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Homework Statement
Proving PV^gamma = constant In adiabatic expansion. Q = 0
Homework Equations
N/A
The Attempt at a Solution
ΔEint = W
nCvdT = PdV = nRT / V dV
∫Cv/T dT = ∫R/V dV
Cv ln(T2/T1) = R ln(V2/V1)
ln(T2/T1) = (R/Cv) ln(V2/V1)
T2/T1 = (V2/V1)R⋅gamma / Cp
P2V2 / P1V1 = (V2/V1)R⋅gamma / Cp
I did some extra rearranging after this point, but it appears that the equation in this form cannot get PV^gamma = constant or for P1V1^gamma = P2V2^gamma. Is there a mistake somewhere?
Thanks.
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