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Unformatted text preview: 1 Homework 5 (due November 15) Problem 51 (3 pts.) Let the dispersion relationship for an ideal Bose gas particles be given by the following scaling law: ε ( p ) ∼ p α What should be the dimensionality of the physical space d for this system to be capable of Bose condensation? Solution: Bose condensation is possible if µ = 0 can be reached at a f nite density, i.e. when the following integral converges: ρ c = 4 π (2 π ~ ) 3 ∞ Z ∙ exp μ ¡ ( p ) T ¶ − 1 ¸ − 1 p 2 dp Divergency is only possible at small p. in this limit, [exp ( ¡ ( p ) /T ) − 1] ∼ p α . Hence, the following integral should converge: P Z p d − α − 1 dp We conclude that d > α Problem 52 (4 pts.) Find the energy density U of a photonic gas in d dimensions, as a function of temperature T (assume all the fundamental constants to be the same as in our world). By using the standard thermodynamic relationships, f nd the corresponding entropy density s , free energy density f , and radiation pressure...
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This note was uploaded on 09/28/2008 for the course PHYS 510 taught by Professor Anon during the Winter '04 term at Cornell.
 Winter '04
 ANON
 mechanics, Work, Statistical Mechanics

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