Chapter3_11 - Classical Partition Function: The classical...

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PHY3063 R. D. Field Department of Physics Chapter3_11.doc University of Florida Maxwell-Boltzman Probability Distribution (1) Consider a system with a large number of physical entities of the same kind which are in thermal equilibrium with each other at a temperature T . The energy of the entities are distributed ( classically ) in a definite manner and the average energy of an entity depends on T . The Maxwell-Boltzmann probability distribution is by E E E Ae Ae E P β = = 0 / ) ( and where P(E)dE is the probability of finding an entity with energy between E and E+dE and where β = 1/E 0 is universal. The energy E of an entity is assumed to be a continuous function ( any value allowed ) which varies from zero to infinity.
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Unformatted text preview: Classical Partition Function: The classical partition function, Z , is defined by = ) ( dE E P Z . Average Energy: The average of an entity is given by 1 ) (log ) ( 1 E Z d d dE E P E Z E = = = >= < Kinetic Theory of Ideal Gasses: From the kinetic theory of gasses we found that the average energy of an entity was given by kT kT kT kT E 2 1 2 1 2 1 2 3 + + = >= < with <E> per degree of freedom = kT 2 1 Equipartition Theorem: The mean value of each independent quadratic term in the energy is equal to kT 2 1 . Tell us how the energy is distributed (partitioned) among the entities!...
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