why does air pressure change with altitude

Atmospheric pressure reduces with altitude for two reasons - both related to gravity. The gravitational attraction(*) between the earth and air molecules is greater for those molecules nearer to earth than those further away - they have more weight - dragging them closer together and increasing the pressure (force per unit area) between them. Molecules further away from the earth have less weight (because gravitational attraction is less) but they are also 'standing' on the molecules below them, causing compression.

Those lower down have to support more molecules above them and are further compressed (pressurised) in the process. (*) Strictly it is the gravitational force minus the effect of the Earth's spin (an effect that is greatest at the equator).

The graph below gives an indication of how pressure varies non-linearly with altitude. (Apologies for using feet rather than metres but most values of altitude are still expressed in this ancient unit. )
Pressure with Height The at any level in the atmosphere may be interpreted as the total weight of the air above a unit area at any elevation. At higher elevations, there are fewer air molecules above a given surface than a similar surface at lower levels.

For example, there are fewer molecules above the 50 km surface than are found above the 12 km surface, which is why the pressure is less at 50 km. What this implies is that atmospheric pressure decreases with increasing height. Since most of the atmosphere's molecules are held close to the earth's surface by the force of gravity, air pressure decreases rapidly at first, then more slowly at higher levels.

Since more than half of the atmosphere's molecules are located below an altitude of 5. 5 km, decreases roughly 50% (to around 500 mb) within the lowest 5. 5 km. Above 5. 5 km, the pressure continues to decrease but at an increasingly slower rate.

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