Thermodynamics: Stats
Terms and Formulae
Terms
Boltzmann Factor
-
Any term of the form
e
-
/τ
is called a Boltzmann
Factor.
/τ
is called a Boltzmann
Factor.
Gibbs Factor
-
Any term of the form
e
(Nμ-)/τ
is called a Gibbs factor.
)/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
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
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
=
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
|
