PHYS427fa08_HW04 - Physics 427 Fall 2008 Homework # 4...

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Unformatted text preview: Physics 427 Fall 2008 Homework # 4 September 15, 2008; due September 22, 2008 1. A system consisting of N Ising spins in a magnetic field B has a multiplicity g which is equal to 1 when all of the spins are in the lower state and also when they are all in the upper state. Hence, σ = 0 when U = −NmB or NmB, and σ has a maximum when U = 0. Draw some graphs qualitatively (no need to actually calculate the numbers) in the range from U = −NmB/3 to U = NmB/3: a.) Draw a graph of σ vs. U. b.) Draw a graph of 1/τ vs. U. c.) Draw a graph of τ vs. U. d.) Draw a graph of CV vs. U. e.) In terms of the Boltzmann distribution, what does it mean for the temperature to be < 0? 2. Kittel and Kroemer: Chapter 3; Problem 2, “Magnetic Susceptibility”. (HINT: You can calculate the energy, U = ‐ <M>B to find <M>.) 3. Kittel and Kroemer: Chapter 3; Problem 9, “Partition Function for Two Systems”. 4. Kittel and Kroemer: Chapter 4; Problem 2, “Surface Temperature of the Sun”. HINTS: See Kittel and Kroemer, Chapter 2, problem 2 σ =‐ σ0 − U2 / 2m2B2N For T<0, think about practical applications. ...
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