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Unformatted text preview: Chem120B Problem Set 5 Due: February 29, 2008 1. Problems 19-7, 19-13, 19-14, and 19-34 in Simon and McQuarries Physical Chemistry . For problem 19-34, notice that the heat capacity C p = parenleftbigg H T parenrightbigg p,N is very large at the transitions between different phases (solid liquid and liquid gas). Explain this fact in terms of fluctuations in energy and/or volume. 2. (i) In the previous assignment you explored how the Gibbs entropy of a probability distribution de- pends on its width. Here you will show that a uniform distribution actually has the largest possible entropy. To do this, you need to find the combination of microstate probabilities p that maximize S = k B p ln p . [We have changed notation slightly from the usual P ( ) to p , which is more convenient for this calculation.] If we think of each p as an independent variable, then the maximum would be specified by parenleftbigg S p parenrightbigg p negationslash = = 0 for each microstate . These probabilities, however, cannot actually vary independently, since they must all sum up to 1. One way to deal with this is to single out one microstate, say = 1 , and write its probability in terms of all the others: p 1 = 1 M summationdisplay =2 p , where M is the total number of microstates. Now we can differentiate S = k B bracketleftBigg p 1 ( p...
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