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# homework8 - Homework#8 PHYS 603 Spring 2008 Deadline...

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Homework #8 — PHYS 603 — Spring 2008 Deadline: Thursday, April 17, 2008, in class Professor Victor Yakovenko Office: 2115 Physics Web page: http://www2.physics.umd.edu/ ~ yakovenk/teaching/ Textbook: Silvio Salinas, Introduction to Statistical Physics Springer, 2001, ISBN 0-387-95119-9 Do not forget to write your name and the homework number! Each problem is worth 10 points. Ch. 9 The Ideal Fermi Gas 1. Problem 9.1. Compressibility of the Fermi gas. [10 points] The compressibility is defined in Eq. (3.43). Only derive an equation for the compress- ibility and do not calculate a numerical value for metallic sodium. 2. Entropy and spin susceptibility of the Fermi gas at T ¿ ε F . [20 points] (a) Entropy of the Fermi gas. As discussed in Problem 3 of Homework 7, the entropy of the Fermi gas is S = γV Z dε D ( ε ) s ( ε ) , s ( ε ) = - f ( ε ) ln f ( ε ) - [1 - f ( ε )] ln[1 - f ( ε )] , (1) where f ( ε ) = [ e β ( ε - μ ) + 1] - 1 is the Fermi distribution function, γ is the number of fermion species ( γ = 2 for spin 1/2), and D ( ε ) is the energy density of states. Sketch the function s ( ε ) in the case T ¿ ε F . Indicate the position, the width, and the height of the peak in this function.

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homework8 - Homework#8 PHYS 603 Spring 2008 Deadline...

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