# Maxwell Boltzmann Formula

## Maxwell Boltzmann Formula

The distribution of energy between identical but differentiated particles is clearly described by the Maxwell Boltzmann Formula. The Maxwell Boltzmann Formula is a mathematical representation of the chi distribution with three degrees of freedom (the components of the velocity vector in Euclidean space) and a scale parameter that measures speeds in units proportional to the square root of the ratio of temperature and particle mass. The classical ideal gas, which represents real gases in an idealised form, is subject to the kinetic theory of gases. However, rarefied gases behave extremely similarly to an ideal gas at ordinary temperatures, and the Maxwell speed distribution is a good approximation for such gases. This is true even for perfect plasmas, which are ionised gases with just the right amount of low density.

### Formula of Maxwell Boltzmann

Maxwell initially derived the distribution in 1860 using heuristics. Later, in the 1870s, Boltzmann conducted extensive research into the physical causes of this distribution. On the basis that the distribution maximises the system’s entropy, the distribution can be deduced. Maxwell also made an early claim that the molecular collisions involve a trend toward equilibrium. Following Maxwell, Ludwig Boltzmann developed the distribution in 1872 and claimed that gases should tend to follow it over time due to collisions. Later, in 1877, he again deduced the distribution using the statistical thermodynamics paradigm. Starting with the outcome known as Maxwell-Boltzmann statistics, the derivations follow Boltzmann’s 1877 derivation (from statistical thermodynamics).

### Solved Example

Solved examples on the Maxwell Boltzmann Formula can be found on the extramarks website.