As an aeroplane climbs or descends, the air pressure in the cabin changes. The air trapped in your middle ear does not always change pressure at exactly the same rate. A pressure difference across the eardrum produces a force, which can feel uncomfortable. A narrow tube called the Eustachian tube connects the middle ear to the throat and helps equalise the pressure. Swallowing or yawning can open this tube. When the pressures become more equal, you may feel or hear a small pop. The effect is a direct example of gas pressure producing forces on surfaces.

The useful part of this physics is that it helps people predict and design real things. Engineers often begin with the same simplified model used in school, test where it works, then add more detail when measurements show that the real situation is more complicated.

A gas is made of particles moving rapidly in random directions. Pressure comes from those particles colliding with the walls of their container and changing momentum. Heating the gas makes the particles move faster, so collisions become more frequent and harder; if the volume cannot increase, the pressure rises. If the gas can expand, pressure, volume and temperature all become linked.