Home / Topics / Kinetic Theory & Statistical Physics
Law of atmospheres
Advanced
Density falls exponentially with height.
n = n₀e^{−mgh/kT}In a uniform-temperature atmosphere density falls as n = n₀e^{−mgh/kT}, scale height kT/mg ≈ 8.5 km for air.
At 8.5 km air density is about 37% of sea level.
Real atmosphere has temperature variation.
In more detail
The law of atmospheres describes how air pressure falls exponentially with altitude, P = P0 exp(−mgh/kT). Heavier gases fall off more quickly with height.
Real-world uses
- Aircraft altimeters estimate altitude from air pressure.
- Mountaineers and high-altitude doctors use pressure falls to plan.
- Pilots and meteorologists know that air density falls with altitude, which affects lift, engine power and weather patterns.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Why does pressure fall exponentially?
Because the weight of each layer of air supports the layers above, and density depends on pressure.
Why is hydrogen rare in the atmosphere?
Light molecules escape to space because they are fast enough at high altitude.
Why does air thin out with height?
Gravity pulls the molecules downward, and the thermal motion spreads them out, so the density falls exponentially.
Related topics in Kinetic Theory & Statistical Physics
Maxwell–Boltzmann distribution · Most probable speed · Average, rms and most probable speeds · Diffusion · Fick's law · Graham's law of effusion