A nonextensive approach for understanding the van der Waals’ equation

Abstract

In order to improve the teaching of the course of statistical physics in universities, in this article we introduce nonextensive statistics, a new statistical theory about complex systems. We study the two modification coefficients a and b in the van der Waals' equation in nonextensive statistics and thus understand the possible relation between the van der Waals' equation and the nonextensivity. We express these coefficients when a real gas is regarded as the nonextensive gas and then relate them to the q-parameter in nonextensive statistics. Furthermore, we derive the q-parameter of a real gas, which contain the intermolecular Lennard-Jones potential, but also strongly depend on the state parameter and molecular number of the gas. From the new statistical physics, we show that the nonextensivity plays a significant role in the coefficients of the van der Waals' equation if the gas contains limited number of molecules or the gas is regarded as a few-body system. This article is suitable to read for senior undergraduate students, graduate students and teachers who teach the course of statistical physics in universities.