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## Homework Statement

Given an imaginary ideal-gas cycle. Assuming constant heat capacities, show that the thermal efficiency is

η = 1 - γ[((V1/V2)-1)/((P3/P2)-1)]

Since i cant show you the cycle we are shown that

l Qh l = which is absolute value of the heat at high temperature = Cv(T3-T2)

l QL l = which is absolute value of the heat at low temperature = Cp(T1-T2)

Cp/Cv = γ

## The Attempt at a Solution

Ok so subing in these equations for thermal efficiency

which is

η = 1 - l QL l / l Qh l

we get...

η = 1 - γ(T1 - T2)/(T3 - T2)

η = 1 - γ((T1/T3) - 1)

This imaginary cycle only has a power stroke and we are assuming that its adiabatic...from this we concluded that

T1V1^(γ-1) = T3V2^(γ-1)

T1P2^((1-γ)/y)=T3P3^((1-γ)/y)

divide each equation we get

V1^(γ-1)/P2^((1-γ)/y) = V2^(γ-1)/P3^((1-γ)/y)

Now im not sure how to rearrange from here to make T1/T3 = (V1/V2)/(P3/P2)

Any suggestions would be greatly appreciative.

Thanks!

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