A mechanical approach to one-dimensional interacting gas

•Traditional interpretation of the van der Waals equation is actually incorrect.•The concept of mean field is trickier than we thought.•For a one-dimensional gas, the idea of particle trajectory can be introduced. Derivations of the van der Waals equation typically use standard recipes involving ens...

Full description

Saved in:
Bibliographic Details
Published inChinese journal of physics (Taipei) Vol. 56; no. 5; pp. 2006 - 2021
Main Authors Wang, Chung-Yang, Chen, Yih-Yuh
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2018
Subjects
Equation of state
Kinetic theory
One-dimensional interacting gas
Statistical mechanics
Thermodynamics
Van der Waals equation
Thermodynamics
One-dimensional interacting gas
Kinetic theory
Van der Waals equation
Statistical mechanics
Equation of state
Online AccessGet full text

Cover

More Information
Summary:•Traditional interpretation of the van der Waals equation is actually incorrect.•The concept of mean field is trickier than we thought.•For a one-dimensional gas, the idea of particle trajectory can be introduced. Derivations of the van der Waals equation typically use standard recipes involving ensemble averages of statistical mechanics. In this work, we study a box of weakly interacting gas particles in one-dimension by explicitly incorporating the mechanical point of view. This has the merit that it not only reproduces the van der Waals equation but also tells us some extra interesting physics not immediately clear from a pure statistical mechanical approach. For example, we show that the traditional handwaving argument leading to van der Waals equation requires closer scrutiny if it is to get things right.
ISSN:0577-9073
DOI:10.1016/j.cjph.2018.09.016