When dealing with a process undergoing reversible compression from state 1 (P1,V1,T1) to γstate 2 (P2,V2,T2), the internal energy dU and the work, dw, are the same: considering dq= 0. Since dU = CvdT = dw. ΔU = w. ΔU = Cv(T2 - T1) w = [(-P1 (V1)^γ/ (-γ+1)][V2^(-γ+1) - V1^(-γ+1)] for reversible adiabatic processes. So my question is, w = [(-P1 (V1)^γ/ (-γ+1)][V2^(-γ+1) - V1^(-γ+1)] = ΔU = Cv(T2 - T1) ? Are they equal? If the state 1 and state 2 are only described with two variables, say (P,V) for both states respectively, that still holds true right?