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1、9-13 The three processes of an air-standard cycle are described. The cycle is to be shown on the P-v and T-s diagrams, and the back work ratio and the thermal efficiency are to be determined.Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligi
2、ble. 3 Air is an ideal gas with constant specific heats.Properties The properties of air are given as R = 0.287 kJ/kg.K, cp = 1.005 kJ/kg.K, cv = 0.718 kJ/kgK, and k = 1.4.Analysis (a) The P-v and T-s diagrams of the cycle are shown in the figures.(b) The temperature at state 2 is K 10kPa 7K)30(12PT
3、 3During process 1-3, we have kJ/g 516.0)K2)(3kJ/g 287.0( (3113, TRPdwinVvDuring process 2-3, we have kJ/g 8.172nK)(20lkJ/g 287.0( 7lnl33,32 RTRTdPwout VvVThe back work ratio is then .4kJ/g 8.17265,32outinbwrHeat input is determined from an energy balance on the cycle during process 1-3,kJ/g 2465kJ/
4、g 172.830)K)(2718.0(,3,3112,outvtinouti wTcqwThe net work output issT321vvP321kJ/g 2.65.18.72,13,2 inoutnetw(c) The thermal efficiency is then .%6.0kJ 2456.inetthq9-21An air-standard cycle executed in a piston-cylinder system is composed of three specified processes. The cycle is to be sketcehed on
5、the P-v and T-s diagrams; the heat and work interactions and the thermal efficiency of the cycle are to be determined; and an expression for thermal efficiency as functions of compression ratio and specific heat ratio is to be obtained. Assumptions 1 The air-standard assumptions are applicable. 2 Ki
6、netic and potential energy changes are negligible. 3 Air is an ideal gas with constant specific heats.Properties The properties of air are given as R = 0.3 kJ/kgK and cv = 0.3 kJ/kgK.Analysis (a) The P-v and T-s diagrams of the cycle are shown in the figures.(b) Noting that 1.42970K kJ/g0.3vckRpProc
7、ess 1-2: Isentropic compression K 4.58)( 293429.0121 kkrTTv kJ/g 20. )3.)(J/g 7.0()(1in,1cw02qFrom ideal gas relation, 29)5(4.832132 TrTvProcess 2-3: Constant pressure heat addition kJ/g 701.3 K )4.5829)(kJ/g 3.0(23332out, TRPdwvsT321vvP321kJ/g 238 K )4.5829)(kJ/g 1()(233,in3,2TchuwqpotProcess 3-1:
8、Constant volume heat rejection / 140. 9)-)(J/k7.0()(131out1,3cqv0w(c) Net work is KkJ/g 3.4970.23.71in2,1out3,2net The thermal efficiency is then .%.0kJ 238497.inetthqw9-32The two isentropic processes in an Otto cycle are replaced with polytropic processes. The heat added to and rejected from this c
9、ycle, and the cycles thermal efficiency are to be determined.Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Air is an ideal gas with constant specific heats.Properties The properties of air at room temperature are R = 0.287 kPam3/k
10、gK, cp = 1.005 kJ/kgK, cv = 0.718 kJ/kgK, and k = 1.4 (Table A-2a).Analysis The temperature at the end of the compression is K 4.537)(8 21.121 nrTTvAnd the temperature at the end of the expansion is 4.7891) 473(13.343 nnrTTvThe integral of the work expression for the polytropic compression giveskJ/g
11、 6.238)18(13.K)2kJ/g287.0(11 3.22 nRTwvSimilarly, the work produced during the expansion isvvP4132kJ/g 0.6541813.K) (47kJ/g 287.0(11 3.4343 nRTwvApplication of the first law to each of the four processes givesJ/ 3.9)24.537)(kJ/g78.0(kJ/g6.238)(121 Tcqv kJ/g 861K4531) 7.03 k/g 2.16K).)(/ .(/.54)(43 w
12、 / 0.2879)kJg 8.114 cqvThe head added and rejected from the cycle arekJ/ 419.530.65.927142out3inqqThe thermal efficiency of this cycle is then0.835inoutthq9-37An ideal Otto cycle with air as the working fluid has a compression ratio of 8. The amount of heat transferred to the air during the heat add
13、ition process, the thermal efficiency, and the thermal efficiency of a Carnot cycle operating between the same temperature limits are to be determined.Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Air is an ideal gas with variable
14、 specific heats.Properties The properties of air are given in Table A-17E.Analysis (a) Process 1-2: isentropic compression.32.14Btu/lbm90R5401 rTvBtu/lbm 1.2804.8.8122 urrrvProcess 2-3: v = constant heat addition. Btu/lb 241. 8.70.4529t/lm.R033uqTinrvvP4132qinqout2400 R540 R(b) Process 3-4: isentrop
15、ic expansion.Btu/lbm 205.435.194.284343 urrvvProcess 4-1: v = constant heat rejection.Bt/lb 0.5.014out q53%tu/lbm 2.43intth(c) The thermal efficiency of a Carnot cycle operating between the same temperature limits is 7.R 01Cth,HLT9-40The expressions for the maximum gas temperature and pressure of an ideal Otto cycle are to be determined when the compression ratio is doubled.Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Air is an ideal gas with constant spe
