Solutions to Homework #10
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1 Solution to Homeork #0 0-6 A teady-lo Carnot enge it ater a te orkg luid operate at peciied condition. e termal eiciency, te preure at te turbe let, and te ork put are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi (a e termal eiciency i determed rom K η t, C 6.% K H (b Note tat + x g K 0 C u, 60 C 0 C.0 Ma (able A K (c e ork can be determed by calculatg te encloed area on te - diagram, u, + x Area g ( 0.( K ( ( ( 0 60( H 0-6 A imple ideal Ranke cycle it ater a te orkg luid operate beteen te peciied preure limit. e maximum termal eiciency o te cycle or a given uality at te turbe exit i to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi For maximum termal eiciency, te uality at tate ould be at it mimum o 8% (mot cloely approace te Carnot cycle, and te propertie at tate ould be (able A- x 0 ka x + x Sce te expanion te turbe i ientropic, g g (0.8( (0.8( K 000 ka 6.70 K. Oter propertie are obtaed a ollo (able A-, A-, and A-6, v v 0 0 ka m /kg v ( kj (0.000 m /kg(000 0ka ka m p, Ma 0 ka RORIEARY MAERIA. 008 e McGra-Hill Companie, Inc. imited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it it permiion.
2 u, and te termal eiciency o te cycle i η t E A imple team Ranke cycle operate beteen te peciied preure limit. e ma lo rate, te poer produced by te turbe, te rate o eat addition, and te termal eiciency o te cycle are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi From te team table (able A-E, A-E, and A-6E, v v 6 pia 69.7 Btu/lbm 0.06 t /lbm v ( Btu (0.06 t /lbm(00 pia.0 pia t 7.6 Btu/lbm Btu/lbm 00 pia 800 F pia p, x 0.0 Btu/lbm.6 Btu/lbm R g + x (0.69( Btu/lbm g η η ( 0.0 (0.90( e ma lo rate o team te cycle i determed rom 000 kj/ Btu m& ( m&.08 lbm/ ( Btu/lbm kj e rate o eat addition i kj ( Q & m& (.08 lbm/( Btu/lbm Btu and te termal eiciency o te cycle i 08 Btu/ 000 kj/ Btu η t Q & 08 Btu/ kj e termal eiciency te previou problem a determed to be e error te termal eiciency caued by neglectg te pump ork i ten 00 pia pia RORIEARY MAERIA. 008 e McGra-Hill Companie, Inc. imited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it it permiion.
3 Error 00.6% A team poer plant operate on a imple ideal Ranke cycle beteen te peciied preure limit. e termal eiciency o te cycle, te ma lo rate o te team, and te temperature rie o te coolg ater are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi (a From te team table (able A-, A-, and A-6, u, and (b v v p, 0 0 ka ( ( m /kg( 7,000 0 ka p, 7 Ma 00 C m /kg K. g kj ka m 0 ka x 0.80 g x η t m & %.,000 kj/ kg/ ( 0.80( 9..6 (c e rate o eat rejection to te coolg ater and it temperature rie are Δ coolgater m & ( mc & (.98 kg/( 96.8 coolgater 70,86 kj/ 70,86 kj/ ( 000 kg/(.8 C 8. C 7 Ma 0 ka RORIEARY MAERIA. 008 e McGra-Hill Companie, Inc. imited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it it permiion.
4 0- A team poer plant tat operate on a reeat Ranke cycle i conidered. e condener preure, te poer put, and te termal eiciency are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi (a From te team table (able A-, A-, and A-6,. Ma C 6.67 K urbe Ma Boiler η Condener ump η ( Ma 0 C 6? ? 6 x η ( ( K 6 η 8. ( 6 ( 0.8( e preure at tate 6 may be determed by a trial-error approac rom te team table or by ug EES rom te above euation: ka, 6 6., (b en, 89.7 v v ka v( / η p kj ( m /kg(, ka / ( p, Cycle analyi: ( + ( m /kg ka m m& ( (7.7 kg/( , kw (c e termal eiciency i 7.7 η t % Ma? 6 6 RORIEARY MAERIA. 008 e McGra-Hill Companie, Inc. imited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it it permiion.
5 -E A teady-lo Carnot rerigeration cycle it rerigerant-a a te orkg luid i conidered. e coeicient o perormance, te uality at te begng o te eat-aborption proce, and te ork put are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi (a Notg tat H 90 pia 7.78 F.8 R and 0 pia.7 F 7. R. CO C H / R, (b roce - i ientropic, and tu x g (.8 R /( 7. R 8.8 ( + x ( 0.0( Btu/lbm R 0 90 pia (c Rememberg tat on a - diagram te area encloed repreent te ork, and 90 pia Btu/lbmR, ( ( ( ( Btu/lbm R 7.9 Btu/lbm, H Q H Q - An ideal vapor-compreion rerigeration cycle it rerigerant-a a te orkg luid i conidered. e CO and te poer reuirement are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi In an ideal vapor-compreion rerigeration cycle, te compreion proce i ientropic, te rerigerant enter te compreor a a aturated vapor at te evaporator preure, and leave te condener a aturated liuid at te condener preure. From te rerigerant table (able A-, A-, and A-, C at. vapor Ma at. liuid Ma C C 07. Ma e ma lo rate o te rerigerant i K 07. (trottlg 00 kj/ m& ( m&.70 kg/ ( e poer reuirement i W & m& ( (.70 kg/( kw e CO o te rerigerator i determed rom it deition, CO R & Q 00 kw 6.9 kw 6.6 Ma C Q H Q W RORIEARY MAERIA. 008 e McGra-Hill Companie, Inc. imited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it it permiion.
6 6-7 An ideal vapor-compreion rerigeration cycle it rerigerant-a a te orkg luid i conidered. e rate o eat removal rom te rerigerated pace, te poer put to te compreor, te rate o eat rejection to te environment, and te CO are to be determed. Aumption Steady operatg condition exit. Ketic and potential energy cange are negligible. Analyi (a In an ideal vapor-compreion rerigeration cycle, te compreion proce i ientropic, te rerigerant enter te compreor a a aturated vapor at te evaporator preure, and leave te condener a aturated liuid at te condener preure. From te rerigerant table (able A- and A-, 0 ka at. vapor 0.9 Ma 0.9 Ma at. liuid ka 0 ka 0.9 Ma ( trottlg K (. C 0.6 en te rate o eat removal rom te rerigerated pace and te poer put to te compreor are determed rom and & Q m& ( ( 0.0 kg/( m& 6.77 kw ( ( 0.0 kg/( kw (b e rate o eat rejection to te environment i determed rom H + & kw W (c e CO o te rerigerator i determed rom it deition, CO R & Q 6.77 kw..0 kw 0.9 Ma Q H 0. Ma Q W RORIEARY MAERIA. 008 e McGra-Hill Companie, Inc. imited ditribution permitted only to teacer and educator or coure preparation. I you are a tudent ug ti Manual, you are ug it it permiion.
( )( ) 7 MPa q in = = 10 kpa q out. 1 h. = s. Thus, and = 38.9% (b) (c) The rate of heat rejection to the cooling water and its temperature rise are
. A team poer plant operate on a imple ideal Ranke cycle beteen te peciied preure limit. e termal eiciency o te cycle, te ma lo rate o te team, and te temperature rie o te coolg ater are to be determed.
Special Topic: Binary Vapor Cycles
0- Special opic: Bary Vapor ycle 0- Bary poer cycle i a cycle ic i actually a combation o to cycle; one te ig temperature region, and te oter te lo temperature region. It purpoe i to creae termal eiciency.
8-4 P 2. = 12 kw. AIR T = const. Therefore, Q &
8-4 8-4 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
v v = = Mixing chamber: = 30 or, = s6 Then, and = 52.4% Turbine Boiler process heater Condenser 7 MPa Q in 0.6 MPa Q proces 10 kpa Q out
0-0- A cogeneration plant i to generate poer and proce eat. art o te team extracted rom te turbe at a relatively ig preure i ued or proce eatg. e poer produced and te utilization actor o te plant are to
T Turbine 8. Boiler fwh fwh I Condenser 4 3 P II P I P III. (a) From the steam tables (Tables A-4, A-5, and A-6), = = 10 MPa. = 0.
- - A team poer plant operate on an ideal regenerative anke cycle it to open feedater eater. e poer put of te poer plant and te termal efficiency of te cycle are to be determed. Aumption Steady operatg
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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
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.6 A upercritical team power plant ha a high preure of 0 Ma and an exit condener temperature of 50 C. he maximum temperature in the boiler i 000 C and the turbine exhaut i aturated vapor here i one open
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