Kinetic Theory — Hard-Sphere Gas

2D hard-disk gas with elastic collisions. Watch the speed distribution relax to Maxwell-Boltzmann f(v)∝v·exp(−mv²/2kT). Measure mean free path, pressure, and temperature from collision statistics.

Gas Parameters

Thermodynamics

Kinetic temperature —
Mean speed ⟨v⟩ —
RMS speed v_rms —
Collisions/step —
Wall pressure —
Maxwell-Boltzmann (2D): f(v) = (mv/kT)·exp(−mv²/2kT)

Most probable speed: v_p = √(kT/m)
Mean speed: ⟨v⟩ = √(πkT/2m)
RMS speed: v_rms = √(2kT/m)

Mean free path: λ = 1/(2√2·nπd²)