A fixed container is fitted with a piston which is attached to a spring of spring constant `k`. The other and of the spring is attached to a rigid wall. Initially the spring is in its natural length and the length of container between the piston and its side wall is `L`. Now an dideal diatomic gas is slowly filled in the container so that the piston moves quasistatically. It pushed the piston by `x` so that the spring now is compressed by `x`. The total rotaional kinetic energy of the gas molecules in terms of the displacement `x` of the piston is (there is vacuum outside the container)

Options

A. `kxL`
B. `4k xL`
C. `kx(x+L)`
D. `(2kx^(2))/(L)`

Explanation

Rotational `K.E=` Rotational degree of freedom`xx(1)/(2)nRT`
`2xx(1)/(2)nRT =nRT =PV`
`=PA,(V)/(A)=` force on piston `(L+X) =kx(L+x)`