Boltzmann distribution: Difference between revisions
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The Maxwell-Boltzmann distribution function is a function ''f(E)'' which gives the | The '''Maxwell-Boltzmann distribution function''' is a function ''f(E)'' which gives the | ||
probability that a | probability that a system in contact with a thermal bath at temperature ''T'' has energy | ||
and is used to describe ''identical'' but ''distinguishable'' particles. | ''E''. This distribution is ''classical'' and is used to describe systems with ''identical'' | ||
but ''distinguishable'' particles. | |||
:<math>f(E) | :<math> f(E) \propto \Omega(E) \exp \left[ - E/k_B T \right] </math>, | ||
where '' | where <math> \Omega \left( E \right) </math> is the degeneracy of the energy <math> E </math>; leading to | ||
:<math> f(E) = \frac{1}{Z} \Omega(E) \exp \left[ -E/k_B T \right] </math>. | |||
where <math>k_B</math> is the [[Boltzmann constant]], ''T'' is the [[temperature]], and the normalization constant ''Z'' is the [[partition function]] of the system. | |||
==See also== | |||
*[[Boltzmann average]] | |||
==References== | |||
[[Category: Statistical mechanics]] | [[Category: Statistical mechanics]] | ||
Latest revision as of 15:36, 17 July 2008
The Maxwell-Boltzmann distribution function is a function f(E) which gives the probability that a system in contact with a thermal bath at temperature T has energy E. This distribution is classical and is used to describe systems with identical but distinguishable particles.
- ,
![{\displaystyle f(E)\propto \Omega (E)\exp \left[-E/k_{B}T\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/725f1e2b5447a4afad931d9e8e7df8b9f9de382f)
where is the degeneracy of the energy ; leading to
- .
![{\displaystyle f(E)={\frac {1}{Z}}\Omega (E)\exp \left[-E/k_{B}T\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/29989eb0fa666f3d8a3535c8e19c64d4ed203c45)
where is the Boltzmann constant, T is the temperature, and the normalization constant Z is the partition function of the system.
