Ideal Gas Equation: Thermodynamic state variables satisfy $PV = nRT = N k_B T$, where $R = 8.314\text{ J/(mol}\cdot\text{K)}$ and $k_B = 1.38\times 10^{-23}\text{ J/K}$.
Kinetic Molecular Theory: Average molecular translational kinetic energy is $\langle KE \rangle = \frac{3}{2}k_B T$. The root-mean-square speed is $v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$.
Maxwell-Boltzmann Speed Distribution: Particle velocity probability density follows $f(v) = 4\pi \left(\frac{M}{2\pi RT}\right)^{3/2} v^2 e^{-M v^2 / (2RT)}$.
Operating Instructions: Adjust chamber volume, temperature, and particle count. Observe real-time wall momentum transfer generating thermodynamic pressure.