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Unformatted text preview: 1 Homework 5 (due November 15) Problem 5-1 (3 pts.) Let the dispersion relationship for an ideal Bose gas particles be given by the following scaling law: ( p ) p 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 = 0 can be reached at a f nite density, i.e. when the following integral converges: c = 4 (2 ~ ) 3 Z exp ( p ) T 1 1 p 2 dp Divergency is only possible at small p. in this limit, [exp ( ( p ) /T ) 1] p . Hence, the following integral should converge: P Z p d 1 dp We conclude that d > Problem 5-2 (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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