7. (10 points) An ideal gas undergoes a reversible change at constant pressure from (T, V)...

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7. (10 points) An ideal gas undergoes a reversible change at constant pressure from (T₁, V₁) to (T2, V₂). a. Starting with the fundamental equation for internal energy in Model 1 of Fundamental.12, show that if the constant-volume heat capacity Cr does not depend on temperature, then the change in entropy for this process is given by T₂ AS = Cy In +nRln T1 V₂ V₁ Be specific about the path you use to derive this formula. b. The result in the previous question was derived assuming that the changes were reversible. Explain why the equation works for any path between the two specified states, no matter whether the path is reversible or irreversible. c. Calculate the entropy change for one mole of N₂ gas that is at an initial state (25.0 L, 298 K) and a final state (50.0 L, 596 K). 7. (10 points) An ideal gas undergoes a reversible change at constant pressure from (T₁, V₁) to (T2, V₂). a. Starting with the fundamental equation for internal energy in Model 1 of Fundamental.12, show that if the constant-volume heat capacity Cr does not depend on temperature, then the change in entropy for this process is given by T₂ AS = Cy In +nRln T1 V₂ V₁ Be specific about the path you use to derive this formula. b. The result in the previous question was derived assuming that the changes were reversible. Explain why the equation works for any path between the two specified states, no matter whether the path is reversible or irreversible. c. Calculate the entropy change for one mole of N₂ gas that is at an initial state (25.0 L, 298 K) and a final state (50.0 L, 596 K).