Free expansion is an irreversible process in thermodynamics  which a volume of gas is kept in one side of a thermally isolated container (via a small partition), with the other side of the container being evacuated. The partition between the two parts of the container is then opened, and the gas fills the whole container.

As per first law of thermodynamics change in internal energy equals the difference of heat added to the system and work done.The system is isolated and no heat transfer occurs with the surroundings therefore temperature remains constant implying work done,change in internal energy and heat added to system all are zero.The only thing that changes is the pressure and volume of the system.

If initial pressure and volume are P1 and V1.Then P1V1=P2V2 where P2 and V2 are final pressure and volume.

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