Alexander Fufaev
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Maxwell Velocity Distribution of Gas Particles

Important Formula

Formula: Maxwell velocity distribution
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 of a particle of the gas.


Mass of a particle of the gas.


Temperature of the gas in Kelvin.

Boltzmann Constant

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

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.