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Air thins with height

Air and fluids · level 4, lesson 3 of 6

A question to start

Climbers on the highest mountains gasp for breath, and aircraft fly where the air is too thin to breathe. How quickly does air thin out as you go up?

The idea

Air pressure comes from the weight of the air above. The higher you go, the less air is left above you, so the pressure drops.

It drops in a neat pattern: every time you go up by the same height, the pressure halves. Call this the halving height.

Air with height Mars Earth
Pressure at the ground 636 Pa 101,400 Pa
Halving height about 7.6 km about 5.9 km
Height where it falls to about 37% (the scale height) 11.0 km 8.5 km

Mars's air thins out more slowly with height than Earth's, mostly because Mars's gravity is weaker.

fulla halfa quarteran eighth height: each step is one halving height

Worked examples

1. On Earth, 5.9 km up, the pressure is about half: about 50,700 Pa.

2. On Earth, 11.8 km up (two halving heights), about a quarter: about 25,000 Pa. Airliners fly near here.

3. On Mars, 15.2 km up (two halving heights), about a quarter of 636 Pa: about 160 Pa.

Try it

  1. Why does air pressure fall as you go up?
  2. On Earth, about what is the pressure 5.9 km up?
  3. On Mars, what is the pressure about 7.6 km below the average ground level, in a deep basin?
  4. On Mars, about what is the pressure 22.8 km up (three halving heights)?
Answers
  1. There is less air above you pressing down.
  2. About half: about 50,700 Pa.
  3. Going down a halving height doubles it: about 1,270 Pa.
  4. An eighth of 636 Pa: about 80 Pa.

Common mistake

"The pressure drops by the same amount for every kilometre." It drops by the same fraction for every kilometre. High up, where there is little air left, the actual drop is small.

Where it leads