[UPSC CSE 2024] Thermodynamics (Q12, 10M)

Prove that the work done by a perfect gas during a quasi-static adiabatic expansion is given by W = \frac{P_i V_i}{\gamma - 1} \left[ 1 - \left( \frac{P_f}{P_i} \right)^{\frac{\gamma - 1}{\gamma}} \right] where \gamma is the ratio of specific heats.