Behaviour of a Gas

A single stone thrown into the air has a motion that is straightforward to describe: Newton's laws of motion, applied to that one object, tell us exactly where it will be at any instant. A gas enclosed in a container is very different. Macroscopically, it is characterised by just three numbers -- pressure, volume and temperature -- yet microscopically it consists of an enormous number of individual molecules (of the order of $10^{23}$ molecules per cubic metre) all in ceaseless, random motion.

It is completely impractical to try to track the position and velocity of every one of these $10^{23}$ molecules individually and then somehow add them up to explain the observed macroscopic pressure, volume or temperature. Unlike the stone, no single molecule's trajectory is representative of the gas's behaviour as a whole. …