Statistical Mechanics Lab

Statistical Mechanics Simulator — Maxwell-Boltzmann Distribution

This statistical mechanics simulator plots the Maxwell-Boltzmann speed distribution for hydrogen, nitrogen, oxygen, or hot plasma at temperatures from 50 to 5000 K. Dashed vertical markers show the most probable speed v_p, average speed v_avg, and root-mean-square speed v_rms. A ghost curve at T = 300 K provides a reference when temperature changes. The right canvas plots Boltzmann factors e^(−E/kT) at four temperatures and shows a bar chart of quantum oscillator microstates, illustrating how energy distributes among states.

What you can do in this simulation

• Adjust temperature (50–5000 K) and observe distribution curve broaden and shift
• Set degrees of freedom (3–7) for different molecular types
• Adjust particle mass (1–100 × 10⁻²⁷ kg) and oscillator count (2–15)
• Switch among gas presets: H₂, N₂, O₂, Hot Plasma
• Compare v_p, v_avg, v_rms markers and read U/DOF in eV from results panel

Concepts covered

Maxwell-Boltzmann distribution · Boltzmann factor · root mean square speed · equipartition theorem · microstates · thermodynamic entropy

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Free to use in your browser — no signup required. Found a bug or have an idea to make it better? Tell us.