PV3/2= constant is the relation obeyed by a perfect gas during an adiabatic process, if the initial temperature of the gas is T, then what will be the final temperature of the gas when it is compressed to half of its initial volume.

given PV3/2=Constant, for a perfect gas  In adiabatic process relation between Pressure P and volume V is PVγ= Constant   on comparing above two equations ⇒γ=3/2  given initial teperature T1=T  final temperature T2=?  initial volume is V1=V;   final volume is V2=V2  In adiabatic process relation between temperature T and volume V is TVγ-1=Constant T1V1γ-1= T2V2γ-1  T1T2=V2V1γ-1  substituting the given values of T1,V1,V2  TT2=121/2  T2=21/2T