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Internal Energy of a Gas System: Partition, Conservation

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I try to simplify my problem here. This is the place where I may have some misunderstanding in the adiabatic process. Consider a uniform cylinder with insulated wall cylinder that has a very thin and mass less partition at middle divide it into two sections. The left section contains gas molecules and the right side is attached to a mass less spring with vacuum condition.

a) As long as the force exerted by the spring is less than the force exerted by the gas, the partition will move to the right correct?
b) The change in internal energy of the gas will not always be the same as the elastic energy stored by the spring correct?
c) Energy is always conserved so where does the energy goes if it is not the same?
d) Does the process have any differences if the middle partition consists of very thin
and very heavy partition.

All the partition with the contact surface is frictionless.

See the attached file.

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The solution answers questions regarding the internal energy of a gas system.

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a) As long as the force exerted by the spring is less than the force exerted by the gas, the partition will move to the right correct? Yes
b) The change in internal energy of the gas will not always be the same as the elastic ...

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