homework11

# homework11 - Homework#11 PHYS 603 Spring 2008 Deadline...

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Homework #11 — PHYS 603 — Spring 2008 Deadline: Thursday, May 8, 2008, in class Professor Victor Yakovenko Oﬃce: 2115 Physics Web page: http://www2.physics.umd.edu/ ~ yakovenk/teaching/ Textbook: Silvio Salinas, Introduction to Statistical Physics Springer, 2001, ISBN 0-387-95119-9 Do not forget to write your name and the homework number! Each problem is worth 10 points. Ch. 12 Phase Transitions. Ch. 13, The Ising Model, is also recommended. This is the last homework! 1. Modiﬁed UMD qualiﬁer problem, August 2002: Boiling and freezing of water at high elevation, the Clausius-Clapeyron relation. (a) The pressure in a liquid or gas decreases as we move away from the Earth. Show that, for a small vertical displacement dz , the change of pressure dP is dP = - ρg dz (1) where ρ ( z ) is the mass density of the ﬂuid. (b) Assuming that the air near the Earth can be treated as a perfect gas in equi- librium with a constant temperature T , show that Eq. (1) yields the Boltzmann distribution for the variation of the number density n ( z ) with the height z . (It is also called the barometric distribution.) (c) Using the Clausius-Clapeyron relation (12.5) dP dT = s G - s L v G - v L = q T Δ v , (2) prove that water (ice) boils (melts) at lower (higher) temperatures when going from the sea level to the top of a mountain. In Eq. (2), s L,G is the entropy per molecule in the liquid or gas phase, v L,G is the volume per molecule in the liquid or gas phase, q is the latent heat per molecule released in the transition, and Δ v is the volume change per molecule at the transition. (d)

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## This note was uploaded on 12/30/2011 for the course PHYSICS 603 taught by Professor V.yakovenco during the Fall '08 term at Maryland.

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homework11 - Homework#11 PHYS 603 Spring 2008 Deadline...

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