The relation between the internal energy U and adiabatic constant γ is

Change in internal energyΔU=μCvΔT ⇒U2−U1=μCvT2−T1 Let initially T1=0 so U1=0 and finally T2=T and U2=UU=μCvT=μT×Cv=PVR×Rγ−1=PVγ−1 (As PV=μRT,∴μT=PV/R  and Cv=R/(γ−1)