final08

final08 - Statistical Mechanics - PHY 5524 Final Exam April...

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Statistical Mechanics — PHY 5524 Final Exam April 25, 2008 1. (35 pts) Consider a gas of photons with dispersion ω = 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 . In what follows you may use, without proof, the fact that the density of states for this system, g ( ω ), defined so that g ( ω ) is the number of single-photon states with angular frequency between ω and ω + , is given by g ( ω ) = V ω 2 π 2 c 3 . (a) For this photon gas, obtain an expression for the grand potential Σ = - k B T ln 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 Σ on volume V and temperature T is of the form Σ V T α and determine the exponent α . (c)
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final08 - Statistical Mechanics - PHY 5524 Final Exam April...

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