quiz3_solutions

# quiz3_solutions - = n+1 (ii) The multiplicity is always 1...

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Name:_________________________________________________ MCB100A/CHEM130 In-section Quiz #3 (Aathavan), Nov 04, 2005. Open book, 15min. A . B . . . . . . ---------------------------- 4 ε -------------------------- ---------------------------- 3 ε -------------------------- ---------------------------- 2 ε -------------------------- ---------------------------- 1 ε -------------------------- ---------O---O------------ 0 -------------O----------- 1. (i)What would be the multiplicity of the system A when its total energy is E= n ε, (n is an integer)? (Hint: You may solve for n=0,1,2,… and then deduce a general expression from it). (ii) Similarly, calculate what the multiplicity of system B will be for E= n ε (i) The multiplicity in this case is the same as the # ways of adding two numbers (from 0-n) to sum up to n

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Unformatted text preview: = n+1 (ii) The multiplicity is always 1 2. You bring into thermal contact systems A and B at energies E=nε each. What will be the equilibrium energies of A and B. What will be the final equilibrium temperature of the two systems? If you prefer dealing with actual numbers, consider n=1, ε =1 (Hint: For a discrete function y(x) you may use, dy/dx = [y n+1-y n ]/[x n+1-x n ]) Let the energy redistribute such that A has n A ε n A +n B = 2n W of the combined system is n A = (n A +1).1 This will be a maximum when n A = 2n and n B =0 So E A = 2nε and E B = 0 T B = ΔE/ΔS = Δε/0 = ∞ T A = ε----------------------------S(2nε+ε) – S(2nε) = ε--------------------------ln(2n+1+1)-ln(2n+1) = ε-------------------------ln(2n+2)/(2n+1)...
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## This note was uploaded on 09/14/2009 for the course MCB 100A taught by Professor Kuryian during the Fall '09 term at Berkeley.

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quiz3_solutions - = n+1 (ii) The multiplicity is always 1...

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