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Boyle's law

Heat and matter · level 5, lesson 4 of 6

A question to start

A balloon is filled with 1 litre of air in a habitat on Mars, then carried out through the airlock into the thin air outside. If it could stretch as much as it liked, how big would it get?

The idea

Squeeze a gas into half the space, keeping its temperature the same, and its particles hit the walls twice as often: the pressure doubles. Let it spread into twice the space, and the pressure halves. This is Boyle's law:

\[pV = \text{constant}, \qquad p_1V_1 = p_2V_2,\]

for a fixed amount of gas at a fixed temperature.

p, Vp/2, 2Vvolumep
A balloon of 1 litre carried outside Mars Earth, at the top of Everest
Pressure inside the habitat or at the start 101 kPa 101 kPa
Pressure outside 0.636 kPa about 33 kPa
Volume it would reach about 160 litres about 3 litres

Worked examples

1. The Mars balloon. \(V_2 = p_1V_1/p_2 = 101 \times 1/0.636 \approx 160\) litres. A real balloon bursts long before.

2. A syringe. 20 cm³ of air at 100 kPa is squeezed to 5 cm³: \(p_2 = 100 \times 20/5 = 400\) kPa.

3. Bubbles. A diver's bubble of 2 cm³ at 300 kPa (20 m deep) rises to 100 kPa at the surface: it grows to 6 cm³.

Try it

  1. A gas at 200 kPa fills 3 litres. What is its volume at 100 kPa, at the same temperature?
  2. Air at 100 kPa in a 10 litre tank is squeezed into 2 litres. What is its new pressure?
  3. Why must the temperature stay the same for Boyle's law to work?
  4. Why do airlocks on Mars let the pressure change slowly?
Answers
  1. \(200 \times 3/100 = 6\) litres.
  2. \(100 \times 10/2 = 500\) kPa.
  3. Changing the temperature changes the pressure too, by changing how fast the particles move.
  4. Gas trapped in a suit, a body or a sealed box would swell suddenly if the pressure fell too fast.

Common mistake

"Half the volume, half the pressure." It is the other way round: squeeze a gas into half the volume and its pressure doubles.

Where it leads