Problem

This problem combines a polytropic process with a specific constraint: the gas doesn't follow the usual $pV^\gamma = \text{constant}$, but instead $pV^2 = \text{constant}$. The key insight is that work done by a gas in any process is $W = \int p \, dV$, and your constraint lets you express $p$ in terms of $V$ alone. Once you substitute that relationship into the work integral, you can evaluate it directly using the given initial and final states.

This problem combines a polytropic process with a specific constraint: the gas doesn't follow the usual $pV^\gamma = \text{constant}$, but instead $pV^2 = \text{constant}$. The key insight is that work done by a gas in any process is $W = \int p \, dV$, and your constraint lets you express $p$ in terms of $V$ alone. Once you substitute that relationship into the work integral, you can evaluate it directly using the given initial and final states.