445lec33 - PHYS 445 Lecture 33 - Non-ideal classical gases...

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PHYS 445 Lecture 33 - Non-ideal classical gases 33 - 1 © 2001 by David Boal, Simon Fraser University. All rights reserved; further resale or copying is strictly prohibited. Lecture 33 - Non-ideal classical gases What's Important: non-ideal classical gases virial coefficient Text : Reif Non-ideal classical gases The previous two lectures on phase transitions have dealt with quantized spins on a lattice. We now move to the continuum problem of phase transitions in a non-ideal gas - that is, a gas of interacting particles. The total energy for a broad category of interaction models can be expressed as H = K + U = (1/2 m ) Σ i p i 2 + Σ j k u jk ( r jk ) (33.1) where the momentum dependence is contained in the kinetic energy term and the coordinate dependence is in the potential energy term ( of course, there exist situations in which the interactions are momentum-dependent too ). For example, the "6-12" Lennard-Jones potential is of the form u ( r ) = u o R r 12 - 2 R r 6 where u o and R are parameters. This potential is strongly repulsive at short range, and weakly attractive at long range. Because of the separation of the Hamiltonian into position and momentum components, the partition function factors as well: Z = 1 N ! 1 h 3 N e - ß ( K + U ) d 3 p 1 .. d 3 p N d 3 r 1 .. d 3 r N = 1 N ! 1 h 3 N e - ß 2 m ( p 1 2 + .. p N 2 ) d 3 p 1 ... d
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This note was uploaded on 09/07/2009 for the course PHYS 445 taught by Professor Davidboal during the Spring '08 term at Simon Fraser.

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445lec33 - PHYS 445 Lecture 33 - Non-ideal classical gases...

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