During an adiabatic process, the pressure of gas is found to be proportional to the cube of its temperature. The ratio of  specific heat ratio γ  for the gas is

in adiabatic process,   relation between pressure P and temperature T is P1-γ.Tγ=Constant  where γ is specific heat ratio ⇒PαTγγ-1   But given PαT3  on comparing above two equations  γγ-1=3 ⇒γ=3γ-3 ⇒2γ=3 ⇒γ=3/2