phys 369 09 hw 8 - Phys. 369, Fall 2009 Homework #8 Due:...

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Phys. 369, Fall 2009 Homework #8 Due: Monday, Nov. 2, beginning of class 100 points total 1. (10 points) In the practice questions for Test 1, we considered the problem of a ball that rolls back and forth in a valley and eventually comes to rest at the bottom of the valley, as illustrated above. a. Suppose that at time t = 0, you release the ball from a position on the side of the valley, and then wait until the ball comes to rest at the bottom of the valley. Assume that the valley heat capacity is large, so that its temperature remains at a constant value T valley , and that there is enough thermal contact between the valley and the ball that the initial and final temperature of the ball are equal to T valley . Give the initial and final values of the internal energy U , entropy S , and free energy F of the ball, in terms of parameters such as the elevation h , mass m, temperature T, and heat capacity C ( T ) of the ball. Make a qualitatively correct graph of U ( t ), S ( t ), and F ( t ). b. How large is the change in the entropy of the valley, relative to the change in the quantities you calculated in part (a)? c. An often valid intuition is that the energy of a system “wants to decrease.” Give a detailed and precise explanation for the fact that the energy U of the ball “wants to decrease” in this example. 2. (16 points) a) Suppose you have a sample of water which initially contains some liquid and some gas. The temperature of this sample is 298 K and the pressure is 1 bar. To be more specific, the liquid water, considered as a separate system, is initially in thermal equilibrium at 298 K and 1 bar. The
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phys 369 09 hw 8 - Phys. 369, Fall 2009 Homework #8 Due:...

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