PS3Solutions

PS3Solutions - Chemistry 120B SP11 Problem Set 3 Solutions Total 50 points 1(11 points See MQS Solutions Manual The graph of f J/f has a local

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Unformatted text preview: Chemistry 120B SP11 Problem Set 3 Solutions Total: 50 points 1. (11 points) See MQS Solutions Manual. The graph of f J /f has a local maximum as a result of degeneracy, encoded in the prefactor (2 J + 1). Without the entropic contribution to the relative probabilities, they would decay exponentially with J . 2. (i) (3 points) S ( E + Δ E ) ≈ S ( E ) + ∂S ∂E N,V Δ E Δ S = S ( E + Δ E )- S ( E ) ≈ ∂S ∂E N,V Δ E Δ S = Δ E T (ii) (3 points) Δ S (1) = Δ E (1) T (1) Δ S (2) = Δ E (2) T (2) Δ S = Δ S (1) + Δ S (2) = Δ E (1) T (1) + Δ E (2) T (2) If Δ E is the magnitude of energy transferred from system 1 to system 2, then Δ E (2) =- Δ E (1) = Δ E . Δ S = Δ E 1 T (2)- 1 T (1) (iii) (3 points) If T (1) > T (2) , the quantity in parentheses is positive. We defined Δ E to be positive. So Δ S is positive. (Any spontaneous process in a system with fixed E , V , and N is accompanied by an increase in entropy. Although the partitioning of energy between systems 1 and 2 is changing, the energy of the composite system is fixed.) 3. (i) (3 points) S ( V + Δ V ) ≈ S ( V ) + ∂S ∂V N,E Δ V Δ S = S ( V + Δ V )- S ( V ) ≈ ∂S ∂V N,E Δ V Δ S = p T Δ V 1 (ii) (3 points) Δ S (1) =...
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This note was uploaded on 09/12/2011 for the course CHEM 107B taught by Professor Jamesames during the Spring '09 term at UC Davis.

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PS3Solutions - Chemistry 120B SP11 Problem Set 3 Solutions Total 50 points 1(11 points See MQS Solutions Manual The graph of f J/f has a local

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