Work done in irreversible adiabatic process

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In an irreversible adiabatic process involving an ideal monoatomic gas in a vertical cylinder, the work done by the external forces (gravity and atmospheric pressure) is equated to the work done by the gas. The system is thermally isolated, and after the piston is released, it oscillates before reaching equilibrium. The key conceptual doubt revolves around how the piston stops without friction, suggesting a need for clarification on energy dissipation in such systems. Understanding the balance of forces and energy conservation principles is crucial to resolving these doubts. The discussion emphasizes the relationship between work done and the behavior of the piston in this thermodynamic scenario.
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This question came some time back in Stony Brooks exam. I have the solution also. But i am having some conceptual doubts. Can someone help me please.

The question is:
Consider ‘n’ moles of an ideal monoatomic 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 volume Vo and temperature To. Next, the piston is released, and after several oscillations (due o gravity) comes to a stop. Disregarding friction and the heat capacity of the piston and cylinder, find the temperature and volume of the gas at equilibrium. The system is thermally isolated, and the pressure outside the cylinder is P.

Here i just want to know if the work done by the external agent.. (i.e. Mg & P.A).. can be taken same as work done by the gas inside the cylinder.
 
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as this is reversible adiabatic process the work done on the gas by the surrounding is the work done by Mg and by atmospheric pressure.
 
yes i think tht bt wht i did not get is how does the piston stop if there is no friction?
 

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