Alexander Fufaev
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Boltzmann Distribution: The Classical Occupation Probability

Important Formula

Formula: Boltzmann Distribution Function
What do the formula symbols mean?


The occupation probability indicates with which probability \(P\) a state with energy \( W \) at temperature \( T \) is occupied by a particle (for example high temperature electron gas).


Energy of a gas particle

Chemical potential

Chemical potential indicates the change in internal energy when the number of particles of the classical gas changes.


Absolute temperature of the gas.

Boltzmann Constant

Boltzmann constant is a physical constant from many-particle physics and has the following exact value: $$ k_{\text B} ~=~ 1.380 \, 649 ~\cdot~ 10^{-23} \, \frac{\mathrm{J}}{\mathrm{K}} $$
Fermi, Bose and Boltzmann distribution - Graphs

The Boltzmann distribution indicates the occupation probability \( P(W) \) that a particle in a system takes on the energy \( W \). The occupation probability depends on the temperature \( T \) of the system.

Fermi, Bose and Boltzmann distribution graphs

The higher the energy, the less likely it is that a particle in the system has this energy.