A room full of invisible bullets
You cannot see air, but you can feel it: it pushes on your eardrums, resists a fast-swung hand, carries sound, and inflates every balloon and tyre. Air is not 'nothing' — a cubic metre of it weighs about 1.2 kg, roughly the mass of a small cat. Something is there. The triumph of kinetic theory is to say exactly what.
The revolutionary picture, built up by Bernoulli, Maxwell and Boltzmann, is this: a gas is an enormous swarm of tiny molecules flying about in ceaseless, random motion, colliding with one another and with the walls of any container. Everything you feel about a gas — its pressure, its temperature — is nothing more than the statistical average of countless molecular collisions. This is the kinetic theory of gases, and it is one of the great success stories of physics.
Four numbers describe the whole gas
You could never track 10²² molecules one by one — and you never need to. Remarkably, the whole state of a gas in a container is captured by just four macroscopic numbers: its pressure P, its volume V, its temperature T, and the amount of gas, measured in moles n. Fix these four and you have fixed everything measurable about the gas.
Pressure is the most physical of these to grasp: it is the force the gas exerts on each unit of area of its container's walls. A gauge reads high pressure when molecules strike the walls hard and often.
Pressure is force per unit area. Its SI unit is the pascal (1 Pa = 1 N/m²); everyday pressures are large, so we often use the atmosphere (1 atm ≈ 1.01 × 10⁵ Pa).
Watch the molecules for yourself
Nothing makes the molecular picture click like watching it. In the box below, each dot is a molecule, bouncing elastically off the walls and never stopping. Turn up the temperature and the dots speed up; shrink the volume and they strike the walls more often. The pressure gauge simply counts those wall-hits — pressure emerging, before your eyes, from pure motion.
The ideal gas: a useful fiction
To turn this picture into equations we make a deliberately simplified model, the ideal gas. We pretend the molecules are vanishingly small points; that they never attract or repel one another except in brief, perfectly elastic collisions; and that they are so spread out that most of the container is empty space. Real gases are not quite like this — but at ordinary densities they come astonishingly close, which is why the model is so powerful.