2021•arXiv (Cornell University)Open access

The Maxwell-Boltzmann Velocity Distribution Function in Detail

Gilberto Jonas Damião, Rodrigues, Cl\'oves Gon\c{c}alves

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.

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Key concepts: Maxwell–Boltzmann distribution, Boltzmann equation, Boltzmann constant, Kinetic theory, Distribution function, Limit (mathematics), Physics, Distribution (mathematics)