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A fixed container is fitted with a pisto...

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)

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