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Unformatted text preview: Chemistry 120B SP11 Problem Set 6 Solutions Total: 50 points 1. (10 points) See MQS Solutions Manual. 2. (i) (3 points) When the membrane is pushed through the solution, the number of microscopic states available to the ions decreases. This means the entropy decreases. This process isnt spontaneous and thus requires work. (ii) (4 points) The minimum amount of work required is the reversible work w rev . Because the energy of the system doesnt change as a result of the purification, the reversible work is equal to the reversible heat flow out of the system. We can also take advantage of the relationship between reversible heat and entropy. E = w rev + q rev = 0 w rev =- q rev =- T S Using Boltzmanns definition of entropy, S = S fresh- S initial = k B ln W fresh- k B ln W initial = k B ln W fresh W initial At fixed T and N , we only need to consider the volume dependence of the partition functions, W V N . Using N = c V (where V denotes the original volume) and V fresh...
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