For an adiabatic process, the relation between pressure ($P$) and temperature ($T$) is given by $P^{1-\gamma}T^\gamma = \text{constant}$, which can be rewritten as $P \propto T^{\frac{\gamma}{\gamma-1}}$. Given that $P \propto T^3$. Equating the powers of $T$, we get: $\frac{\gamma}{\gamma - 1} = 3$ $\gamma = 3\gamma - 3$ $2\gamma = 3 \implies \gamma = \frac{3}{2}$ Since the ratio of specific heats $\frac{C_P}{C_V} = \gamma$, the value is $\frac{3}{2}$.