(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A possible ideal-gas cycle operates as follows:

(i) from an initial state (p1,V1) the gas is cooled at constant pressure to (p1,V2);

(ii) the gas is heated at constant volume to (p2,V2);

(iii) the gas expands adiabatically back to (p1,V1).

Assuming constant heat capacities, show that the thermal eficiency is:

1-ɣ[((V1/V2) - 1) / ((p2/p1) -1)]

2. Relevant equations

I used first law of thermal dynamics, n = W/Qh, differential forms of Cv and Cp.

change in energy for the complete cycle = 0, therefor W = Qh + Ql.

3. The attempt at a solution

Using efficiency = W / heat absorbed.

I attempted to find the W and Q of the 3 processes separately.

I was using for Isobaric: dW = -Pdv but im pretty sure this is incorrect because no where does it state it is a reversible process. But the book for the class only shows reversible processes for examples and does not actually show a isobaric or isochoric process in any example.

I tried using the differential form of Cv and Cp and rearranging them to find dQ, but failed.

I have used 4 or 5 sheets of paper, trying every way i could think of to work this problem out. I know im missing something and if someone could just point me in the right direction I would gladly appreciate it and work out the problem on my own.

Thanks

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# Efficiency of an ideal-gas cycle.

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