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# Maxwell Velocity Distribution of Gas Particles

## Important Formula

What do the formula symbols mean?

## Distribution function

Relative frequency density $$f(\class{blue}{v})$$. The area under this curve, between two velocities, indicates the percentage $$p(v_1, v_2)$$ of the particles in the velocity interval under consideration: $p(v_1, v_2) ~=~ \int_{v_1}^{v_2} f(\class{blue}{v}) \, \text{d}v$

The unit of $$f(\class{blue}{v})$$ is $$\mathrm{s}/\mathrm{m}$$.

## Velocity

Unit
Velocity of a particle of the gas.

## Mass

Unit
Mass of a particle of the gas.

## Temperature

Unit
Temperature of the gas in Kelvin.

## 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 Maxwell velocity distribution is a statistical distribution of the velocities $$\class{blue}{v}$$ of particles with mass $$\class{brown}{m}$$ in an ideal gas at a specific temperature $$T$$. This distribution was developed by James Clerk Maxwell and is a crucial component of kinetic gas theory.