A diesel engine operates on the following , cycle, beginningat p 0 , V 0 , T 0 :

Question

A diesel engine operates on the following , cycle, beginningat p0, V0, T0: (a) Adiabatic compression to V0/25; (b) Constant-pressure heating to V0/16; (c) Adiabatic expansion to V0; (d) Constant-volume cooling to T0 Compute the change in T for each leg in terms of T0and determine the efficiency of the cycle. Assume Cv = 2R. A diesel engine operates on the following , cycle, beginningat p0, V0, T0: (a) Adiabatic compression to V0/25; (b) Constant-pressure heating to V0/16; (c) Adiabatic expansion to V0; (d) Constant-volume cooling to T0 Compute the change in T for each leg in terms of T0and determine the efficiency of the cycle. Assume Cv = 2R. Compute the change in T for each leg in terms of T0and determine the efficiency of the cycle. Assume Cv = 2R.

Explanation / Answer

Cv = 2R, Cp = 3R, = 3/2 = 1.5 a) T0, V0 --> T1,V0/25 use TV-1 = constant T0V0-1 =T1(V0/25)-1 T1 = T0*251.5-1 =5T0 b) 5T0, V0/25 --> T2,V0/16 use T/V = constant (5T0)/(V0/25) =(T2)/(V0/16) T2 = 125T0/16 c) 125T0/16, V0/16 --> T3,V0 use TV-1 = constant (125T0/16)(V0/16)-1 =T3V0-1 T3 = 125T0/64 d) 125T0/64, V0 --> T0,V0 during b), Q = nCpT = n(3R)(125T0/16 -5T0) = (135/16)nRT0 during d) Q' = nCvT = n(2R)(125T0/64 -T0) = (61/32)nRT0 efficiency = 1 - Q'/Q = 1 - 61/270 = 77.4%

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