A nonextensive approach for understanding the van der Waals' equation

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.