Solutions to Homework #9
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1 9- Soltions to Homewok #9 9-5 he fo pocesses of an ai-standad cycle ae descibed. he cycle is to be shown on - and -s diagams, and e net wok pt and e emal efficiency ae to be detemed. Assmptions he ai-standad assmptions ae applicable. Ketic and potential enegy changes ae negligible. Ai is an ideal gas wi aiable specific heats. opeties he popeties of ai ae gien able A-7. Analysis (b) he popeties of ai at aios states ae 00K 800 K 800 ka 00 ka Fom enegy balances, h h 00.9 kj/kg ka 668 ka h (.86) 87. kj/kg K 59.8 K ( 800 ka) 89. kj/kg 59.8 K 668 ka ( 0) 9.0 h 88. kj/kg kj/kg kj/kg s w net, kj/kg (c) hen e emal efficiency becomes η w net, 570.kJ/kg 5.9% 098.0kJ/kg 9- he ee pocesses of an ai-standad cycle ae descibed. he cycle is to be shown on - and -s diagams, and e net wok pe cycle and e emal efficiency ae to be detemed. Assmptions he ai-standad assmptions ae applicable. Ketic and potential enegy changes ae negligible. Ai is an ideal gas wi aiable specific heats. opeties he popeties of ai ae gien able A-7. Analysis (b) he popeties of ai at aios states ae RORIEARY MAERIAL. 008 he McGaw-Hill Companies, Inc. Limited distibtion pemitted only to teaches and edcatos fo cose pepaation. If yo ae a stdent sg is Manal, yo ae sg it wi pemission.
2 9-90 K 06.9 kj/kg h 90.6 kj/kg 80 ka 95 ka ( 90 K) 60 K kj/kg, 07. Q m 95 ka 80 ka ( 07.) 5.8 ( ) ( 0.00 kg)( ) h 80.8 kj/kg 06.9 kj/kg.07 kj Q m h ( h ) ( 0.00 kg)( ) kj/kg.65 kj W net, Q Q kj Wnet, 0. kj (c) η 0.% Q.07 kj s 9-8 An ideal Otto cycle wi ai as e wokg flid has a compession atio of 9.5. he highest pesse and tempeate e cycle, e amont of heat tansfeed, e emal efficiency, and e mean effectie pesse ae to be detemed. Assmptions he ai-standad assmptions ae applicable. Ketic and potential enegy changes ae negligible. Ai is an ideal gas wi constant specific heats. opeties he popeties of ai at oom tempeate ae c p.005 kj/kg K, c 0.78 kj/kg K, R 0.87 kj/kg K, and k. (able A-). Analysis (a) ocess -: isentopic compession. k ( 08 K)( 9.5) ocess -: isentopic expansion K K 08 K ( 9.5) ( 00 ka) 8 ka Q Q k ( 800 K)( ) 969 K ocess -: constant heat addition. (b) V m R 969 K ka K ( ka)( m ) ( 0.87 ka m /kg K)( 08 K) ( 8 ) 607 ka kg ( ) mc ( ) ( kg)( 0.78 kj/kg K)( ) K kj Q m (c) ocess -: constant heat ejection. Q ( ) ( kg)( 0.78 kj/kg K)( ) K 0.0 kj m( ) mc RORIEARY MAERIAL. 008 he McGaw-Hill Companies, Inc. Limited distibtion pemitted only to teaches and edcatos fo cose pepaation. If yo ae a stdent sg is Manal, yo ae sg it wi pemission.
3 9- W net Q Q kj W η Q net, 0.50 kj 59.% kj (d) V max V m V Wnet, Wnet, ME V V V ( / ) 0.50 kj ( m )( /9.5) ka m kj 65 ka 9-0E An ideal Otto cycle wi ai as e wokg flid has a compession atio of 8. he amont of heat tansfeed to e ai dg e heat addition pocess, e emal efficiency, and e emal efficiency of a Canot cycle opeatg between e same tempeate limits ae to be detemed. Assmptions he ai-standad assmptions ae applicable. Ketic and potential enegy changes ae negligible. Ai is an ideal gas wi aiable specific heats. 00 R opeties he popeties of ai ae gien able A-7E. Analysis (a) ocess -: isentopic compession. 9.0Bt/lbm 50R 50 R. 8 ocess -: constant heat addition. 00R (.) Bt/lbm 5.70 Bt/lbm.9 (b) ocess -: isentopic expansion Bt/lbm ocess -: constant heat ejection. ()(.9) Bt/lbm Bt/lbm η.50 Bt/lbm 5.0%. Bt/lbm L 50 R (c) η,c 77.5% 00 R H 9-57 An ideal diesel cycle has a a ctoff atio of.. he powe podced is to be detemed. Assmptions he ai-standad assmptions ae applicable. Ketic and potential enegy changes ae negligible. Ai is an ideal gas wi constant specific heats. opeties he popeties of ai at oom tempeate ae c p.005 kj/kg K, c 0.78 kj/kg K, R 0.87 kj/kg K, and k. (able A-a). RORIEARY MAERIAL. 008 he McGaw-Hill Companies, Inc. Limited distibtion pemitted only to teaches and edcatos fo cose pepaation. If yo ae a stdent sg is Manal, yo ae sg it wi pemission.
4 9- Analysis he specific olme of e ai at e stat of e compession is R ( 0.87 ka m /kg K)(88 K) m 95 ka he total ai mass taken by all 8 cyldes when ey ae chaged is m N ΔV πb S / π (0.0 m) (0. m)/ cyl N cyl (8) m /kg /kg kg he ate at which ai is pocessed by e enge is detemed fom mn& m& N e ( kg/cycle)(600/60 e/s) 0.55 kg/s e/cycle sce ee ae two eoltions pe cycle a fo-stoke enge. he compession atio is At e end of e compession, e ai tempeate is k. ( 0) 95.6 K (88 K) Application of e fist law and wok tegal to e constant pesse heat addition gies p c ( ) (.005 kj/kg K)(7 95.6)K 5 kj/kg while e emal efficiency is k. c η k k( ). c 0 he powe podced by is enge is en W& net mw & net 05.kW m& η..(. ) (0.55 kg/s)(0.6867)(5 kj/kg) RORIEARY MAERIAL. 008 he McGaw-Hill Companies, Inc. Limited distibtion pemitted only to teaches and edcatos fo cose pepaation. If yo ae a stdent sg is Manal, yo ae sg it wi pemission.
5 E An ai-standad Diesel cycle wi a compession atio of 8. is consideed. he ctoff atio, e heat ejection pe nit mass, and e emal efficiency ae to be detemed. Assmptions he ai-standad assmptions ae applicable. Ketic and potential enegy changes ae negligible. Ai is an ideal gas wi aiable specific heats. opeties he popeties of ai ae gien able A-7E. Analysis (a) ocess -: isentopic compession. 9.0 Bt/lbm 50 R. 8. (.) 7.9 h ocess -: constant heat addition. 000 R R 6.6 R 0.05 Bt/lbm 000 R (b) 000 R h h h ocess -: isentopic expansion Bt/lbm Bt/lbm ocess -: constant heat ejection Bt/lbm (c) η 59.% 88.6 Bt/lbm Bt/lbm (.80) Bt/lbm RORIEARY MAERIAL. 008 he McGaw-Hill Companies, Inc. Limited distibtion pemitted only to teaches and edcatos fo cose pepaation. If yo ae a stdent sg is Manal, yo ae sg it wi pemission.
6 E An ai-standad Diesel cycle wi a compession atio of 8. is consideed. he ctoff atio, e heat ejection pe nit mass, and e emal efficiency ae to be detemed. Assmptions he ai-standad assmptions ae applicable. Ketic and potential enegy changes ae negligible. Ai is an ideal gas wi constant specific heats. opeties he popeties of ai at oom tempeate ae c p 0.0 Bt/lbm.R, c 0.7 Bt/lbm.R, and k. (able A-E). Analysis (a) ocess -: isentopic compession. k 0. ( 50R)( 8.) 7R ocess -: constant heat addition. 000 R.7 7 R (b) h h c ( ) ( 0.0 Bt/lbm.R)( 000 7) R 06 Bt/lbm p ocess -: isentopic expansion. k k 0..7 ocess -: constant heat ejection. (c) η c ( ) ( 0.7 Bt/lbm.R)( 7 50) 08 Bt/lbm 6.6% 06 Bt/lbm.7 8. ( 000 R) 7 R R 08 Bt/lbm RORIEARY MAERIAL. 008 he McGaw-Hill Companies, Inc. Limited distibtion pemitted only to teaches and edcatos fo cose pepaation. If yo ae a stdent sg is Manal, yo ae sg it wi pemission.
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