Lapsel

Meet Lapsel, a puff of air who cools down steadily as he rises up a mountain.

Air pressure drops with height. When a parcel of dry air rises, it expands into the lower pressure around it. Expanding takes work, and that energy comes from the air itself, so it cools even though no heat leaves.

The rate of cooling is Γ = g/cₚ. With g = 9.81 m/s² and the specific heat of dry air cₚ ≈ 1004 J/(kg·K), Γ ≈ 0.0098 K/m. That is close to 10 °C for every kilometre of height.

Moist air cools more slowly once clouds start to form, because water vapour gives off heat as it condenses. That rate is often nearer 5 to 6 °C per kilometre.

Lapsel explains why mountaintops are cold, and why warm air sinking down the far side of a range arrives as a dry warm wind, like the foehn of the Alps. Pilots and weather forecasters use this rate to predict where clouds will form.