Forming MixturesA system consists initially of nA moles of

Chapter 12, Problem 29P

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A system consists initially of \(n_{\mathrm{A}}\) moles of gas A at pressure p and temperature T and \(n_{\mathrm{B}}\) moles of gas B separate from gas A but at the same pressure and temperature. The gases are allowed to mix with no heat or work interactions with the surroundings. The final equilibrium pressure and temperature are p and T, respectively, and the mixing occurs with no change in total volume.

(a) Assuming ideal gas behavior, obtain an expression for the entropy produced in terms of \(\bar{R}, n_{\mathrm{A}}, \text { and } n_{\mathrm{B}}\)

(b) Using the result of part (a), demonstrate that the entropy produced has a positive value.

(c) Would entropy be produced when samples of the same gas at the same temperature and pressure mix? Explain.

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