homework3 - Physics 262 Statistical Physics Fall 2008 Problem Set 3 due Wed Oct 8 Reading Parthria Sections 3.6-3.10 Chapter 4 1 Show that the canonical

homework3 - Physics 262 Statistical Physics Fall 2008...

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Physics 262 : Statistical Physics Fall 2008 Problem Set 3 due: Wed Oct 8 Reading: Parthria, Sections 3.6-3.10, Chapter 4. 1. Show that the canonical partition function, Z N , of a classical ideal gas of N particles in a box of volume V at a temperature T can be written as Z N = 1 N ! V λ 3 N (1) where λ h/ 2 πmk B T is the thermal de Broglie wavelength. From this result for Z N , obtain an exact expression for the grand canonical partition function, Z gc , as a function of the chemical potential μ , V , and T . Obtain expressions for S , P , and N from Z gc , and thence the equation of state. 2. (Parthria 3.15) Show that the classical canonical partition function of an extreme relativistic gas of N particles with dispersion ε = pc is Z N = 1 N ! 8 πV k B T hc ! 3 N (2) Show that this gas has PV = E/ 3, E = 3 Nk B T , and γ = 4 / 3. 3. Entropy of mixing (see also Parthria Section 1.5) Consider ideal gases of two species A and B . Initially, we have N A molecules of ideal gas A at equilibrium in a box of volume V A
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