homework4 - Homework #4 PHYS 603 Spring 2008 Deadline:...

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Homework #4 — PHYS 603 — Spring 2008 Deadline: Thursday, March 6, 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. 4 Microcanonical Ensemble 1. Problem 4.1, Spin chain with energy S 2 j . 2. Problem 4.4, Entropy of the Boltzmann gas. Derive the general equations shown in this problem. In the last sentence, I believe the answer - k B T ln T is wrong. To derive the entropy of the Boltzmann gas, use the following procedure. In the spirit of Eq. (4.51), in the continuous limit the occupation numbers become N j N = P j P ( p ) = e - p 2 / 2 mT Z 1 , (1) where the normalizing factor Z 1 is given by a formula similar to Eq. (4.49), but written more accurately Z 1 = Z d 3 pd 3 r (2 π ¯ h ) 2 e - p 2 / 2 mT = V ˆ 2 πmT 2 π ¯ h ! 3 (2) The entropy per particle s = - j P j ln P j becomes s = - Z d 3 pd 3 r (2 π ¯ h ) 2 P ( p ) ln P ( p ) = - Z d 3 pd 3 r (2 π ¯ h ) 2 P ( p ) ˆ - p 2 2 mT - ln Z 1 ! = ln
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homework4 - Homework #4 PHYS 603 Spring 2008 Deadline:...

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