Imagine we have two boxes with n and n moles of ideal gas each; the boxes...

 

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Imagine we have two boxes with n and n moles of ideal gas each; the boxes are in thermal contact with each other and the combined system is isolated from the world and has a total energy E. Using the Sackur-Tetrode equation to obtain the entropies, show that the total entropy of the two boxes together is maximized when the energy in the two boxes is split in the ratio ni: n2. Problem 4 Consider an ideal gas at pressure P and volume V. It is allowed to expand to volume V2 in such a way that the entropy remains constant (an isentropic or reversible adiabatic expansion). How must the total energy of the gas change? Show that PV/3 = P2V5/3 Imagine we have two boxes with n and n moles of ideal gas each; the boxes are in thermal contact with each other and the combined system is isolated from the world and has a total energy E. Using the Sackur-Tetrode equation to obtain the entropies, show that the total entropy of the two boxes together is maximized when the energy in the two boxes is split in the ratio ni: n2. Problem 4 Consider an ideal gas at pressure P and volume V. It is allowed to expand to volume V2 in such a way that the entropy remains constant (an isentropic or reversible adiabatic expansion). How must the total energy of the gas change? Show that PV/3 = P2V5/3

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To show that the total entropy of the two boxes is maximized when the energy in the two boxes is split in the ratio n12 we can use the SackurTetrode e... View the full answer