Second half of chapter 1 notes. This is the part that actually starts feeling like physics: temperature, pressure, and density as the three variables that define the state of the air, plus why the atmosphere ends up looking like a layer cake.

Temperature is basically a bookkeeping trick for average molecular speed: wind is molecules moving together in one direction, temperature is molecules moving randomly. You have to use Kelvin for any actual thermodynamics, Celsius is fine for everyday differences since a degree is the same size in both scales. Standard sea-level temperature is defined as 15°C (288 K).

Pressure is force per area from all those molecules bouncing around, and at any point in a fluid it pushes equally in every direction (isotropic). It’s only at a solid surface that the sideways components cancel out and you’re left with the part pushing perpendicular to the surface. What’s actually useful: pressure at any height is just the weight of all the air sitting above that point, per unit area. That’s why pressure drops fastest near the ground, air down there is being squeezed by the weight of everything above it, so it’s denser and the pressure gradient is steeper. Higher up, there’s less air overhead and the compression eases off, so pressure decreases more gently. It’s roughly exponential with height, with a scale height around 7.3 km at typical temperatures, and because it decreases monotonically with altitude, it doubles as an altitude proxy, which is literally how aircraft altimeters work.

Density behaves the same way (about 8.55 km scale height, standard sea-level value 1.225 kg/m^3), and the three variables are tied together by the ideal gas law, P = rho times R times T, using R = 287 J/(kg K) for dry air. Water vapor throws this off a little since H2O (18 g/mol) is lighter than average air (28.96 g/mol), so humid air at the same pressure and temperature is actually less dense than dry air, not more, the opposite of what “heavy, humid air” makes it sound like. The fix is virtual temperature: instead of changing the gas constant every time humidity changes, you bump up T to a fictitious Tv that lets the dry-air constant keep working. In one worked example (35°C, 30 g/kg mixing ratio), virtual temperature comes out to 40.6°C, over 5 degrees higher than the actual air temperature.

Stack up pressure and temperature by height and you get the standard atmosphere: troposphere from the ground to about 11 km, where temperature drops steadily (6.5°C per km) and basically all clouds and weather live; then the stratosphere out to 47 km, warmed by ozone absorbing UV; the mesosphere out to about 85 km, cooling again; and the thermosphere above that. The three points where temperature turns around and starts rising again all mark an altitude where solar radiation gets absorbed: ozone catching UV near the stratopause, the ground catching visible light, the thermosphere catching most of the rest. And apparently we all live inside the bottom sliver of the troposphere called the atmospheric boundary layer, 0.3 to 3 km thick, the part that actually feels the ground: gets dragged by surface friction, heated by day, cooled by night. That’s the whole slice of atmosphere any of us has personally experienced.

One aside I liked: molecules escape to space from around 550 km up (the “critical radius”), and whether a gas actually escapes depends on its molecular weight. Light ones like H2 and He can reach escape velocity even though the exosphere isn’t hot enough for the average molecule to do it, just the fast tail of the speed distribution manages it. Heavier O2 basically never gets there, which is a big part of why we still have oxygen to breathe.

Still more of chapter 1 left after this: hydrostatic equilibrium, the hypsometric equation, and how barometers actually work.