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Question

In the arrangement shown in figure, gas is thermally insulated. An ideal gas is filled in the cylinder having pressure P greater than atmospheric pressure P0. The spring of force constant K is initially unstreteched. The piston of mass m and area s is frictionless. In equilibrium, the piston rises up a distance x0, then

A
Final pressure of the gas is P0+Kx0s+mgs
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B
Work done by the gas is 12Kx20+mgx0
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C
Decrease in internal energy of the gas is 12Kx20+mgx0+P0sx0
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D
All of the above
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Solution

The correct options are
A Final pressure of the gas is P0+Kx0s+mgs
C Decrease in internal energy of the gas is 12Kx20+mgx0+P0sx0
Equilibrium of piston gives
Ps=P0S+Kx0+mg
P=P0+Kx0s+mgs
Work done by the gas
W=P0ΔV+12Kx20+mgx0=P0sx0+12Kx20+mgx0
Also, W=ΔU
Decrease in internal energy of the gas =P0sx0+12Kx20+mgx0

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