PS1Sol - ME 212 PS 1 Solutions 1) An ideal Otto cycle with...

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1 ) An ideal Otto cycle with air as the working fluid has a compression ratio of 9.5. The highest pressure and temperature in the cycle, the amount of heat transferred, the thermal efficiency, and the mean effective pressure 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 c p = 1.005 kJ/kg·K, c v = 0.718 kJ/kg·K, R = 0.287 kJ/kg·K, and k = 1.4 (Table A-2). Analysis ( a ) Process 1-2: isentropic compression. P ±² ± ² kPa 2338 kPa 100 K 308 K 757.9 9.5 K 757.9 9.5 K 308 1 1 2 2 1 2 1 1 1 2 2 2 0.4 1 2 1 1 2 ³ ´ ´ µ · · ¸ ¹ ³ ³ º» º ³ ³ ³ ´ ´ µ · · ¸ ¹ ³ ¼ P T T P T P T P T T k vv Q out Q in 2 3 1 4 Process 3-4: isentropic expansion. ± ² K 1969 ³ ³ ´ ´ µ · · ¸ ¹ ³ ¼ 0.4 1 3 4 4 3 9.5 K 800 k T T Process 2-3: = constant heat addition. kPa 6072 ³ ´ ´ µ · · ¸ ¹ ³ ³ º ³ kPa 2338 K 757.9 K 1969 2 2 3 3 2 2 2 3 3 3 P T T P T P T P ( b ) ± ² kg 10 788 . 6 K 308 K /kg m kPa 0.287 m 0.0006 kPa 100 4 3 3 1 1 1 ¼ ½ ³ ¾ ¾ ³ ³ RT P m V ± ² ± ² kJ 0.590 ³ ¼ ¾ ½ ³ ¼ ³ ¼ ³ ¼ K 757.9 1969 K kJ/kg 0.718 kg 10 6.788 4 2 3 2 3 in T T mc u u m Q (c) Process 4-1: = constant heat rejection. ± ² ± ² kJ 0.2 40 K 308 800 K kJ/kg 0.718 kg 10 6.788 ) ( 4 1 4 1 4 out ³ ¼ ¾ ½ ¼ ³ ¼ ³ ¼ ³ ¼ T T mc u u m Q kJ 0.350 240 . 0 590 . 0 out in net ³ ¼ ³ ¼ ³ Q Q W 59.4% ³ ³ ³ kJ 0.590 kJ 0.350 in out net, th Q W ¿ ( d ) kPa 652 ³ ´ ´ µ · · ¸ ¹ ¾ ¼ ³ ¼ ³ ¼ ³ ³ ³ kJ m kPa 1/9.5 1 m 0.0006 kJ 0.350 ) / 1 1 ( MEP 3 3 1 out net, 2 1 out net, max 2 min r W W r VV
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2) A four-cylinder ideal diesel engine with air as the working fluid has a compression ratio of 17 and a cutoff ratio of 2.2. The power the engine will deliver at 1500 rpm is to be determined. Assumptions 1 The cold 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 c p = 1.005 kJ/kg·K, c v = 0.718 kJ/kg·K, R = 0.287 kJ/kg·K, and k = 1.4 (Table A-2). Analysis Process 1-2: isentropic compression. P Q out Q in 3 2 1 4 ±² ± ² K 1019 17 K 328 0.4 1 2 1 1 2 ³ ³ ´ ´ µ · · ¸ ¹ ³ º k T T V Process 2-3: P = constant heat addition.
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PS1Sol - ME 212 PS 1 Solutions 1) An ideal Otto cycle with...

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