A Computational Model of Maxwell’s Distribution for Undergraduates

Abstract

In this paper we employ a numerical approach to perform simulations of Maxwell distribution for several dimensionalities, based on the Central Limit Theorem. We show that by increasing the number of molecules of the gas N, the simulated distributions tend toward the respective theoretical distributions. Also, we observed that by increasing the model temperature n, the distribution shifted toward higher speeds, in agreement with theoretical results. The numerical simulations provide a physical definition of the concept of temperature. The codes used to perform the simulations are quite easy to construct and implement, while the results strikingly satisfy theoretical expectations. Furthermore, the actual approach makes it possible to skip the mathematical details and explain the distribution by just following the algorithm of simulations. We recommend such approach as a demonstrative tool that can be shown in a lecture class thus enriching the teaching quality and improving students’ understanding.