FYKOS Year 27 Series 2 Problem 3 — torturing the piston · FYKOS 27 #27.2.3

This problem traces a gas through three distinct processes: adiabatic compression (fast, no heat exchange), isochoric cooling (held fixed, heat flows out), and then free expansion back to equilibrium. The key insight is recognizing that each stage follows different thermodynamic rules—adiabatic uses $PV^\gamma = \text{const}$, cooling at constant volume uses $P/T = \text{const}$, and the final state depends on whether the piston can rise freely or is constrained by atmospheric pressure. You'll need to track how pressure and temperature change through each step to predict the piston's behavior.

This problem traces a gas through three distinct processes: adiabatic compression (fast, no heat exchange), isochoric cooling (held fixed, heat flows out), and then free expansion back to equilibrium. The key insight is recognizing that each stage follows different thermodynamic rules—adiabatic uses $PV^\gamma = \text{const}$, cooling at constant volume uses $P/T = \text{const}$, and the final state depends on whether the piston can rise freely or is constrained by atmospheric pressure. You'll need to track how pressure and temperature change through each step to predict the piston's behavior.