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Air pressure

Heat and matter · level 5, lesson 2 of 6

A question to start

You cannot feel it, but Earth's air presses on every square metre of you with a force of about 100,000 N, like ten tonnes. On Mars it is less than a hundredth of that. Where does air pressure come from?

The idea

Air has weight. The whole height of air above you is pulled down by gravity and presses on the ground and on you. At the ground, the pressure is the weight of the air above each square metre:

\[p = \frac{m g}{A}.\]

Air also presses sideways and upwards just as hard, which is why you are not crushed: the air inside your body pushes back.

Air pressure at the surface Mars Earth
Average 636 Pa (0.6 kPa) 101,400 Pa (101 kPa)
Through the seasons 400 to 870 Pa changes by a few percent
Height in which pressure falls by about 63% 11.0 km 8.5 km
Earth: 10,300 kgMars: 171 kg

Mars's pressure rises and falls through its year because, each winter, part of its carbon dioxide air freezes onto a polar cap, and in spring it comes back.

Worked examples

1. Mass of air over 1 m². \(m = pA/g\). Earth: \(101{,}400/9.81 = 10{,}340\) kg. Mars: \(636/3.71 = 171\) kg.

2. Force on a window. A 1 m² window on Earth has \(101{,}400\) N pushing on each side. If the air inside is at Earth pressure and outside is Mars air, the window feels \(101{,}400 - 636 \approx 100{,}800\) N pushing outwards: about the weight of ten tonnes on Earth.

3. Units. 1 kPa = 1,000 Pa. Mars's 636 Pa is 0.636 kPa, also written 6.36 mbar.

Try it

  1. Why does air press on things?
  2. How many times higher is Earth's average air pressure than Mars's?
  3. A Mars habitat at 70 kPa inside has a 2 m² hatch. What is the force on it from the difference in pressure?
  4. Why does Mars's air pressure change through the year?
Answers
  1. It has weight: gravity pulls the air above down onto everything below.
  2. \(101{,}400/636 \approx 160\) times.
  3. \((70{,}000 - 636) \times 2 \approx 139{,}000\) N, outwards.
  4. Part of the carbon dioxide air freezes onto the winter pole, then turns back into gas in spring.

Common mistake

"Air pressure only pushes down." It pushes equally in all directions at a point. A sealed can is not crushed because the air inside pushes out as hard as the air outside pushes in.

Where it leads