hw04soln - 1 Homework 4 (due November 1) Problem 4-1 (4...

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1 Homework 4 (due November 1) Problem 4-1 (4 pts.) Find the mean—square f uctuation of the number of particles in a volume V , for a system with the given equation of state: P = P ( ρ, T ) Apply your result to ideal and van der Waals gases Solution = T log X N exp μ F µN T D ( N h N i ) 2 E = T μ 2 ∂µ 2 V,T = T μ ∂N ∂µ V,T VdP = Ndµ + SdT μ ∂µ ∂N V,T = V N μ ∂P ∂N V,T = 1 ρV μ ∂P ∂ρ V,T D ( N h N i ) 2 E = T μ ∂N ∂µ V,T = TρV μ ∂P ∂ρ 1 V,T Ideal gas P = : D ( N h N i ) 2 E = ρV = N VdW gas, P = Tρ/ (1 v o ρ ) ±ρ 2 / 2 : D ( N h N i ) 2 E = ρV " 1 (1 v o ρ ) 2 ±ρ # 1 Problem 4-2 (6 pts.) Consider a binary mixture of liquids with the same volume per molecule v 0 . Its free energy is given by F ( φ )= Z d r v o h log φ + T (1 φ )log(1 φ )+ ± 2 (1 φ ) φ i . Here
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This note was uploaded on 09/28/2008 for the course PHYS 510 taught by Professor Anon during the Winter '04 term at Cornell University (Engineering School).

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hw04soln - 1 Homework 4 (due November 1) Problem 4-1 (4...

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