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utkarshakash
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Homework Statement
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 a distance H from its equilibrium position and then kept in the elevated position long enough for the thermodynamic equilibrium to be reestablished. 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?
The Attempt at a Solution
Let the piston initially be situated at a distance l from bottom of cylinder and let P1 be the pressure of the gas inside. Let M be the mass of piston. Doing force balance on piston gives
Mg+P0A = P1A
where A =area of cross-section and P0 = atmospheric pressure
When the piston is taken to height H let pressure inside be P2.
[itex]\dfrac{P_1 l}{T_0} = \dfrac{P_2 (l+H)}{T_2} [/itex]
After cylinder is insulated and piston is released, the process will be adiabatic
Let final height of piston from bottom of cylinder be l'.
[itex]P_2 (l+H)^{\gamma} = P_1 l'^{\gamma} [/itex]
But how do I eliminate T2 and l?