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homework7

# homework7 - Homework#7 PHYS 603 Spring 2008 Deadline...

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Homework #7 — PHYS 603 — Spring 2008 Deadline: Thursday, April 10, 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. 7 The Grand Canonical and Pressure Ensembles 1. (a) Problem 7.2. Relativistic gas with ε = cp . Just calculate the grand partition function and the grand thermodynamic poten- tial. You don’t need to do the rest of the problem and use Eq. (7.71). (b) Problem 7.4. h N ) 2 i for the ideal gases. Do the problem for the ideal gases with both the quadratic dispersion ε = p 2 / 2 m and the linear dispersion ε = cp . 2. Problem 7.6. The chemical potential of the adsorbed gas. Assume that the adsorbed molecules have the binding energy to the surface - ² 0 relative to the unbound state. Assume that each adsorption center can be occupied by, at most, one molecule. Notice that the entropy for a similar problem was calculated in Problems 2.7 and 4.5. Ch. 8 The Ideal Quantum Gas 3. Modified Problem 8.2. The entropies of the Fermi, Bose, and classical gases. This formulation of the problem follows the book by Landau and Lifshitz “Statistical Physics, Part I”, Secs. 40 and 55. Let us consider an element of the phase space, which has the following number of the quantum states G j = d 3 r d 3 p (2 π ¯ h ) 3 . (1) We assume that the phase space element, on one hand, is big enough so that G j 1, and, on the other hand, is small enough, so that the quantum states in this element have approximately the same energy ε j . (In the simplest case, ε j = p 2 j / 2 m , where p j is the momentum corresponding to this element.)

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