During an adiabatic process, the pressure of a gas is found to be proportional to cube of its absolu — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

We are given $P \propto T^3 \implies P T^{-3} = \text{constant}$. The standard adiabatic gas relation connects $P$ and $T$ as $P^{1-\gamma} T^\gamma = \text{constant}$, which re-writes to $P T^{\frac{\gamma}{1-\gamma}} = \text{constant}$. Equating exponents: $\frac{\gamma}{1-\gamma} = -3 \implies \gamma = -3 + 3\gamma \implies 2\gamma = 3 \implies \gamma = 3/2$.