Two quick notes from class today

(1) I found a small typo in the heat capacity calculations handout. In the last equation on the first page, there is a T1^2 that should be a T1^3. A corrected version is posted on the website. Also, if you find any more typos, please let me know so that I can correct the document.

(2) In discussing the microscopic derivation of the entropy, I neglected to mention the following: since S = k ln Omega, and since Omega counts the number of configurations of molecules, the second law really says that molecules like to maximize their number of configurations. This underlies the statement that the entropy always increases; molecules never spontaneously decide to choose a smaller subset of configurations than the total number that are available to them.

Earlier we had said that the second law is not about increasing disorder. Instead, it is about increasing numbers of configurations. The two are not the same. For example, if one very quickly cools a liquid below its freezing temperature and then suddenly places it in an isolated container, as the liquid starts to freeze, the entropy increases. This actually happens because there are more configurations when some of the liquid becomes frozen. This seems counterintuitive, since one intuitively wants to think of a liquid as having more configurations than a crystal. But for very low temperature liquids, there are simply less configurations for the molecules than there would be if some of those molecules could vibrate around lattice sites in a crystal. One can even calculate this and show it to be true. Therefore, our intuitive notion of "order" and "disorder" is not really quantitative, and not always related to the number of configurations, which is what is really important.