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The gas laws

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For a fixed amount of gas, pressure depends on volume and on temperature. Two equations link them.

Pressure and volume (constant temperature)

If a gas is squashed into a smaller volume, its molecules hit the walls more often, so the pressure increases.
p1V1 = p2V2
Halve the volume and the pressure doubles.

Pressure and temperature (constant volume)

If a gas is heated in a fixed volume, its molecules move faster, hitting the walls more often and harder, so the pressure increases.
p1 ÷ T1 = p2 ÷ T2
T must be in kelvin. Pressure is proportional to Kelvin temperature.

Worked example

A gas at 100 kPa and 27 °C is heated to 127 °C in a sealed can.
T1 = 300 K, T2 = 400 K.
p2 = p1 × T2 ÷ T1 = 100 × 400 ÷ 300 = 133 kPa (3 s.f.)
Worked example

A gas has a volume of 200 cm3 at 150 kPa. It is compressed to 50 cm3 at constant temperature. What is the new pressure?

  1. p1V1 = p2V2
  2. 150 × 200 = p2 × 50
  3. p2 = 30 000 ÷ 50

Answer: 600 kPa

Key idea

At constant temperature, p1V1 = p2V2: smaller volume, higher pressure. At constant volume, p1/T1 = p2/T2 with T in kelvin: higher temperature, higher pressure. Both are explained by how often and how hard molecules hit the walls.

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