Question #42191

A vertical cylindrical container with adiabatic walls contains $n$ moles of a monatomic ideal gas. It is fitted with a frictionless, adiabatic piston of mass $M$ and cross-sectional area $A$. The atmospheric pressure is $P_0$, and it is given that $P_0 = \frac{Mg}{A}$. Initially, the container is placed in an elevator accelerating upwards with an acceleration $a = g$ (where $g$ is the acceleration due to gravity). The gas is in thermal and mechanical equilibrium with an initial volume $V_0$. Suddenly, the elevator's acceleration drops to zero and it continues to move with a constant upward velocity. The gas expands and eventually reaches a new equilibrium state with volume $V_f$. Find the ratio $\frac{V_f}{V_0}$.