A thermally insulated chamber of volume `2V_(0)` is divided by a frictionless piston of area `S` into two equal part `A` and `B`. Part `A` has an ideal gas at pressrue `P_(0)` and temperature `T_(0)` and part `B` is vacuum. A massless spring of force constant `K` is connected with the piston and the wall of the container as shown. Initially the spring is unstretched. The gas inside chamber `A` is allowed to expand. Let in equilibrium the spring be compressed by `x_(0)`. Then

Options

A. (a)Final pressure of the gas is `("kx"_(0))/(S)`
B. (b)Work done by the gas is `(1)/(2)"kx"_(0)^(2)`
C. (c)Change in internal energy of the gas is `-(1)/(2)kx_(0)^(2)`
D. (d)Temperature of the gas is decreased.

Answer

A, B, C, D

Explanation

Final pressure =`(kx_(0))/(S)`
Work done by gas = `P.E` stored in spring =`1//2kx_(0)^(2)`
Change in internal energy
`DeltaU = |-DeltaW| = 1//2 kx_(0)^(2)`
As gas expands, `DeltaT` is negative.