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

Options

A. Final temperature of the gas is `("kx"_(0)6)/(S)`
B. Work done by the gas is `(1)/(2)"kx"_(0)^(2)`
C. Change in internal energy of the gas is `(1)/(2)kx_(0)^(2)`
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.