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Sandbox Physics

Thermodynamics · molecular motion

Kinetic Theory

Hard spheres bounce elastically off one another and all six box walls. Individual collisions look random, but their speeds settle toward the 3D Maxwell-Boltzmann distribution tracked by the live histogram.

Interactive modelKinetic Theory
Particles170
Temperature1.00
Pressure0.00
Mean speed0.00

Physics tutorial

Ideal gas: how macroscopic laws emerge from collisions

BackgroundA gas contains many continually colliding particles. Temperature describes their mean energy scale, while pressure comes from momentum transferred to container walls.

Why it mattersIt shows how statistical distributions predict macroscopic behavior without tracking every particle.

Start with the essentials

Focus question
Why do random collisions produce stable, repeatable pressure and temperature?
One-sentence intuition
Individual collisions are unpredictable, but averages over many independent events become stable.

Core mathematical model

Ideal-gas equation

PV=NkBTPV=Nk_{\mathrm B}T

At fixed volume, increasing particle count or temperature raises pressure.

Mean translational energy in 3D

⟨K⟩=32kBT\langle K\rangle=\frac{3}{2}k_{\mathrm B}T

Each of three translational degrees of freedom contributes kBT/2.

Common difficulties

Temperature is not one particle speed

Typical misconceptionAll particles at one temperature move equally fast.

Better mental modelTemperature sets the energy scale of a broad speed distribution.

Pressure is not mutual repulsion

Typical misconceptionGas pressure mainly comes from particles pushing each other apart.

Better mental modelIdeal-gas pressure is momentum flux from particles striking the walls.

Run the experiment

  1. 01

    Observe statistical stability

    Choose Warm and let the histogram settle.

    What to observe: Individual bins fluctuate while the overall distribution stabilizes.
  2. 02

    Change only temperature

    Hold count fixed and heat the gas.

    What to observe: The distribution shifts and broadens while speed and pressure rise.
  3. 03

    Change only particle count

    Hold temperature fixed and add particles.

    What to observe: Mean speed stays similar while pressure increases.