The Maxwell-Boltzmann Speed Distribution

Temperature measures the average kinetic energy of a huge collection of particles, not the kinetic energy of any one particle. Inside a gas, atoms collide billions of times per second, and each collision can speed one atom up while slowing another down. Energy gets passed around constantly, so at any instant some atoms are crawling along slowly, most are near some typical speed, and a few are sprinting. Plot how many atoms have each speed and you get the Maxwell-Boltzmann curve: it rises from zero, peaks at the most probable speed, then tails off toward high speeds without ever quite reaching zero. That tail matters — even at room temperature a small fraction of molecules move fast enough to escape a liquid surface or clear an activation energy barrier in a reaction.

Heat the gas up and the whole curve responds. The peak moves right, since the typical particle now carries more kinetic energy. But the curve also flattens and spreads, because higher average energy gives collisions more room to create a wider range of outcomes — some atoms barely nudged, others flung to very high speeds. The curve does not just slide over; it stretches, with the tail at high speeds growing noticeably longer and fatter.

This distribution is the atomic-level story behind the macroscopic gas laws covered elsewhere in the unit: pressure, temperature, and internal energy are really just statistics computed over this curve of speeds. It also explains evaporation. Molecules in the fast tail have enough energy to break free from a liquid's surface. As they leave, the average speed of what remains drops, which is why evaporation cools a puddle, and why the puddle's own distribution keeps losing its fastest members over time.