Undergraduate · 20 min

An ideal gas as a molecular-dynamics box

Watch Newton’s laws act on individual particles and see pressure emerge from their collisions with the piston.

Goal

Connect the microscopic picture — speeds, collision frequency — to the macroscopic law PV = nRT.

Apparatus and reagents

The hard-disk MD simulation with N = 60 particles, a movable piston, and temperature and volume controls.

Procedure

Set T = 300 K and V at mid-range; let the particles thermalise and note the motion.
Raise T toward 1000 K and compare the mean speed and the frequency of wall impacts.
Shrink V at fixed T: the box narrows and wall collisions become more frequent — P rises as 1/V.
Estimate the relative change: doubling T roughly doubles the mean kinetic energy, while the rms speed grows only by √2.

What to observe

Pressure is not an input but an outcome: more frequent, harder wall collisions at higher T or smaller V.
Collisions between particles randomise directions and speeds without changing the mean kinetic energy — the signature of thermalisation.

Explanation

Each particle obeys F = ma; the thermostat is replaced by a global scaling of speeds set by T. In a real MD code (LAMMPS, GROMACS) the same loop integrates Newton’s equations with a Lennard-Jones or quantum-derived force field, and pressure is computed from the virial of wall/ particle forces. The hard-disk model here is the ancestor of those simulations — and it already shows the fluctuation of instantaneous quantities around their ensemble averages.

History of the experiment

Alder and Wainwright ran the first hard-sphere MD on early computers in 1957; Rahman simulated liquid argon with a realistic potential in 1964. Karplus, McCammon and others carried the method to proteins, work crowned by the 2013 Nobel Prize in Chemistry for multiscale models.

Chemists behind it

Josiah Willard Gibbs Martin Karplus