Fall 2010 problem set 7 uc berkeley page 4 the first

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Unformatted text preview: Fall 2010. Problem Set 7 UC Berkeley Page 4 The first thing to note is that the question does not specify how many grid boxes the chamber is divided into (i.e., the value of M is not specified). This is because the value of M is not important in the calculation of differences in entropy, as long as M is sufficiently large (i.e., M >>N, where N is the total number of atoms). We explain why this is so below. The question also asks us to use the probabilistic definition of entropy. To do this, we assume that each side of the chamber is divided into M grid boxes. Each grid box can be in one of 3 states: (i) occupied by A, (ii) occupied by B, or (iii) empty. Notice that the number of B molecules in each chamber does not change in State i or State ii. In this case, the change in entropy depends only on the entropy of the A molecules. Let us first understand why this is so. We can ignore the B molecules because: Let the number of molecules be denoted A1,left, B1,left, etc. For the left side, probability of a grid box being in each of these three states is given by: B1, left M − ( A1, left + B1, left ) , pB1, left = and pempty, left = ≈1 M M M The last term is essentially equal to 1 because the number of A and B molecules is very small compare...
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This note was uploaded on 01/27/2011 for the course MCB 100A taught by Professor Kuryian during the Spring '09 term at University of California, Berkeley.

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