c
$P \propto {T^3};\,\,\,\,\,\,P{T^{ - 3}}=constant$ $...(i)$
For an adiabatic process; $P{T^{\frac{\gamma }{{1 - \gamma }}}}=constant$ $...(ii)$
Comparing $(i)$ and $(ii)$, we get
$\frac{\gamma }{{1 - \gamma }} = - 3\,\,;\,\,\gamma = - 3 + 3\gamma $
$ - 2\gamma = - 3\,\,or\,\,\gamma = \frac{3}{2}$
$As\,\,\,\gamma = \frac{{{C_p}}}{{{C_v}}}\,\,\,\therefore \,\,\,\frac{{{C_p}}}{{{C_v}}} = \frac{3}{2}$