445lec14 - PHYS 445 Lecture 14 - Grand canonical ensemble...

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PHYS 445 Lecture 14 - Grand canonical ensemble 14 - 1 © 2001 by David Boal, Simon Fraser University. All rights reserved; further resale or copying is strictly prohibited. Lecture 14 - Grand canonical ensemble What's Important: weakly interacting systems entropy and probability grand canonical ensemble Text : Reif Secs. 6.7 and 6.8 on approximation techniques can be read independently. Weakly interacting systems If two systems A and A' are weakly interacting, then their combined energy will be approximately equal to the sum of their individual energies: E rs o = E r + E' s + [ no interaction energy ] In the absence of a interaction piece, the partition function of the whole system separates into a product of individual partition functions Z o = Σ rs exp(- ßE rs o ) = Σ r exp(- ßE r o ) Σ s exp(- ßE s o ) = Z Z' . (14.1) Lastly, quantities such as energy and entropy which depend on ln Z , are additive according to Eq. (14.1). Entropy and probability In terms of the partition function, the entropy is written as S = k B (ln Z + ß E ). (14.2) The mean energy can be expressed in terms of Boltzmann factors or, after dividing by
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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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445lec14 - PHYS 445 Lecture 14 - Grand canonical ensemble...

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