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# Boltzmann Distribution: The Classical Occupation Probability

## Important Formula

What do the formula symbols mean?

## Probability

Unit
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

Unit
Energy of a gas particle

## Chemical potential

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

## Temperature

Unit
Absolute temperature of the gas.

## Boltzmann Constant

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

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.

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