The box in Figure 19.19 contains seven gas particles in compartment (mathrm{A}) and five in compartment (mathrm{B}),

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The box in Figure 19.19 contains seven gas particles in compartment \(\mathrm{A}\) and five in compartment \(\mathrm{B}\), and the partition separating the compartments is free to move. Let the volume of the box be \(V\) and the initial ratio of the compartment volumes be \(V_{\mathrm{B}, \mathrm{i}} / V_{\mathrm{A}, \mathrm{i}}=3\). What is the change in the entropy of this gas as it evolves from this macrostate to equilibrium?

Data from Figure 19.19

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