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# homework9 - Homework#9 PHYS 404 Fall 2011 Deadline Tuesday...

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Homework #9 — PHYS 404 — Fall 2011 Deadline: Tuesday, November 10, 2011, in class Professor Victor Yakovenko Office: 2115 Physics Web page: http://www2.physics.umd.edu/ ~ yakovenk/teaching/ Textbook: Daniel V. Schroeder, An Introduction to Thermal Physics Addison Wesley Longman, 2000, ISBN 0-201-38027-7 Do not forget to write your name and the homework number! Total score is 30 points. Ch. 5 Free Energy and Chemical Thermodynamics 1. Problem 5.22, 5 points. μ ( P ) for a gas. Additional question: In Problem 1.16, you derived how the pressure P ( z ) changes with the height z . Substituting P ( z ) into Eq. (5.40), prove the formula for μ ( z ) given in Problem 3.37. Hint: In general, the constant of integration in Eq. (5.40) may depend on z : μ ( T, P, z ) = μ 0 ( T, z ) + kT ln( P/P 0 ) . (1) Eq. (1) gives the chemical potential of a gas at the given temperature T , pressure P , and height z . Atmosphere is in diffusive equilibrium (molecules can move anywhere), so the chemical potential must be constant at all heights z , i.e.

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homework9 - Homework#9 PHYS 404 Fall 2011 Deadline Tuesday...

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