A simplistic pedagogical formulation of a thermal speed distribution using a relativistic framework

TL;DR

This paper introduces a simple, pedagogical approach for undergraduates to understand relativistic thermal speed distributions, extending classical kinetic theory without complex mathematics, and includes computational techniques for enhanced learning.

Contribution

It presents an accessible, relativistically extended kinetic theory framework for undergraduates, building on Maxwell-Boltzmann principles with simple tools and computational methods.

Findings

Relativistic thermal speed distribution differs from Maxwell-Boltzmann at high temperatures.

The approach is simple, accessible, and suitable for undergraduate teaching.

Implications of relativistic effects are demonstrated and compared with classical results.

Abstract

A novel pedagogical technique is presented that can be used in the undergraduate (UG) class to formulate a relativistically extended Kinetic Theory of Gases and thermal speed distribution, while assuming the basic thermal symmetry arguments of the famous Maxwell-Boltzmann distribution as presented at the UG level. The adopted framework can be used by students to understand the physics in a thermally governed system at high temperature and speeds, without having to indulge in high level tensor based mathematics, as has been done by the previous works in the subject. Our approach, a logical extension of that proposed by Maxwell, will first recapitulate what is taught and known in the UG class and then present a methodology inspired from the Maxwell-Boltzmann framework that will help students to understand and derive the physics of relativistic thermal systems. The methodology uses simple tools well known to undergraduates and involves a component of computational techniques that can be used to involve students in this exercise. We have tried to place the current work in a larger perspective in regard to the earlier works done and emphasize on it's simplicity and accessibility to students. Towards the end, interesting implications of the relativistically extended distribution are presented and compared with the Maxwell-Boltzmann results at various temperatures.