Pressure falls with height

1. Atmospheric pressure is greatest at sea level and decreases as altitude increases.
2. At the top of Ben Nevis, about $1350m$ above sea level, the pressure is roughly $86000Pa$, compared with about $100000Pa$ at sea level.
3. At the cruising height of an airliner, about $11km$, it is only about $23000Pa$, which is why aircraft cabins are pressurised.
4. The atmospheric pressure at any point is caused by the weight of the air above that point.
5. Moving upwards leaves part of the atmosphere below you, so the column of air above you is shorter.
6. A shorter column of air has less mass and so a smaller weight.
7. A smaller weight of air pressing on each square metre means a lower pressure.

The effect of density

1. Air is a gas and can be compressed, so the air near the ground is squashed by the weight of all the air above it.
2. This makes the air at low altitude denser, with more molecules packed into each cubic metre.
3. Higher up there is less air above to do the squashing, so the air is less dense.
4. With fewer molecules in each cubic metre, fewer molecules collide with each square metre of a surface every second.
5. Fewer collisions per second give a smaller force on each unit area, so the pressure is lower.
6. In the simple uniform-density model, the pressure falls by the same amount for every metre you climb and reaches zero at the top of the model atmosphere.
7. In the real atmosphere the density also falls with height, so the pressure drops quickly near the ground and more slowly higher up, fading gradually instead of stopping at a sharp edge.
8. About half of the air lies below a height of roughly $5.5km$, so the pressure there is about half of its sea-level value.

Effects of lower pressure at altitude

1. A sealed crisp packet carried up a mountain or onto an aeroplane swells, because the pressure of the air inside it is now greater than the pressure outside.
2. Your ears pop in a lift, a plane or a car climbing a hill, because the air trapped behind each eardrum briefly has a higher pressure than the air outside until the two pressures equalise.
3. Climbers high on Everest often use bottled oxygen, because each breath of the low-density air contains far fewer oxygen molecules than a breath at sea level.