A nonextensive approach for understanding the van der Waals' equation

TL;DR

This paper introduces nonextensive statistics to analyze the van der Waals' equation, revealing how nonextensivity influences gas behavior, especially in systems with few molecules or limited size.

Contribution

It establishes a connection between nonextensive statistics and the van der Waals' equation, deriving coefficients and the q-parameter for real gases with Lennard-Jones potential.

Findings

Nonextensivity significantly affects van der Waals coefficients in small or few-body systems.

Derived q-parameter depends on state variables and molecular number.

Provides educational insights for teaching statistical physics.

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.