Atmospheric pressure

This example uses calculus.

Gases, unlike liquids, are quite compressible, and at a given temperature, the density of a gas is approximately proportional to the pressure. The proportionality constant is discussed in section A.2, but for now let's just call it k, ρ = kP. Using this fact, we can find the variation of atmospheric pressure with altitude, assuming constant temperature:

Pressure falls off exponentially with height. There is no sharp cutoff to the atmosphere, but the exponential gets extremely small by the time you're ten or a hundred miles up.