Lecture Notes2

Constants stefan boltzman constant 56710 8wm2k4 bohr

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Unformatted text preview: x rN r r ∏N ! i i 1 ⋅ 3 ⋅ 5 ⋅ ⋅ ⋅ ( n − 1) π 1 / 2 , n = even 2(2a ) n / 2 a ∞ 2 I n = ∫ x n e − ax dx = n +1 0 Γ( ) 2 , n = odd 2 a ( n +1 ) / 2 6. Constants: Stefan-Boltzman constant σ=5.67×10-8W/m2K4, Bohr Magneton: 9.273×10-21erg gauss-1 2 Ch. 2 The Canonical Ensemble A! W (a ) = ∏ ak ! aj 1 Pj = = AA k j a * j a ∂ λnW ( a ) − α ∑ a k − β ∑ a k E k = 0 ∂ aj k k p = ∑ pjPj = − ∑ W ( a )a ( a ) a = A W (a ) ∑ ∂E j − β εj e −βε j ∑e ∑ ∂V j j ∂E j p j = − ∂V N − ∂ E = − p + β Ep − β E p ∂V N ,β j ∂ E ∂ p + β ∂V ∂β = − p N ,β N ,V ∂E ∂p − T = −p ∂V T , N ∂T N ,V S= E + kλnQ + const T −− − ∂ p = E p − Ep ∂β N ,V W ( a , b) = A! B! ∏a !∏b ! j k j k d E = ∑ E j d P j + ∑ P j dE j = δq rev − δw rev j j ∂λnQ E = kT 2 ∂T N ,V ∂λnQ p = kT ∂V N ,T ∂λnQ S = kT + kλnQ ∂T N ,V A( N , V , T ) = − kTλnQ ( N ,V , T ) 3 Ch. 3 Formula Table Microcanonical ensemble, S = k ln Ω 1 ∂ ln Ω = kT ∂ E N ,V µ ∂ ln Ω = − kT ∂N V , E Canonical ensemble, Ω( N , V , E ) =degeneracy p µ 1 dS = dE + dV − dN T T T p ∂ ln Ω = kT ∂ V N , E Q( N ,V , T ) = ∑ e − βE j ( N ,V ) j A = − kT ln Q dA = − SdT − pdV + µdN ∂ ln Q p = kT ∂V N ,T ∂ ln Q S = k ln Q + kT ∂T N ,V ∂ ln Q µ = − kT ∂N V ,T Grand canonical ensemble, ∂ ln Q E = kT 2 ∂T N ,V Ξ(V , T , µ ) = ∑ N ∑e − βE j e µN kT j pV = kT ln...
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This document was uploaded on 03/26/2014 for the course PH 641 at NJIT.

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