How Is Engine Efficiency Calculated Using V1/V2 in Thermodynamic Cycles?

[davidchen9568]

Homework Statement

Four thermodynamic processes A,B,C,D are shown in the picture. A and C are adiabatic processes. Pressure is held constant during B, and volume is constant during D. An engine run from A->B->C->D->... What is the efficiency of this engine (in terms of V1/V2)?

Homework Equations

$$p{ V }^{ \gamma }=const.\\ W=\int { PdV } \\ efficiency=\frac { W }{ { Q }_{ in }^{ } }$$

The Attempt at a Solution

This is a problem I encountered in an exam. I labeled all points with P1,P2,P3,V1,V2,V3. The work done is the area enclosed in the picture. Heat absorbed is (work done in B) + (internal energy gained in B). But I can't write the answer with only V1/V2. I am wondering whether there is an answer.

 

[TSny]

The efficiency cannot be written in terms of only V1/V2. An ideal diesel engine has this type of cylce. So, you might do a search on efficiency of a diesel cycle.

 

[davidchen9568]

Thanks for the reply. Now the problem is solved.
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