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homework9

# homework9 - Homework#9 PHYS 603 Spring 2008 Deadline...

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Homework #9 — PHYS 603 — Spring 2008 Deadline: Thursday, April 24, 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. 10 Free Bosons: Bose-Einstein Condensation; Photon Gas 1. Problem 10.3. Bose gas with an internal degree of freedom. Assume that the gas is in 3 dimensions. Write down a general equation for determining the Bose-Einstein condensation temperature T 0 , but do not solve it in general case, because it does not have a simple solution. What is the value of the chemical potential μ at T 0 ? Determine T 0 in the limiting cases ² 1 ¿ ¯ h 2 n 2 / 3 /m and ² 1 ¯ h 2 n 2 / 3 /m (take the limits ² 1 0 and ² 1 → ∞ to answer this question). Is there Bose-Einstein condensation in this problem in 2 dimensions and 1 dimension? Explain why. 2. Temperature dependences for parabolic and linear dispersion. Assuming that the degeneracy is γ = 1, the general expressions for the number of particles, internal energy, and entropy per unit volume of a gas are n = N V = Z dε D ( ε ) f ( ε ) , u = U V = Z dε D ( ε ) ε f ( ε ) , s = S V = Z dε D ( ε ) s ( ε ) , (1) where s ( ε ) = [ f ( ε ) + 1] ln[ f ( ε ) + 1] - f ( ε ) ln f ( ε ) and f ( ε ) = [ e β ( ε - μ ) - 1] - 1 are the entropy function and the occupation number for a Bose gas.

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