Gas Pressure and Boyle's Law

Gas pressure results from particles colliding with the walls of a container. Pressure increases when the temperature rises or when the volume decreases. Boyle's Law states that for a fixed mass of gas at constant temperature, pressure and volume are inversely proportional.

What Causes Gas Pressure?

A gas consists of particles moving randomly at high speeds. When these particles collide with the walls of a container, they exert a force. The total force per unit area on the walls is the gas pressure.

More collisions per second → greater pressure.

Factors Affecting Gas Pressure

Change	Effect on pressure	Reason
Increase temperature	Pressure increases	Particles move faster → more frequent/harder collisions
Decrease volume	Pressure increases	Particles in a smaller space → more frequent collisions
Add more gas (more particles)	Pressure increases	More particles → more collisions per second

Boyle's Law

At constant temperature, for a fixed mass of gas:

$P_1 V_1 = P_2 V_2$

Pressure and volume are inversely proportional: if you double the pressure, the volume halves.

$P \propto \frac{1}{V}$

Boyle's Law Calculation

A gas has a pressure of 100 kPa and a volume of 4 litres. The volume is compressed to 2 litres (temperature stays the same). Find the new pressure.

$P_1 V_1 = P_2 V_2$ $100 \times 4 = P_2 \times 2$ $P_2 = \frac{400}{2} = 200 \text{ kPa}$

Note

Boyle's Law only applies when temperature is constant. If temperature changes, a different gas law is needed.

Units of Pressure

Pressure is measured in Pascals (Pa): $1 \text{ Pa} = 1 \text{ N/m}^2$

Atmospheric pressure at sea level ≈ 101,000 Pa = 101 kPa.

Real world: Car tyre pressure in winter

A car tyre is inflated to 220 kPa in summer at 30 °C. On a cold winter morning at −10 °C, the gas particles inside slow down and collide less frequently with the tyre walls — so the pressure drops. Drivers are advised to check tyre pressure in cold weather because underinflated tyres reduce fuel efficiency and handling safety.

Real world: Aerosol spray cans

A spray can (e.g. deodorant or paint) contains gas under high pressure — typically 3 to 8 times atmospheric pressure. When you press the valve, gas escapes and its volume suddenly increases. By Boyle's Law (P₁V₁ = P₂V₂), as volume increases the pressure drops, driving the liquid contents out as a fine spray. This is why cans feel pressurised and why they must never be thrown on a fire.

Real world: Bicycle pump

You push the handle of a bicycle pump down, compressing the air inside. If the cylinder volume halves from 0.6 L to 0.3 L at constant temperature:

$P_2 = \frac{P_1 V_1}{V_2} = \frac{101 \times 0.6}{0.3} = 202 \text{ kPa}$

The pressure doubles, pushing air into the tyre until the tyre pressure equals the pump pressure.

Tip Where do you see this in real life? Bicycle pumps, aerosol cans, car tyres, footballs, scuba tanks, and even fizzy drinks bottles all involve gas pressure — check them out next time you use one!

Practice Problems

A gas at 200 kPa occupies a volume of 3 m³. What is the new pressure if the volume is increased to 6 m³ at constant temperature?

Show answer

P₁V₁ = P₂V₂ → 200 × 3 = P₂ × 6 → P₂ = 600/6 = 100 kPa. Pressure halved as volume doubled.

Why does a bicycle tyre feel firmer in warm weather?

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Higher temperature means gas particles move faster and collide more frequently with the tyre walls, increasing the gas pressure inside the tyre.

A sealed syringe contains gas at 150 kPa with volume 20 cm³. The plunger is pushed until the volume is 5 cm³. What is the new pressure? (constant temperature)

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P₁V₁ = P₂V₂ → 150 × 20 = P₂ × 5 → P₂ = 3000/5 = 600 kPa.