What is the value of work during free expansion?

During free expansion, the process occurs without any external pressure acting on the system, and there is no opposing force exerted on the gas. In essence, a gas expands into a vacuum or an environment where no work can be done against another pressure.

Work is defined in thermodynamics as being done when a force is applied to move an object or change its state. In the case of free expansion, since the gas is not pushing against any external pressure, it does not perform any work during the expansion process. Therefore, the value of work done in this scenario is zero.

This is consistent with the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In free expansion, if no work is done, the internal energy change solely depends on the heat transfer, but in an isolated system, typically there is no heat transfer either. Thus, the work remains zero.