Thermodynamic Processes question from NEET 2013

Answer: (b)

1. Adiabatic in $P$-$T$ form: $P^{1-\gamma}T^\gamma = \text{const}$, so $P \propto T^{\gamma/(\gamma-1)}$.
2. Given $P \propto T^3$: $\frac{\gamma}{\gamma - 1} = 3 \Rightarrow \gamma = 3\gamma - 3 \Rightarrow \gamma = \frac{3}{2}$
3. So the answer is (b) $\frac{3}{2}$.