ProbSet7_solutions(2)

So when we take the difference between the entropies

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Unformatted text preview: f A molecules. Likewise, the entropy of state 2 is given by: S2 = − k B ⎡ A2, left × (ln A2, left ) + A2, right × (ln A2, right ) ⎤ + kB ( Atotal )ln M ⎣ ⎦ Comparing these expressions for S1 and S2 we can see that the last term, which is the only term involving M, is the same in both cases. So when we take the difference between the entropies (i.e., S1-S2) the term involving M disappears. Bottom line: to compare the entropies we only need to calculate the terms involving the numbers of A molecules. Now we can work out which state has higher entropy. S1 = − k B ⎡ A1, left × (ln A1, left ) + A1, right × (ln A1, right ) ⎤ + kB ( Atotal )ln M ⎣ ⎦ = − kB ⎡ 0.33 × 10 6 × ln(0.33 × 10 6 ) + 0.67 × 10 6 × ln(0.67 × 10 6 ) ⎤ + k B ( Atotal )ln M ⎣ ⎦ = − kB ⎡ 4.193 × 10 6 + 8.988 × 10 6 ⎤ + kB ( Atotal )ln M ⎣ ⎦ = − kB ⎡13.181 × 10 6 ⎤ + kB ( Atotal )ln M ⎣ ⎦ And: S2 = − k B ⎡ A2, left × (ln A2, left ) + A2, right × (ln A2, right ) ⎤ + kB ( Atotal )ln M ⎣ ⎦ = − kB ⎡ 0.32 × 10...
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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 Berkeley.

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