Solution:

$P \propto T^3$ or $P T^{-3} = \text{constant}$. We know that for an adiabatic process $P^{1-\gamma} T^{\gamma} = \text{constant}$ or $P T^{\frac{\gamma}{1-\gamma}} = \text{constant}$. Comparing the powers of $T$, $\frac{\gamma}{1-\gamma} = -3 \Rightarrow \gamma = -3 + 3\gamma \Rightarrow 2\gamma = 3 \Rightarrow \gamma = 3/2$.