• id: JTHERM-02-N07
• title: Distribution of Molecular Speeds
• tags: maxwell-boltzmann, distribution, speed

Not all molecules in a gas have the same speed. The Maxwell-Boltzmann distribution $f(v) = 4\pi n(m/2\pi k_BT)^{3/2}v^2 e^{-mv^2/(2k_BT)}$ gives the number of molecules per unit speed interval. The distribution has key features: (1) starts at zero for $v = 0$, (2) rises to a maximum at $v_p$, (3) falls exponentially at high speeds. At higher temperatures, the peak shifts right (higher $v_p$) and the curve broadens and flattens, but the total area under the curve (total number of molecules) remains constant. Heavier molecules have narrower distributions at the same temperature.