Sobre la distribución de velocidades y energías moleculares de Maxwell-Boltzmann: Desarrollo teórico - matemático, validación experimental y simulación con Python

Abstract

During the last quarter of the 19th century, the idea developed that heat was the manifestation of the energy produced by the movement of the molecules that make up objects. To continue delving into this idea, it was essential to understand the movement of each molecule from the Newtonian point of view, but carrying out this analysis is extremely complicated, if we take into account that in at least 1 cm^3 of air there are a number of molecules of the order of 10^19. Therefore, James Clerk Maxwell, extending the ideas of Ludwig Boltzmann, used the rules of the calculus of probabilities to model the behavior of gas molecules, creating the distribution functions of their velocities and energies. Next, the theoretical-mathematical demonstration of these functions, deduced in 1876, is presented, together with the obtaining of notable results of the kinetic molecular theory of gases, such as: the most probable speed, the mean speed, the root mean square speed, the most probable kinetic energy and the average kinetic energy per molecule. On the other hand, these theoretical functions are validated with the implementation of an experimental device. Additionally, a Python code capable of simulating the chaotic thermal movement of particles inside a gas is developed, showing their speed and energy distribution in real time.