A portion of helium gas in a vertical cylindrical container is in thermodynamic equilibrium with the — Thermodynamics and Thermochemistry Chemistry Question
Question
A portion of helium gas in a vertical cylindrical container is in thermodynamic equilibrium with the surroundings. The gas is confined by a movable heavy piston. The piston is slowly elevated by a distance $H$ from its equilibrium position and then kept in the elevated position long enough for the thermodynamic equilibrium to be re-established. After that, the container is insulated and then the piston is released. After the piston comes to rest, what is the new equilibrium position of the piston with respect to initial position?
💡 Solution & Explanation
Re-equilibration at elevated height gives a strictly higher volume at original temperature $T_0$. Irreversible adiabatic release equates work done by the constant weight/atmosphere to internal energy change. Resolving $T_f$ using $C_P$ and $C_V$ (1.5R and 2.5R for He) returns a proportional height scaling mapped to exactly $0.4H$ above the initial rest level.