The Maxwell-Boltzmann Velocity Distribution Function in Detail

TL;DR

This paper provides a detailed, didactic demonstration of the Maxwell-Boltzmann velocity distribution law, explaining its derivation from kinetic theory and discussing its experimental validation and applicability limits.

Contribution

It offers a comprehensive, accessible derivation of the Maxwell-Boltzmann law, filling a gap in educational materials for introductory science courses.

Findings

Good agreement with experimental results

Clear derivation from kinetic theory

Discussion of applicability limits

Abstract

Despite its importance, in the introductory disciplines of exact science courses, the demonstration of the Maxwell-Boltzmann velocity distribution law is not explained, only its final equation is shown. In order to fill this deficiency, in this work we try to show in detail, in a very didactic way, the demonstration of such a law. For this, the kinetic theory of gases is initially introduced. The good agreement of the Maxwell-Boltzmann velocity distribution law with experimental results and its applicability limit is also presented.