hw5solv2

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/29/2011 for the course PHYSICS 404 taught by Professor Anlage during the Fall '11 term at Maryland.

### Page1 / 5

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online