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Consider n moles of an ideal monatomic gas placed in a vertical cylinder. The top of the cylinder is closed by a piston of mass M and cross-section A. Initially the piston is fixed, and the gas has temperature T0 and volume V0. Next, the piston is released, and after several oscillations comes to a stop.Disregarding friction and the heat capacity of the piston and cylinder, find the temperature and volume of the gas in equilibrium. The system is thermally isolated, and the pressure outside the cylinder is P0.

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