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I am solving a problem that analyzes a classical ideal monoatomic gas. After determining the partition function, free energy and entropy, it asks me to analyze the variation of entropy if I had a wall between a box and mixed two gases that are equal. In the microcanonical ensemble the variation is zero, but here the in the canonical ensemble, I have to take in account different factors like temperature. How do I approach the problem from the canonical ensemble perspective?

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