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. Pressure of the gas at equilibrium is `(Kx_(0))/(S)`
B. Work done by the gas is `(1)/(2)Kx_(0)^(2)`
C. Increase in internal energy of the gas is `(1)/(2)Kx_(0)^(2)`
D. Temperature of the gas is decreased

Answer

A, D