & & &. We take te turbe a te yte, ic i a cntrl vlue ce a cre te bundary. e energy balance fr ti teady-fl yte can be exreed te rate fr a Subtitutg, E & & (teady E Eyte Rate f net energy tranfer by eat, rk, and a & ( + V E& W& / Rate f cange ternal, ketic, tential, etc. energie E& W& & + & ( & + V V + V / (8 / kj/ & &. kg/ ( / kj/kg / 8 / Ma SEAM ka / MW e reverible (r axiu er ut i detered fr te rate fr f te exergy balance alied n te turbe and ettg te exergy detructin ter equal t zer, X X & & Ratef net exergy tranfer by eat, rk,and a (reverible (teady X detryed X yte & & Ratef exergy detructin W& X& X& & ψ W& rev, Ratef cange f exergy rev, & ( ψ ψ & [( + & ψ ( ke e ] 8-9 Subtitutg, W & rev, W& & ( kw (. kg/(98 K( kj/kg K 88 kw (b e ecnd-la efficiency f a turbe i te rati f te actual rk ut t te reverible rk, W& η II W& rev, MW.88 MW 8.% Dicuin Nte tat.9% ercent f te rk tential f te tea i ated a it fl trug te turbe durg ti rce. RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

15 8- butin gae exand a turbe fr a ecified tate t anter ecified tate. e exergy f te gae at te let and te reverible rk ut f te turbe are t be detered. Autin i i a teady-fl rce ce tere i n cange it tie. tential energy cange are negligible. e teerature f te urrundg i given t be. e cbutin gae are ideal gae it cntant ecific eat. rertie e cntant reure ecific eat and te ecific eat rati are given t be c. kj/kg.k and k.. e ga cntant R i detered fr R c c c c / k c ( / k (. kj/kg K( /.. kj/kg K v 8- Analyi (a e exergy f te gae at te turbe let i ily te fl exergy, ere u, V ψ ( + + gz c ln R ln 7 K (. kj/kg Kln (. kj/kg Kln 98 K. kj/kg K 8 ka ka 8 ka 9 GAS URBINE ka ( / ψ (. kj/kg.k(9 (98 K(. kj/kg K + kj/kg / 7.8 kj/kg (b e reverible (r axiu rk ut i detered fr an exergy balance alied n te turbe and ettg te exergy detructin ter equal t zer, ere X X & & Ratef net exergy tranfer by eat,rk,anda (reverible (teady Xdetryed Xyte & & Ratef exergy detructin W& X& X& & ψ W& rev, Ratef cange f exergy rev, & ( ψ ψ & [( ( ke e + & ψ ] and V ke V ( / ( / kj/kg / c ln R ln 9 K ka (. kj/kg Kln (. kj/kg Kln 7 K 8 ka.99 kj/kg K 9. kj/kg en te reverible rk ut n a unit a bai bece rev, + ( ke c ( + ( ke (. kj/kg K(9 + (98 K(.99 kj/kg K 9. kj/kg.9 kj/kg RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

16 8-79 A rigid tank itially cnta aturated R-a var. e tank i cnnected t a uly le, and R-a i alled t enter te tank. e a f te R-a tat entered te tank and te exergy detryed durg ti rce are t be detered. Autin i i an unteady rce ce te cnditin it te device are cangg durg te rce, but it can be analyzed a a unifr-fl rce ce te tate f fluid at te let rea cntant. Ketic and tential energie are negligible. ere are n rk teractin vlved. e directin f eat tranfer i t te tank (ill be verified. rertie e rertie f refrigerant are (able A- trug A- 8-7 v v g. Ma u u g at. Ma Ma.7.8 kj/kg / kg.9 kj/kg K R-a. Ma v v f. Ma u u f at. liquid i. Ma i i Ma Ma 9. kj/kg. kj/kg K.9.9 kj/kg / kg. kj/kg K R-a.. Ma Sat. var Analyi We take te tank a te yte, ic i a cntrl vlue. Ntg tat te icrcic energie f flg and nnflg fluid are rereented by entaly and ternal energy u, reectively, te a and energy balance fr ti unifr-fl yte can be exreed a Ma balance: i Energy balance: E E Net energy tranfer by eat, rk, and a Q + i i yte ange ternal, ketic, tential, etc.energie u Eyte u (a e itial and te fal ae te tank are V..98 kg v.7 /kg V v en fr te a balance i. 9. kg.9 /kg kg (ce W ke e e eat tranfer durg ti rce i detered fr te energy balance t be Q + u u (. kg (9. kj/kg + (9.(.9 kj/kg (.98 kg( 7 kj i i.8 kj/kg Q RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

17 (b e exergy detryed durg a rce can be detered fr an exergy balance r directly fr it defitin X S. e entry eratin S ti cae i detered fr an entry balance n an detryed extended yte tat clude te tank and it iediate urrundg tat te bundary teerature f te extended yte i te urrundg teerature urr at all tie. It give S S Net entry tranfer by eat and a Q b, i detered t be X detryed S { Entry eratin + + S i + i S 8. kj Syte ange entry S S (8 K 9. tank ( tank Q i i i i Q Subtitutg, te exergy detructin [ (7 kj/(8 K ] 8-8 RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

18 8-8 Liquid ater i eated a caber by ixg it it uereated tea. Fr a ecified ixg teerature, te a fl rate f te tea and te rate f exergy detructin are t be detered. Autin i i a teady-fl rce ce tere i n cange it tie. Ketic and tential energy cange are negligible. ere are n rk teractin. rertie Ntg tat < ka., te cld ater and te exit ixture trea exit a a creed liquid, ic can be arxiated a a aturated liquid at te given teerature. Fr able A- trug A-, ka kj/kg.7 kj/kg K kj/ 8-77 ka ka 8 f 87. kj/kg 7.8 kj/kg kj/kg.7 kj/kg K Analyi (a We take te ixg caber a te yte, ic i a cntrl vlue. e a and energy balance fr ti teady-fl yte can be exreed te rate fr a kg/ MIXING HAMBER ka 8 (teady Ma balance: & & & yte & + & & Energy balance: E & & (teady E Eyte Rate f net energy tranfer by eat, rk, and a E& & + & Rate f cange ternal, ketic, tential, etc.energie E& Q& & + & &Q & + & & + & & + & bg te t relatin give ( ( ( & Q& & ( (/ kj/ ( kg/(.98. ( 87.. kj/kg Slvg fr and ubtitutg, te a fl rate f te uereated tea i detered t be Al, & & & + & kg/ kj/kg.9 kg/ (b e exergy detryed durg a rce can be detered fr an exergy balance r directly fr it defitin X S ere te entry eratin S i detered fr an entry balance n an extended detryed yte tat clude te ixg caber and it iediate urrundg. It give S S & & Rate f net entry tranfer by eat and a & + & & + Q& b,urr S& { Rate f entry eratin + S& S& yte Rate f cange f entry S& Subtitutg, te exergy detructin i detered t be X& detryed & & & Q& + Q& S & & + & & b, urr (98 K( / 98kW/K kw RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

19 8-88 Water i eated by t il a eat excanger. e let teerature f te il and te rate f exergy detructin it te eat excanger are t be detered. Autin Steady eratg cnditin exit. e eat excanger i ell-ulated tat eat l t te urrundg i negligible and tu eat tranfer fr te t fluid i equal t te eat tranfer t te cld fluid. ange te ketic and tential energie f fluid trea are negligible. Fluid rertie are cntant. rertie e ecific eat f ater and il are given t be.8 and. kj/kg., reectively. Analyi We take te cld ater tube a te yte, ic i a cntrl vlue. e energy balance fr ti teady-fl yte can be exreed te rate fr a E E & & Rate f net energy tranfer by eat, rk, and a Q& E& + & Q& Rate f cange ternal, ketic, tential, etc. energie E& & c & (teady Eyte & (ce ke e ( en te rate f eat tranfer t te cld ater ti eat excanger bece Q& [ c & ( ] ater 7 Water. kg/ (. kg/(.8 kj/kg. (7 9. kw Oil 7 kg/ ( tube ae Ntg tat eat ga by te ater i equal t te eat l by te il, te let teerature f te t ater i detered fr Q& [ c & ( ] il Q& c & 9. kw 7 9. ( kg/(. kj/kg. (b e rate f entry eratin it te eat excanger i detered by alyg te rate fr f te entry balance n te entire eat excanger: & ater S S & & Rate f net entry tranfer by eat and a & + & + & il & & ater + & & il S& { Rate f entry eratin + S& + S& S& (teady S& yte & Rate f cange f entry (ce Q ater ( + & Ntg tat bt fluid trea are liquid (creible ubtance, te rate f entry eratin i detered t be S& & ater c ln + & il c ln (. kg/(.8 kj/kg.k ln + ( kg/(. kj/kg.k ln.7 kw/k e exergy detryed durg a rce can be detered fr an exergy balance r directly fr it defitin X S, detryed il ( 8-79 X & detryed S& (98 K(.7 kw/k 9 kw RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

20 8- Ht exaut gae leavg an ternal cbutin enge i t be ued t bta aturated tea an adiabatic eat excanger. e rate at ic te tea i btaed, te rate f exergy detructin, and te ecnd-la efficiency are t be detered. Autin Steady eratg cnditin exit. Ketic and tential energy cange are negligible. Air rertie are ued fr exaut gae. reure dr te eat excanger are negligible. rertie e ga cntant f air i R.87 kjkg.k. e ecific eat f air at te average teerature f exaut gae ( K i c. kj/kg.k (able A-. Analyi (a We dente te let and exit tate f exaut gae by ( and ( and tat f te ater by ( and (. e rertie f ater are (able A- 8.9 kj/kg x.99 kj/kg.k 79. kj/kg x. kj/kg.k An energy balance n te eat excanger give & a + & & a + & & c & ( a ( Ex. ga ka Sat. va. (.8 kg/(. kj/kg ( & ( kJ/kg &.7 kg/ (b e ecific exergy cange f eac trea a it fl te eat excanger i Heat Excanger Water 8-9 a c ln ( + 7 K (.8 kg/(. kj/kg.kln.8 kj/kg.k ( + 7 K ψ c a ψ ( (. kj/kg. ( - ( + 7 K(-.8 kj/kg.k 9. kj/kg 9.9 kj/kg a ( ( kJ/kg ( + 7 K(..99kJ/kg.K e exergy detructin i detered fr an exergy balance n te eat excanger t be r X& X& det det & ψ + & a a 8.98 kw ψ (.8 kg/(-9. kj/kg + (.7 kg/(9.9 kj/kg 8.98 kw (c e ecnd-la efficiency fr a eat excanger ay be defed a te exergy creae f te cld fluid divided by te exergy decreae f te t fluid. at i, & ψ (.7 kg/(9.9 kj/kg ηii. & ψ (.8 kg/(-9. kj/kg a a RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

21 9-9 An ideal Ott cycle it air a te rkg fluid a a crein rati f 9.. e iget reure and teerature te cycle, te aunt f eat tranferred, te teral efficiency, and te ean effective reure are t be detered. Autin e air-tandard autin are alicable. Ketic and tential energy cange are negligible. Air i an ideal ga it cntant ecific eat. rertie e rertie f air at r teerature are c. kj/kg K, c v.78 kj/kg K, R.87 kj/kg K, and k. (able A-. Analyi (a rce -: ientric crein. v v v v k rce -: ientric exanin. k ( 8 K( 9. v v v 9. v rce -: v cntant eat additin K. ( 8 K( 99 K 77.9 K 8 K ( 9. ( ka 8 ka Q Q v 9- (b v v 99 K ka 77.9 K V R ( ka(. (.87 ka /kg K( 8 K ( 8 7 ka.788 kg ( u c ( (.788 kg(.78 kj/kg K( K.9 kj Q u v (c rce -: v cntant eat rejectin. Q v ( (.788 kg(.78 kj/kg K( 8 8 K. kj ( u u c W net Q Q.9.. kj η t W Q net,. kj 9.%.9 kj (d V ax V V r Wnet, Wnet, ME V V V ( / r. kj (. ( /9. ka kj ka RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

22 9- A gale enge erate n an Ott cycle. e crein and exanin rcee are deled a lytric. e teerature at te end f exanin rce, te net rk ut, te teral efficiency, te ean effective reure, te enge eed fr a given net er, and te ecific fuel cnutin are t be detered. Autin e air-tandard autin are alicable. Ketic and tential energy cange are negligible. Air i an ideal ga it cntant ecific eat. rertie e rertie f air at 8 K are c. kj/kg K, c v.8 kj/kg K, R.87 kj/kg K, and k.9 (able A-b. Analyi (a rce -: lytric crein v v n n v v ( K(.-. K. ( ka( 8 ka R( (.87 kj/kg K(. K. kj/kg n. rce -: cntant vlue eat additin 8 ka 8 ka (. K K ( q u u cv (.8 kj/kg K(. K kj/kg rce -: lytric exanin. v v n.- ( K 98 K n v. v ( 8 ka. ka R( (.87 kj/kg K(98 K kj/kg n. rce -: cntant vlue eat rejectin. (b e net rk ut and te teral efficiency are net,. 79 kj/kg net, 79 kj/kg η t. 9 9.% q kj/kg (c e ean effective reure i detered a fll R v (.87 ka /kg K( K ka v ax v v r net, net, ME v v v ( / r 79 kj/kg.8897 (.8897 /kg( / /kg v ka kj ax Q 98 ka Q V 9-9 RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

23 9- (d e clearance vlue and te ttal vlue f te enge at te begng f crein rce (tate are r V Vc + V d c Vc c Vc +. V. V V c + Vd e ttal a cntaed te cylder i t V R ( ka/.7 (.87 ka /kg K( K e enge eed fr a net er ut f kw i W n& & t net net.978 kg kj/ ( rev/cycle 8 rev/ (.978 kg(79 kj/kg cycle Nte tat tere are t revlutin ne cycle fur-trke enge. (e e a f fuel burned durg ne cycle i (.978 kg a t f AF f Fally, te ecific fuel cnutin i f f f f. kg fc f t net. kg (.978 kg(79 kj/kg g kj 7 g/kw kg kw RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

24 9- An ideal dual cycle a a crein rati f and cutff rati f.. e teral efficiency, aunt f eat added, and te axiu ga reure and teerature are t be detered. Autin e air-tandard autin are alicable. Ketic and tential energy cange are negligible. Air i an ideal ga it cntant ecific eat. rertie e rertie f air at r teerature are c. kj/kg K, c v.78 kj/kg K, R.87 kj/kg K, and k. (able A-a. Analyi e ecific vlue f te air at te tart f te crein i v R (.87 ka /kg K(9 K. 8 ka and te ecific vlue at te end f te crein i v v /kg.78 r. e reure at te end f te crein i v v k r and te axiu reure i x k (8 ka e teerature at te end f te crein i and /kg. ( 9 ka r (.(9 ka 89 ka k v k r (9 K v x 89 ka (8. K 9 ka Fr te defitin f cutff rati e reag tate teerature are ten. ( 8. K K v r v r v (.(.78 /kg.9 c x x c v.9 ( K K v x.78 v v k.9 ( K.. 7. K Alyg te firt la and rk exrein t te eat additin rcee give q c v e eat rejected i ( x + c ( x (.78 kj/kg K( 8.K + (. kj/kg K( K. kj/kg q v c ( (.78 kj/kg K(7. 9K 97. kj/kg /kg /kg x q v q 9- en, η t q q 97. kj/kg.. kj/kg RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

25 9- A ix-cylder crein ignitin enge erate n te ideal Dieel cycle. e axiu teerature te cycle, te cutff rati, te net rk ut er cycle, te teral efficiency, te ean effective reure, te net er ut, and te ecific fuel cnutin are t be detered. Autin e air-tandard autin are alicable. Ketic and tential energy cange are negligible. Air i an ideal ga it cntant ecific eat. rertie e rertie f air at 8 K are c. kj/kg K, c v.8 kj/kg K, R.87 kj/kg K, and k.9 (able A-b. Analyi (a rce -: Ientric crein 9-8 k v.9- ( K( 9 v k v v 9. K.9 ( 9 ka( 9 ka e clearance vlue and te ttal vlue f te enge at te begng f crein rce (tate are Q V c Vc + V d r V c.778 V V + V c d Vc +. 9 V e ttal a cntaed te cylder i V R (9 ka(.78 (.87 ka /kg K( K e a f fuel burned durg ne cycle i AF a f rce -: cntant reure eat additin Q v f f c.88 kg (.88 kg f 8 f. kg Q f q η (. kg(, kj/kg(.98 e cutff rati i HV c f.7 kj c (.7 kj (.88 kg(.8 kj/kg.k( 9. K K β K 9. K. Q (b V V r 9 (.( V βv V V RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

26 9-9 rce -: ientric exanin. k V.99 ( K V.78 k V V rce - : cntant vue eat rejectin..99 ( ka.9 ka K ( (.88 kg (.8 kj/kg K( 8 K. kj Q cv e net rk ut and te teral efficiency are W net, Q Q.7..7 kj Wnet,.7 kj η t %.7 kj Q (c e ean effective reure i detered t be W net,.7 kj ME V V ( (d e er fr enge eed f 7 r i W& net W net ka kj 87 ka n& 7 (rev/ (.7 kj/cycle 9. kw ( rev/cycle Nte tat tere are t revlutin ne cycle fur-trke enge. (e Fally, te ecific fuel cnutin i fc f W net. kg g kj g/kw.7 kj/kg kg kw RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

27 9-9 A ile Braytn cycle it air a te rkg fluid erate beteen te ecified teerature and reure liit. e effect f nn-ientric crer and turbe n te back-rk rati i t be cared. Autin Steady eratg cnditin exit. e air-tandard autin are alicable. Ketic and tential energy cange are negligible. Air i an ideal ga it cntant ecific eat. rertie e rertie f air at r teerature are c. kj/kg K and k. (able A-a. Analyi Fr te crein rce, ( k / k./. (88 K( 8.8 K η c c Fr te exanin rce, ( + ( η ( k / k./. (87 K K.9 9. K 87 K 88 K q q 9-9 η c ( c ( η ( 87 (.9( K e ientric and actual rk f crer and turbe are W, c ( (. kj/kg K(8.8 88K 99. kj/kg W c ( (. kj/kg K(8.9 88K. kj/kg W urb, c ( (. kj/kg K(87 9.K. kj/kg W urb c ( (. kj/kg K(87 7.K. kj/kg e back rk rati fr 9% efficient crer and ientric turbe cae i r b W W urb,. kj/kg.77. kj/kg e back rk rati fr 9% efficient turbe and ientric crer cae i r b W W, urb 99. kj/kg. kj/kg e t reult are alt identical..7 RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

28 9- A ga-turbe lant erate n te ile Braytn cycle. e net er ut, te back rk rati, and te teral efficiency are t be detered. Autin e air-tandard autin are alicable. Ketic and tential energy cange are negligible. Air i an ideal ga it variable ecific eat. rertie e ga cntant f air i R.87 kj/kg K (able A-. Analyi (a Fr ti rble, e ue te rertie fr EES ftare. Reeber tat fr an ideal ga, entaly i a functin f teerature nly erea entry i functin f bt teerature and reure. rce -: rein ka. kj/kg.79 kj/kg K ka.79 kj/kg.k 7.7 kj/kg re. ka 7.7. η.8 8. kj/kg. rce -: Exanin 99. kj/kg η Ma butin caber urbe We cannt fd te entaly at tate directly. Hever, ug te fllg le EES tgeter it te ientric efficiency relatin, e fd 87 kj/kg, º,.7 kj/kg.k. e lutin by and uld require a trialerrr arac. _entaly(air, entry(air, _, entaly(air, _, _ e a fl rate i detered fr V & & R e net er ut i ( ka(7/ / (.87 ka /kg K( + 7 K.99 kg/ W & & (.99 kg/(8..kj/kg kw, ( W & & ( (.99 kg/(87 99.kJ/kg,88 kw W &, net (b e back rk rati i r b W& W&,88 kw W& W&,,,, kw,88 kw. (c e rate f eat ut and te teral efficiency are Q & & ( (.99 kg/(87 8.kJ/kg,788 kw W& net kw η t. 9 9.% Q&,788 kw 9-7 RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

29 A Braytn cycle it reeratin ug air a te rkg fluid i cnidered. e air teerature at te turbe exit, te net rk ut, and te teral efficiency are t be detered. Autin e air tandard autin are alicable. Air i an ideal ga it variable ecific eat. Ketic and tential energy cange are negligible. rertie e rertie f air are given able A-7. Analyi (a e rertie f air at variu tate are u, (b r r K η K r r η ( 7( K net. kj/kg r. r (..88. ( / η. + (.. /(.7 9. kj/kg η. kj/kg 7.8 kj/kg 8. kj/kg ( 9. (.8( kj/kg,, ( ( ( ( kj/kg. K K q (c en, ε + ε 8. q η t q net ( + (.( 8.9 kj/kg.% 8.8 kj/kg kj/kg kj/kg RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

30 9-9 An ideal ga-turbe cycle it t tage f crein and t tage f exanin i cnidered. e back rk rati and te teral efficiency f te cycle are t be detered fr te cae f it and it a reeratr. Autin e air tandard autin are alicable. Air i an ideal ga it variable ecific eat. Ketic and tential energy cange are negligible. rertie e rertie f air are given able A-7. Analyi (a e rk ut t eac tage f crer are identical, are te rk ut f eac tage f te turbe ce ti i an ideal cycle. en, u, r q η K r,, b net t r K ((.8 ( kj/kg 79. ( (..9. kj/kg ( ( kj/kg,, r r.9 kj/kg r r. kj/kg.%.8 kj/kg 7 8. kj/kg 9. kj/kg ( + ( ( ( q, net 7,.8..7 kj/kg.7 kj/kg.8% 97.9 kj/kg K K 97.9 kj/kg (b Wen a reeratr i ued, r b rea te ae. e teral efficiency ti cae bece q q η re t q ε q ( (.7( 9..,ld net 8 q re kj/kg.7 kj/kg.% 79. kj/kg. kj/kg 9 q RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

31 9- A turbfan enge eratg n an ideal cycle rduce, N f trut. e air teerature at te fan let needed t rduce ti trut i t be detered. Autin Steady eratg cnditin exit. e air tandard autin are alicable. Air i an ideal ga it cntant ecific eat at r teerature. e turbe rk ut i equal t te crer rk ut. rertie e rertie f air at r teerature are R.87 ka /kg K, c. kj/kg K and k. (able A- a. Analyi e ttal a fl rate i 9- N, v R AV & v & e (.87 ka ( K. ka πd V π (. v 7. kg/ & 8. kg/ 8 8 /kg / 7. kg/. /kg q q e a fl rate trug te fan i & f & & e kg/ In rder t rduce te ecified trut frce, te velcity at te fan exit ill be F & f V ( Vexit let V, N kg / ( / + 9. kg/ N F exit V let + & f 8. / An energy balance n te trea ag trug te fan give c ( V exit V V exit let V c let (8. / ( / K (. kj/kg K. K kj/kg / RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

32 9- A ure jet enge eratg n an ideal cycle i cnidered. e velcity at te nzzle exit and te trut rduced are t be detered. Autin Steady eratg cnditin exit. e air tandard autin are alicable. Air i an ideal ga it cntant ecific eat at r teerature. e turbe rk ut i equal t te crer rk ut. rertie e rertie f air at r teerature are R.87 ka /kg K, c. kj/kg K and k. (able A- a. Analyi (a We aue te aircraft i tatinary and te air i vg tard te aircraft at a velcity f V /. Ideally, te air ill leave te diffuer it a negligible velcity (V. Diffuer: q E& E& + V / c E& (teady yte + V ( V + c rer: urbe: c, / k / V K + ( k / ( r ( ( (.88 ka ( k / k turb, E& E& V + ( / ( (. kj/kg K 88.7 K K kj/kg / ( ka.88 ka 8. ka./. ( 88.7 K(.7 K r K Nzzle: ( k / k ka ( 8 K 8. ka (teady E& E& E& E& E& r V + V V exit / yte + V / V V + e a fl rate trug te enge i πd c V./. c 88.7 K ( c (./. ( + V / 9. K ( (. kj/kg K( K.8 / (.8 ka ( K R 7 v.8 ka AV & v V π (. v e trut frce erated i ten F & ( V V exit let / kj/kg /kg / 9. kg/.8 /kg N (9. kg/(.8 / kg / 9, N q 9-7 RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

33 9- A turbjet aircraft flyg at an altitude f 9 i eratg n te ideal jet rulin cycle. e velcity f exaut gae, te rulive er develed, and te rate f fuel cnutin are t be detered. Autin Steady eratg cnditin exit. e air tandard autin are alicable. Air i an ideal ga it cntant ecific eat at r teerature. Ketic and tential energie are negligible, excet at te diffuer let and te nzzle exit. e turbe rk ut i equal t te crer rk ut. rertie e rertie f air at r teerature are c. kj/kg.k and k. (able A-a. Analyi (a We aue te aircraft i tatinary and te air i vg tard te aircraft at a velcity f V /. Ideally, te air ill leave te diffuer it a negligible velcity (V. Diffuer: E& E& + V rer: urbe: r Nzzle: c, / c E& (teady yte + V ( V + c / k / V K + ( k / ( r ( ( (. ka ( k / k turb, E& E& V + ( / ( (. kj/kg K 9.9 K K kj/kg / ( ka. ka 7. ka V./../. ( 9.9 K( 9.7 K K E& E& + V / E& ( k (teady yte + V / V + / k V ( K c c ka 7. ka E& E& 9.9 K ( c ( ( + V /./. 8. K Q i 9-8 r (b (c V / kj/kg & W Q& & fuel ( (. kj/kg K( K / & V ( V V ( kg/( /( /,7 kw exit & let aircraft kj/kg / ( c & ( ( kg/(. kj/kg K( 9.7 Q& 8, kj/. kg/ HV,7 kj/kg K 8, kj/ RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

34 9- A turbjet aircraft tat a a reure rate f 9 i tatinary n te grund. e frce tat ut be alied n te brake t ld te lane tatinary i t be detered. Autin Steady eratg cnditin exit. e air tandard autin are alicable. Air i an ideal ga it variable ecific eat. Ketic and tential energie are negligible, excet at te nzzle exit. rertie e rertie f air are given able A-7. Analyi (a Ug variable ecific eat fr air, rer: q 9 K r Q& & fuel Q& & r 9. kj/kg r (( 9. HV..8 (. kg/(,7 kj/kg, kj/ 7. kj/kg kg/.7 kj/kg, kj/ q 9- q + q kj/kg r 8. urbe: r c, + turb, kj/kg Nzzle: r E& E& + V r E& / r E& E& / ( 8. (teady yte + V V + V kj/kg V / kj/kg ( ( ( kj/kg 98. / Brake frce rut & ( V V ( kg/( 98. / 9,7 N exit let N kg / RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

35 9- e ttal exergy detructin aciated it te Braytn cycle decribed rb. 9- and te exergy at te exaut gae at te turbe exit are t be detered. rertie e ga cntant f air i R.87 kj/kg K (able A-. Analyi Fr rb. 9-, q 8.8, q 7.7 kj/kg, and K 8. kj/kg K 8. kj/kg 78. kj/kg.798 kj/kg K.7 kj/kg K.9 kj/kg K.97 kj/kg K.8 kj/kg K and, fr an energy balance n te eat excanger, K K q 9- u, 8. ( kj/kg.8 kj/kg K x x x detryed, detryed, detryed, re x x detryed, detryed, ( ( 9 K ( (.87 kj/kg K ln( 7 ( ( 9 K (.97.9 (.87kJ/kg K ln( /7,re ( + ( + ( 9 K( ( 9 K,,,, [ ] [( ( ] 8.8 kj/kg K qr qr +, R, R Rln Rln 7.7 kj/kg 9 K Rln Rln 8.9 kj/kg.8.7 kj/kg q kj/kg q + ( 9 K kj/kg N tg 9 K 9. kj/kg and 9 K.8 kj/kg K, te trea exergy at te exit f te reeratr (tate i detered fr H L kj/kg ere u, φ ( ( + + gz V Rln kj/kg K φ ( 9 K(.89 kj/kg. kj/kg K RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

36 9-79 A ga-turbe lant erate n te reerative Braytn cycle it reeatg and terclg. e back rk rati, te net rk ut, te teral efficiency, te ecnd-la efficiency, and te exergie at te exit f te cbutin caber and te reeratr are t be detered. Autin e air-tandard autin are alicable. Ketic and tential energy cange are negligible. Air i an ideal ga it variable ecific eat. rertie e ga cntant f air i R.87 kj/kg K. Analyi (a Fr ti rble, e ue te rertie fr EES ftare. Reeber tat fr an ideal ga, entaly i a functin f teerature nly erea entry i functin f bt teerature and reure. Otiu terclg and reeatg reure i ((. ka rce -, -: rein K K ka. kj/kg.7 kj/kg K. ka.7 kj/kg.k 8.79 kj/kg η.8. K K. ka.78 kj/kg ka. kj/kg.k. kj/kg K. kj/kg..78 η.8.78 rce -7, 8-9: Exanin K K ka. kj/kg K 7. ka 7. kj/kg.k η 8 K K 8 8. ka 8.9 kj/kg kj/kg kj/kg.99 kj/kg K.88 kj/kg 7.8 kj/kg 7. kj/kg 7 q ka kj/kg.k kj/kg RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

37 ycle analyi: η kj/kg , + 7. kj/kg 9-, kj/kg r b,, 7... net kj/kg,, Reeratr analyi: ε re 9 7. K ka.7 kj/kg K (b q kj/kg 7. kj/kg q re kj/kg η t q net (c e ecnd-la efficieny f te cycle i defed a te rati f actual teral efficiency t te axiu ible teral efficiency (arnt efficiency. e axiu teerature fr te cycle can be taken t be te turbe let teerature. at i, and K η ax.78 K η II η t η ax (d e exergie at te cbutin caber exit and te reeratr exit are x x (.9.kJ/kg ( K(..7kJ/kg.K 9.7 kj/kg ( (7..kJ/kg ( K(.7.7kJ/kg.K 8.8 kj/kg ( RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

38 - A -MW cal-fired tea er lant erate n a ile ideal Ranke cycle beteen te ecified reure liit. e verall lant efficiency and te required rate f te cal uly are t be detered. Autin Steady eratg cnditin exit. Ketic and tential energy cange are negligible. Analyi (a Fr te tea table (able A-, A-, and A-, v v, ka ka.9 kj/kg. /kg v( (. /kg( 9 ka kj ka 9. kj/kg kj/kg, 9 Ma. kj/kg.8 kj/kg K ka f.8.79 x.88 fg 7. + x.9 + e teral efficiency i detered fr f fg (.88( kj/kg 9Ma Q ka Q -8 and u, q q η verall η t q η t q kj/kg kj/kg η cb η.99 (.99(.7( % (b en te required rate f cal uly bece and & Q& cal W& η Q& net verall cal, kj/.8, kj/, kj/. kg/.9 tn/ 9, kj/kg RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

39 - A tea er lant tat erate n a reeat Ranke cycle i cnidered. e cndener reure, te net er ut, and te teral efficiency are t be detered. Autin Steady eratg cnditin exit. Ketic and tential energy cange are negligible. Analyi (a Fr te tea table (able A-, A-, and A-,. Ma Ma η kj/kg? η? x.9 Ma η 7..7 kj/kg K 98. kj/kg ( (.8( kj/kg 7.8 kj/kg K (Eq. (Eq. η kj/kg ( 8. (.8( 8. (Eq. Biler. Ma? u ndener urbe e reure at tate ay be detered by a trial-errr arac fr te tea table r by ug EES fr te abve tree equatin: (b en, 9.7 ka,. kj/kg, v v, ycle analyi: q q W& net 9.7 ka ka v( / η kj (. /kg(, 9.7 ka / (.9. + kj/kg, 89.7 kj/kg ( + ( & ( q q. /kg ka kj/kg kj/kg kj/kg (c e teral efficiency i η t (7.7 kg/(.8-7.7kj/kg q 7.7 kj/kg. 9.9% q.8 kj/kg, kw - RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

40 - - A tea er lant erate n an ideal reerative Ranke cycle it t en feedater eater. e net er ut f te er lant and te teral efficiency f te cycle are t be detered. Autin Steady eratg cnditin exit. Ketic and tential energy cange are negligible. Analyi 7 urbe Biler 8 9 f II f I ndener III II I Ma. Ma. Ma ka y y 9 - y - z (a Fr te tea table (able A-, A-, and A-, v v I, v ka ka 7.7 kj/kg. /kg ( (. /kg( ka + I,. Ma f at.liquid v v II, kj/kg ( (. /kg( ka. kj/kg. Ma f at.liquid v v III, v v + II, kj ka ( (. /kg(, ka. kj/kg + III, 7 Ma 7 8. Ma Ma x kj/kg Ma Ma Ma.8 kj/kg.9 kj/kg K 8.8 kj/kg 7.8 kj/kg kj/kg 9 9 f f fg + x 9.7+ /kg /kg fg kj ka kj ka. kj/kg (.9(. 8.7 kj/kg RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

41 ka 7 x f f fg + x fg (.89(.. kj/kg - e fractin f tea extracted i detered fr te teady-fl energy balance equatin alied t te feedater eater. Ntg tat Q & W & ke e, FWH-: E& E& E& i i E& E& & (teady yte & e e & & & y 8 + ( y ( ere y i te fractin f tea extracted fr te turbe ( & 8/ &. Slvg fr y, FWH-: y & ii & ee &.7 & & ( y z ( y z 9 + ere z i te fractin f tea extracted fr te turbe ( & 9/ & at te ecnd tage. Slvg fr z, en, and z y q q W & net ( ( kj/kg ( y z( (.7.7(. 7.7 q q kj/kg ( kg/( 88. kj/kg,. MW & kw net net (b e teral efficiency i η t q q.8 kj/kg 7.% 9. kj/kg.8 kj/kg RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.

42 - An ideal reerative Ranke cycle it a cled feedater eater i cnidered. e rk rduced by te turbe, te rk cnued by te u, and te eat added te biler are t be detered. Autin Steady eratg cnditin exit. Ketic and tential energy cange are negligible. Analyi Fr te tea table (able A-, A-, and A-, v v, ka ka. kj/kg.7 /kg v ( kj (.7 /kg( ka ka. kj/kg kj/kg, ka ka ka x. kj/kg.7 kj/kg K 8.9 kj/kg f fg + x f (.87(7..7 kj/kg Fr an ideal cled feedater eater, te feedater i eated t te exit teerature f te extracted tea, ic ideally leave te eater a a aturated liquid at te extractin reure. 7 ka 7 7. kj/kg x kj/kg 8 7 ka fg 7. kj/kg An energy balance n te eat excanger give te fractin f tea extracted fr te turbe ( & / & fr cled feedater eater: & ii & ee & + & & + & Rearrangg, en, Al, y y,, q + + y 7. kj/kg ( y( kj/kg net,, 7.9. η 77.8 t net q. Biler led f q 7 Ma Ma 7 8 ka q y u (.7( kj/kg 77.8 kj/kg 8 -y urbe ndener - RORIEARY MAERIAL. e McGra-Hill anie, Inc. Liited ditributin eritted nly t teacer and educatr fr cure rearatin. If yu are a tudent ug ti Manual, yu are ug it it eriin.