$\begin{aligned}
& \mathrm{P} \propto \mathrm{T}^3 \
& \mathrm{PT}^{-3}=\text { constant } \
& \because \frac{\mathrm{PV}}{\mathrm{T}}=\mathrm{nR}=\text { constant from ideal gas equation } \
& (\mathrm{P})(\mathrm{PV})^{-3}=\text { constant } \
& \mathrm{P}^{-2} \mathrm{~V}^{-3}=\text { cosntant }...(i)
\end{aligned}\becauseProcessequationforadiabaticprocessis\mathrm{PV}^{\mathrm{y}}=\text { constant }...(ii)Comparingequation(1)and(2)\frac{C_P}{C_V}=y=\frac{3}{2}$