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## Homework Statement

I'm trying to find an expression for the efficiency of a stirling engine operating with an ideal diatomic gas, and cycling through a volume V and a multiple of its compression ratio, r, Vr.

## Homework Equations

processes:

1-2 isothermal expansion

2-3 isochoric cooling

3-4 isothermal compression

4-1 isochoric heating

r=compression ratio

Th=high temperature

Tl=low temperature

Work=W1 proc. 1-2 (nRTh)ln(r)

Work=W2 proc. 3-4 (nRTl)ln(1/r)

Work Net= W1-W2= nRln(r)(Th-Tl) since ln=-ln(1/r)

Heat Input=Qh=nCv(Th-Tl)=(5/2)R(Th-Tl)

Efficiency=e=W Net/Heat Input=[nRln(r)(Th-Tl)]/[(5/2)nR(Th-Tl)

Canceling:e=(5/2)ln(r)

This does not Make sense since efficiency for an engine with an equal compression ration of say r=10 operating at a Temp high of 300k and low of 200k would have a carnot efficiency of (1/3) while with the above equation e=.92 which is impossible.