This simulation demonstrates the Maxwell-Boltzmann speed distribution — a fundamental result from kinetic theory of gases that describes how particle speeds are distributed in an ideal gas at thermal equilibrium.

Controls:

• Number of particles (N): Adjust from 100 to 10,000 particles. More particles give smoother statistical distributions but may slow the simulation.
• Temperature (T): Controls the average kinetic energy of particles. Higher temperature means faster particles on average.

What you see:

• Left panel: Gas chamber showing particles (black dots) undergoing elastic collisions with each other and the walls.
• Right panel: Real-time histogram of particle speeds compared to the theoretical Maxwell distribution.

Understanding the histogram:

• Grey bars: Measured speed distribution from the simulation. Axes are given local simulation units, not to real-life scale.
• Red curve: Theoretical 2D Maxwell distribution: f(v) = (v/σ²) × exp(-v²/2σ²)
• v_mp (blue): Most probable speed — peak of the distribution.
• v_mean (red): Mean (average) speed of all particles.
• v_rms (purple): Root-mean-square speed — related to average kinetic energy.

Things to explore:

• Increase temperature and watch the distribution shift right and broaden.
• Notice that v_mp < v_mean < v_rms always holds (the distribution is asymmetric).
• Use more particles to see the histogram match the theoretical curve more closely.
• Observe how quickly the system reaches equilibrium after changing parameters.

Note: This is a 2D simulation, so it uses the 2D Maxwell distribution. The characteristic speed ratios differ slightly from the 3D case you may see in textbooks.