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Unformatted text preview: Physics 112, Fall 2010: Holzapfel Problem Set 2 (6 problems). Due Monday, September 13, 5 PM Problem 1 : Paramagnetism (a) Kittel, Problem 2.2 (b) Roughly plot the entropy and the temperature as a function of energy. Notice that the temperature is negative for some values of U. If a system a with negative temperature is brought into contact with a system at positive temperature, which way will the energy flow? You may wish to consult Thermodynamics and statistical mechanics at negative absolute temperatures, Phys. Rev. 103 , 20 (1956). Problem 2 : Crystal Disorientations N atoms are arranged to lie on a simple cubic lattice. Then M of these atoms are moved from their lattice sites to lie at the interstices of the lattice, that is points which lie centrally between the lattice sites. Assume that the atoms are placed in the interstices in a way which is completely independent of the positions of the vacancies. a) Show that the number of ways of taking M atoms from the N lattice sites and placing them on the N interstices is: g ( N , M ) = N ! M ! ( N- M ) ! 2 . (1) (b) Suppose that the energy required to move an atom from its lattice site into any interstitial site is . The energy of the system is then U = M if there are M displaced atoms. Use our definition of entropy and temperature in terms of the entropy to show that:...
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