HW11Solv3 - Homework 11 Solution Physics 404 - Spring 2011...

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Physics 404 - Spring 2011 Homework 11 Solutions Question 1 Kittel+Kromer, Chpater 10, Problem 1 a) We know the Helmholtz free energy of the vdW gas: F vdW = - ± log ² n Q ( V - Nb ) N ³ + 1 ´ - N 2 a V (1) The entropy can be found from σ = - ∂F ∂τ µ µ µ µ V (2) = N ± log ² n Q ( V - Nb ) N ³ + 1 ´ + ± N n Q ( V - Nb ) ( V - Nb ) N dn Q ´ (3) Using n Q = ( 2 π ¯ h 2 ) 3 / 2 we obtain σ = N ± log ² n Q ( V - Nb ) N ³ + 5 2 ´ (4) b) The energy U can be obtained from F by differentiation w.r.t. τ or simply using F = U - τσ : U = F + τσ (5) = - ± log ² N Q ( V - Nb ) N ³ + 1 ´ - N 2 a V + τ × N ± log ² n Q ( V - Nb ) N ³ + 5 2 ´ (6) = 3 2 - N 2 a V (7) which is the ideal gas energy plus the vdW correction for attractive interactions. Question 2 Kittel+Kromer, Chpater 10, Problem 2 We will use the C-C equation dp dT = L T Δ V (8) together with the ideal gas law Δ V τ/p . Here we have an approximate equality since the volume of the liquid phase is not exactly zero, but it is negligible compared to the volume
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HW11Solv3 - Homework 11 Solution Physics 404 - Spring 2011...

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