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Thermodynamics: Stats

Terms and Formulae

Introduction and Summary

The Partition Function

Terms

Boltzmann Factor  -  Any term of the form e -/τ is called a Boltzmann Factor.
Gibbs Factor  -  Any term of the form e (Nμ-)/τ is called a Gibbs factor.
Gibbs Sum  -  The Gibbs Sum is the sum of all of the Gibbs Factors for the states and numbers of a system, and is given by:

Z G(μ, τ) = e (Nμ-)/τ

Partition Function  -  The Partition Function represents the sum of all of the Boltzmann Factors for the states of a system, and is given by:

Z = e -/τ

Planck distribution function  -  The Planck distribution function describes the average number of photons < s > in a particular frequency σ for blackbody radiation and is given by:

< s > =

Stefan-Boltzmann law of radiation  -  The Stefan-Boltzmann law of radiation gives the energy density of radiation in a cavity, as can be expressed:

= τ 4

Formulae

 
The probability of finding a system in energy state if the system is in thermal contact with a reservoir

P() =

 
The entropy of blackbody radiation

σ = ()3

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