Boltzmann Equation for Entropy:
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From my understanding, free expansion is the same as a irreversible expansion which is when there is no external pressure on the system. If the system has no external pressure and if the gas is expanding against no external pressure, the gas is said to expand freely. Because there is no expansion against an external pressure, the expanding gas does no work, because work is equal to FD which is external force times distance traveled. No external force no work.
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