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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 sum-over-states 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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