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In the arrangement shown in Fig. gas is ...

In the arrangement shown in Fig. gas is thermally insulated. An ideal gas is filled in the cylinder having pressure `P_(0)` (gt atmospheric pressure `P_(a)`). The spring of force constant `K` is initially unstretched. The piston of mass `m` and area `S` is frictionless. In equilibrium, the piston rises up by distance `x_(0)`, then

A

final pressure of the gas is `p_(a)+(k X_(0))/(S)+(mg)/(S)`

B

work done by the gas is `(1)/(2)k X_(0)^(2)+mg X_(0)`

C

decrease in internal energy of the gas is `(1)/(2)K X_(0)^(2)+mg X_(0)+p_(a)S x_(0)`

D

work done by the gas is `(1)/(2)k X_(0)^(2)`

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The correct Answer is:
A, C
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