Lecture Notes2

Kt n t p e j e pv kt 4 ch 4 boltzmann fermi dirac

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Unformatted text preview: Ξ d ( pV ) = SdT + Ndµ + pdV ∂ ln Ξ S = k ln Ξ + kT ∂T V , µ ∂ ln Ξ N = kT ∂µ V ,T ln Ξ ∂ ln Ξ p = kT = kT V ∂V µ ,T ∂ ln Ξ E = − ∂β V ,γ Isothermal-isobaric ensemble, ∆( N , T , p ) = ∑ E ∑ Ω( N ,V , E )e V G = − kT ln ∆ dG = − SdT + Vdp + µdN ∂ ln ∆ S = k ln ∆ + kT ∂T N , p ∂ ln ∆ V = − kT ∂p N ,T ∂ ln ∆ µ = − kT ∂N T , p − βE j e − pV kT 4 Ch. 4 Boltzmann, Fermi-Dirac and Bose-Einstein Statistics 1. Boltzmann Statistics Partition function for a single particle : q(V , T ) = ∑ e −ε i / kT i Partition Function for the system : Probabilit y for particles in jth state : Q(N,V,T) = ( q(V , T )) N or q N / N ! nj N = e − ε j / kT q 2. Fermi-Dirac & Bose-Einstein Statistics: ( Grand Canonical Ensemble ) ∞ ∞ −β εn Ξ(V , T , µ ) = ∑ λ N ∑ * e ∑i i i = ∑ n =0 = n =0 { nk } max n1 max n2 ∑ ∑Λ ∏ (λe n1 = 0 n2 = 0 k where λ = e βµ , ∴ Ξ FD = ∏ (1 ± λe − βε k ) BE − βε k ∑ ∏ (λ e * { nk } − βε k )k k max nk ) k = ∏ ∑ (λe − βε k ) k k nk = 0 F - D : n kmax = 1 , B - E : nkmax = ∞ ±1 k...
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This document was uploaded on 03/26/2014 for the course PH 641 at NJIT.

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