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;  4T0

(b) Constant-pressure heating to V0/16;  2.81T0

(c) Adiabatic expansion toV0;     -5.86T0

(d) Constant-volume cooling toT0     -.953T0

Compute the change in T for each leg in terms of T0and determine the efficiency of the cycle 77%. Assume Cv = 2R.
The answers are in yellow but no matter what I do I cannot getto them. Please help and explain. Thanks. A diesel engine operates on the following , cycle, beginningat p0, V0, T0: (a) Adiabatic compression to V0/25;  4T0 (b) Constant-pressure heating to V0/16;  2.81T0 (c) Adiabatic expansion toV0;     -5.86T0 (d) Constant-volume cooling toT0     -.953T0

Compute the change in T for each leg in terms of T0and determine the efficiency of the cycle 77%. Assume Cv = 2R.
The answers are in yellow but no matter what I do I cannot getto them. Please help and explain. Thanks. Compute the change in T for each leg in terms of T0and determine the efficiency of the cycle 77%. Assume Cv = 2R. The answers are in yellow but no matter what I do I cannot getto them. Please help and explain. Thanks.

Explanation / Answer

(a) Adiabatic compression =Cp/Cv=3/2=1.5 T*V^(-1)=constant => T=To*Vo^(1.5-1)/(Vo/25)^(1.5-1) =>T=5To =>T=5To-To=4To => P2=Po/To*5To*25=125 Po (b)Constant-pressure heating to V0/16 V/T=constant T=5To*25/16=7.81 To => T=7.81To-5To=2.81 To (c) Adiabatic expansion to V0 T=7.81To*(Vo/16)^0.5/Vo^0.5 => T=1.95 To =>P=Po*1.95*To/To=1.95*Po T=T-7.81To= -5.86 To (d) Constant-volume cooling to T0 T=To-1.95To=-0.95 To the efficiency of the cycle total work done by gas: W=-n*2R*4To+n*2R*5.86*To+125Po*(1/16-1/25)*Vo =3.72*PoVo+125Po*(1/16-1/25)*Vo=6.532PoVo absorbed energy (in Constant-pressure heating to V0/16;) Q=125Po*(1/16-1/25)*Vo +n*2*R*2.81*To=8.433PoVo => efficiency e=W/Q=77% T=To-1.95To=-0.95 To the efficiency of the cycle total work done by gas: W=-n*2R*4To+n*2R*5.86*To+125Po*(1/16-1/25)*Vo =3.72*PoVo+125Po*(1/16-1/25)*Vo=6.532PoVo absorbed energy (in Constant-pressure heating to V0/16;) Q=125Po*(1/16-1/25)*Vo +n*2*R*2.81*To=8.433PoVo => efficiency e=W/Q=77%

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