velocity distribution function

The velocity distribution function describes how molecular velocities are distributed on average within a gas. It indicates that there will be a few very slow molecules, a few very fast ones, and most will have velocities near an average value. This concept is fundamental to the kinetic theory of gases, which aims to explain gas properties based on molecular motion and interactions.1

The Maxwell-Boltzmann distribution, first proposed by James Clerk Maxwell and later generalized by Ludwig Boltzmann, provides a statistical description of the energies and velocities of molecules in a classical gas at equilibrium. The distribution function, often denoted as f_M–B, is expressed as Ce^−E/kT, where E is the total energy, T is the absolute temperature, k is the Boltzmann constant, and C is a normalizing constant. This function allows for the calculation of various gas properties by averaging over the distribution.21