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Question

In the arrangement shown in the figure, gas is thermally insulated. An ideal gas is filled in the cylinder having pressure Po (greater than atmospheric pressure Pa). A spring of force constant k is initially unstrecthed. The piston of mass m and ares s is frictionless. In equilibrium, the piston rises up by distance xo, then

A
final pressure of the gas is Pa+kxos+mgs
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B
work done by the gas 12kx2o+mgxo
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C
Internal energy of the gas decreases
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D
all the above
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Solution

The correct option is C Internal energy of the gas decreases
At equilibrium, the forces acting on the piston is given by
Ps=Pa+kxo+mg
P=Pa+kxos+mgs

Work done by the gas,
W.d=Psxo=Pasxo+mgxo+12kx2o

Internal energy decreases as the gas does some work to push the piston

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