Lecture Notes2

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 &amp; 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...
View Full Document

## This document was uploaded on 03/26/2014 for the course PH 641 at NJIT.

Ask a homework question - tutors are online