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→Compressible effects
=== Compressible effects ===
In the simplified model, it is assumed that the density of air is a constant. The Equation of State clearly says otherwise: density depends on pressure and pressure depends on density. Here we run into a problem and the problem can no longer be solved by simple algebra: the powerful mathematical tool of calculus must be used.
Even this is under the assumption that the temperature is a constant. The additional complexity is that the temperature in the atmosphere varies greatly, and you can feel this quite easily by climbing onto a hill and note the temperature drop (just make sure you use a thermometer instead of feeling, to isolate the effect of windchill). At low altitudes, as a rule of thumb, the temperature will reduce by 0.6°C for every 100 meters' raise of altitude.
The temperature of the air greatly depends on the heat transfer between the ground and the air: it is the ground that absorbs the radiation from the sun and heats up, the air is transparent so the absorptivity is quite low in the visible spectrum. Generally, the higher the altitude, the less heat the air will get from the ground, and, as a result, the air will become cooler.
This section sounds rather pessimistic, but the purpose is to demonstrate that there is no easy way to model the pressure and temperature distribution in the atmosphere accurately.
=== The International Standard Atmosphere ===
