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PHYS427fa08_HW12

PHYS427fa08_HW12 - Physics 427 Fall 2008 Homework 12 due 1...

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Unformatted text preview: Physics 427 Fall 2008 Homework # 12 November 10, 2008; due November 17, 2008 1. Kittel and Kroemer: Chapter 9; Problem 2 “Thermal ionization of hydrogen” 2. Kittel and Kroemer: Chapter 9; Problem 3 “Ionization of donor impurities in semiconductors” 3. Kittel and Kroemer: Chapter 9; Problem 5 “Particle‐antiparticle equilibrium” 4. This problem illustrates the basic features of the statistical mechanics of thermal expansion and related phenomena. Consider a one‐dimensional chain of length L, made of N one‐dimensional harmonic oscillators. We assume that the energy of the chain is given by N α 1⎞ ⎛ E = (L - Lo )2 + ∑ ⎜ N i + ⎟hω 2 2⎠ i=1 ⎝ where Lo and α are constants. The oscillator angular frequency ω is a function of L. You are given ω and dω/dL. a.) Find the equilibrium length of the chain at T = 0. The answer is not Lo. b.) Find the Helmholtz free energy F, the Gibbs free energy G, and the enthalpy H of the chain. c.) Will the chain expand or shrink as it is heated? You may not want to complete the calculation, but tell in complete detail how you would do it. ...
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