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jrklx250s
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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 can't 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 I am 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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