Chemistry - Thermodynamics - I Question with Solution | TestHub
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?
Options:
Answer:
Solution:
Let the initial gas column height be L (area A) and the constant pressure from atmosphere plus piston weight be P, so nRT0 = PLA. After the slow isothermal lift the column is (L+H) at T0. On release the piston moves irreversibly and adiabatically against constant P until the final pressure is P again. Helium: CV = 1.5R. 1.5 nR(T2 - T0) = -P(V2 - V1), i.e. 1.5(PV2 - PLA) = -P(V2 - (L+H)A). So 2.5V2 = (2.5L + H)A and V2 = (L + 0.4H)A. The piston ends 0.4H above its initial position, independent of L. Matches (a).
