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Unformatted text preview: PHYS 445 Lecture 13  Partition function Z 13  1 2001 by David Boal, Simon Fraser University. All rights reserved; further resale or copying is strictly prohibited. Lecture 13  Partition function Z What's Important: partition function fluctuations and specific heat work and Z entropy and Z Text : Reif Partition function The sum over the Boltzmann factors exp( E r ) appears so frequently in statistical mechanics that it is given a special name, the partition function Z Z e E r r (13.1) This sumoverstates involves all accessible states r of the system. The partition function is useful for more than just notational convenience. Consider the mean energy, which we can write for discrete states as E = E r e E r r e E r r But the numerator can also be expressed as E r e E r r =  e E r r =  e E r r =  Z (13.2) Therefore, we can write the mean energy in the elegant form E =  1 Z Z =  ln Z (13.3) The partition function can also be used to determine the fluctuations in the energy. The mean squared deviation is E 2 = E E ( 29 2 = E 2 E 2 (13.4) The mean energy has already been determined, so what we need next is to calculate the mean square of the energy, starting with the analog of Eq. (13.2) E r 2 e E r r = ...
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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.
 Spring '08
 DavidBoal
 Physics, Work, Entropy, Heat

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