1. The problem statement, all variables and given/known data Proving PV^gamma = constant In adiabatic expansion. Q = 0 2. Relevant equations N/A 3. 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.