Related Experiment Video
Updated: Jul 17, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Statistical mechanics of two hard spheres in a box
Masayuki Uranagase1, Toyonori Munakata
1Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
Abstract:
We investigate some statistical mechanical properties of a system consisting of two hard spheres in a D-dimensional rectangular box (D=1, 2, ...). We give a theoretical method for computing a configurational partition function Zc,D of this system and compare the equation of state obtained from Zc,D with molecular dynamics simulations. Especially in D=3, we give a fully analytic expression for the pressure which turns out to have one or more negative compressibility regions when the box size is small.
Related Concept Videos
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about the...
Reduced Mass Coordinates: Isolated Two-body Problem
Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving
First Law: Particles in One-dimensional Equilibrium
Electric Field of a Non Uniformly Charged Sphere
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
Maxwell-Boltzmann Distribution: Problem Solving
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
