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Unformatted text preview: Physics 5524 Statistical Mechanics Problem Set 11 Due: Wednesday, Apr. 14 11.1 Problem 18, Chapter 7 of Pathria, Pg. 191. 11.2 Consider a gas of photons with dispersion ( ~ k ) = c | ~ k | where c is the speed of light. The photons are confined to a three-dimensional volume V and are in thermal equilibrium at temperature T . (a) For this photon gas, obtain an expression for the grand potential =- k B Tln Z where Z is the grand partition function (remember that the chemical potential for photons is zero). This expression will involve an integral over frequency which you should not try to evaluate. (b) Show that the dependence of on volume V and temperature T is of the form V T and determine the exponent . (c) Show that the dependence of the entropy of this gas S on volume V and temperature T is of the form S V T , and determine the exponent . (d) Now assume this gas undergoes an adiabatic (i.e. S = 0) expansion with initial temperature T i = 3000 K and final temperature...
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