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

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.Comment: 13 pages, 5 figures, Publication accepted in Pramana - Journal of Physics (Indian Academy of Sciences). Revised version has an additional section, discussing previous work on relativistic Kinetic Theory in section 2.1 and comparison with these in section 6. Arguments for formulating a relativistic thermal speed distributions have been enriched and made more clear and categorical in section