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**Unformatted text preview: **Problem Set 3: Due by Mar. 13 in class Problem 1. At low temperatures, the heat capacity (at a constant pressure) of a solid is a function of temperature and specifically follows the law 3 ) ( aT T C P = where a is a positive constant. This is what the Debye’s theory of heat capacity implies at a low temperature (T < ~10 K) and was a triumph of quantum mechanics back in the early 20 th century. Show that under a constant pressure, ) ( ) ( T bC T S P = where b is another constant. What is the value of b ? Problem 2. Two blocks of the same metal and same size are at different temperatures T 1 and T 2 . Each block’s heat capacity at a constant pressure is C P . These blocks are brought together and allowed to come to the same temperature. It is done at a constant pressure and it is assumed that C P is temperature-independent. Assume that the entire blocks are thermally isolated from the surrounding. (a) Express the entropy change of the two blocks (block 1 + block 2) with C P , T 1 and T 2 . (b) Is this change spontaneous? Assume that these two blocks are isolated from the surrounding....

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