During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature (P propto T^3). The ratio of s…

For an adiabatic process, the relation between pressure and temperature is given by $P^{1-\gamma} T^\gamma = \text{constant}$, which implies $P T^{\frac{\gamma}{1-\gamma}} = \text{constant}$. Comparing with $P \propto T^3$, we get $\frac{\gamma}{1-\gamma} = 3$. Solving for $\gamma$: $\gamma = 3 - 3\gamma \implies 4\gamma = 3 \implies \gamma = 3/2$.