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Boltzmann Factor
*** Shopping-Tip: Boltzmann Factor
In
physics, the '''Boltzmann factor''' is a weighting factor determining the relative probability of a state in a system in
thermodynamic equilibrium at a
temperature (''T'').
:
Where ''k''
''B'' is
Boltzmann's constant, and ''E'' is
energy.
This is ''not'' a
probability function by itself, because it is not normalized. However, the ratio of the probabilities of two states is given by the ratio of their Boltzmann factors. To normalize the Boltzmann factor into a probability, one simply divides it by the sum ''Z'' of the Boltzmann factors of all possible states of a system, which is called the
partition function (statistical mechanics) partition function. This gives the
Boltzmann distribution.
From the Boltzmann factor, one can then derive the
Maxwell-Boltzmann statistics,
Bose-Einstein statistics, and
Fermi-Dirac statistics that govern classical
particles as well as
quantum mechanics quantum mechanical bosons, and
fermions, respectively.
See also
*
Boltzmann relation (plasma physics)
References
* Charles Kittel and Herbert Kroemer, ''Thermal Physics'', 2nd ed. (Freeman & Co.: New York, 1980).
Category:Thermodynamics
Category:Statistical mechanics
see
Boltzmann factor
