ProbSet7_solutions(2)

The next thing to realize is that when calculating

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Unformatted text preview: molecules will cancel out. So we only need to consider the entropy of the A molecules. The next thing to realize is that when calculating differences in entropy, the value of M does not matter when the probabilistic definition of entropy is used (i.e., M is very large). Value of M does not matter: Chem C130/MCB C100A. Fall 2010. Problem Set 7 UC Berkeley Page 5 S1 = − Mk B ⎡ pA1, left ln pA1, left + pA1, right ln pA1, right ⎤ ⎣ ⎦ ⎡ A1, left ⎛ A1, left ⎞ A1, right ⎛ A1, right ⎞ ⎤ × ln ⎜ = − Mk B ⎢ ⎟ + M × ln ⎜ M ⎟ ⎥ ⎝M⎠ ⎝ ⎠⎦ ⎣M Cancelling the M terms we get: ⎡ ⎛ A1, left ⎞ ⎛ A1, right ⎞ ⎤ S1 = − k B ⎢ A1, left × ln ⎜ ⎟ + A1, right × ln ⎜ M ⎟ ⎥ ⎝M⎠ ⎝ ⎠⎦ ⎣ = − kB ⎡ A1, left × (ln A1, left − ln M ) + A1, right × (ln A1, right − ln M ) ⎤ ⎣ ⎦ = − kB ⎡ A1, left × (ln A1, left ) + A1, right × (ln A1, right ) − ( A1, left + A1, right )ln M ⎤ ⎣ ⎦ = − kB ⎡ A1, left × (ln A1, left ) + A1, right × (ln A1, right ) ⎤ + kB ( Atotal )ln M ⎣ ⎦ In the last step Atotal is the total number o...
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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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