hw5solv2 - Homework #5 Solutions Question 1) K+K Chapter 3,...

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Homework #5 Solutions Question 1) K+K Chapter 3, Problem 9. The partition function is a sum of Boltzmann factors over every state of the composite system, without regard to total energy, etc Z = X s e - ε s The combined system has energies ε s = ε 1 + ε 2 . These states are the combination of every possible state of system 1 and system 2 Z (1+2) Z = X s e - ( ε 1 + ε 2 ) = X s 1 X s 2 e - ( ε s 1 + ε s 2 ) = X s 1 e - ε s 1 X s 2 e - ε s 2 Z (1 + 2) = Z (1) Z (2) This can be generalized to N independent distinguishable systems that exchange energy at fixed τ Z (1 + 2 + ··· N ) = Z (1) Z (2) ··· Z ( N ) This gets more complicated though if we are talking about N indistinguishable particles in the system. In that case we have to worry about not counting states more than once. Question 2) K+K Chapter 3, Problem 2. With the results of the last problem in mind, start with the partition function of a single spin: Z 1 = e mB/τ + e - mB/τ = 2 cosh( mB/τ ) We can get the magnetization by taking the average of the magnetic moment
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This note was uploaded on 12/29/2011 for the course PHYSICS 404 taught by Professor Anlage during the Fall '11 term at Maryland.

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hw5solv2 - Homework #5 Solutions Question 1) K+K Chapter 3,...

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