# hw5 - PHYS 333 Winter 2009 Assignment 5 Due 5:00 pm Friday...

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Unformatted text preview: PHYS 333 Winter 2009 Assignment 5 Due: 5:00 pm Friday February 20 Most of these problems are from Schroeder’s book. 1. A question concerning the mathematics of the T dS equation. In class, and in the textbook, we have seen the T dS equation: T dS = dU + P dV In many traditional textbooks, this equation is derived from thermodynamics, and then used to derive the two identities ∂S ∂U V = 1 T and ∂S ∂V U = P T (a) There is one other identity that can be obtained directly from the T dS equation. What is it? In class, and in the textbook, we introduced the enthalpy, H = U + P V . (b) There is a T dS equation that involves H and P , not U and V . What is it? (c) Use this equation to derive three more thermodynamic identities. The heat capacity at constant volume is defined as C V = ∂U ∂T V and that at constant pressure is C P = ∂H ∂T P (d) Show that C V = T ∂S ∂T V and that C P = T ∂S ∂T P 2. Para-magnetism and adiabatic demagnetisation. Starting with Schroeder 3.23. The entropy of a 2-state para-magnet (as discussed in class, see also Schroeder, pages 98 – 107), is related to the multiplicity Ω given by Ω = N ! /N ↑ ! N ↓ ! 1 The up-spins N ↑ and the down-spins N ↓ have, respectively, energies- μB and + μB in a magnetic field B . Thus the total magnetic energy is U M = μB ( N ↓- N ↑ ) and Schroeder shows on page 104 that U M =- NμB tanh ( μB/k B T ) However, the magnetisation is...
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hw5 - PHYS 333 Winter 2009 Assignment 5 Due 5:00 pm Friday...

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