Thermodynamics: Stats

Study Guide

Terms and Formulae

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Terms and Formulae

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:

= τ⁴

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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