Chapter3_11 - Classical Partition Function The classical...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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!...
View Full Document

This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

Ask a homework question - tutors are online