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.
1-2 isothermal expansion
2-3 isochoric cooling
3-4 isothermal compression
4-1 isochoric heating
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)
Efficiency=e=W Net/Heat Input=[nRln(r)(Th-Tl)]/[(5/2)nR(Th-Tl)
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.