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Expansions of a Perfect Gas

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I started doing this problem but I could way off here. I think that for part C it is the Joule-Kelvin expansion. So the final temperature would be T1 plus a hairy integral. For part B) it seem like it is just the Joule expansion. However, I am not sure if I manipulated the partial derivatives in the right way. Part A I can't figure out. I think I would start with the 1st law in the differential form. Drop the dS term and try to manipulate the derivatives again. However, I do not know what type of expansion this would be. If someone could do this problem from A to C I would really appreciate it.

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I started doing this problem but I could way off here. I think that for part C it is the Joule-Kelvin expansion. So the final temperature would be T1 plus a hairy integral. For part B) it seem like it is just the Joule expansion. However, I am not sure if I manipulated the partial derivatives in the right way. Part A I can't figure out. I think I would start with the 1st law in the differential form. Drop the dS term and try to manipulate the derivatives again. However, I do not know what type of expansion this would be. If someone could do this problem from A to C I would really appreciate it.

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