Gas Pressure and Temperature: An Introduction to the Gas Laws

A balloon full of tiny bullets

Blow up a balloon and it feels firm. What is pushing back against your squeeze? Not a solid — just air, which is mostly empty space. The answer lies in the particle model: a gas is a swarm of fast-moving particles, far apart, bouncing off everything in their path. The drumming of those particles against the balloon's inner surface is what we call pressure. By studying how pressure, volume and temperature depend on each other, scientists discovered the gas laws — simple, reliable rules that engineers still use to design engines, scuba gear and aircraft cabins.

This lesson builds directly on the particle model of matter, so make sure you are happy with the idea of particles in constant motion.

What is gas pressure, really?

In a gas, particles are spread out and zoom around at high speed in random directions — roughly 500 m/s for air at room temperature. They constantly collide with the walls of their container. Each tiny collision pushes on the wall with a tiny force. Because there are trillions upon trillions of collisions every second, they add up to a steady, measurable push spread over the area of the wall.

Pressure = force ÷ area. Gas pressure is the total force from particle collisions divided by the area they strike.

This immediately tells us what can change the pressure: anything that makes the collisions more frequent or harder. There are three levers — volume, temperature and the number of particles — and the gas laws describe each one. (For more on how force and area combine, see pressure in liquids and gases.)

Boyle's law: squeezing a gas

Imagine a fixed amount of gas at a fixed temperature in a cylinder with a movable piston. Push the piston in to halve the volume. The same number of particles now occupy a smaller space, so they hit the walls twice as often — the pressure doubles. This is Boyle's law:

At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume: P₁ × V₁ = P₂ × V₂

Worked example 1. A diver's lungs hold 6 litres of air at the surface, where the pressure is 100 kPa. The diver descends to where the pressure is 300 kPa. If the air stays at the same temperature, what volume would that air occupy?

P₁V₁ = P₂V₂ 100 × 6 = 300 × V₂ V₂ = 600 ÷ 300 = 2 litres.

The air is squeezed to a third of its volume — which is exactly why divers must never hold their breath while rising, as the reverse happens and the expanding air can injure the lungs.

The pressure law: heating a sealed gas

Now fix the volume (a sealed, rigid can) and change the temperature instead. Heating the gas gives its particles more kinetic energy, so they move faster. They strike the walls more often and harder, so the pressure rises. This is the pressure law (sometimes called Gay-Lussac's law):

At constant volume, the pressure of a fixed mass of gas is proportional to its absolute (kelvin) temperature: P₁ ÷ T₁ = P₂ ÷ T₂

This is why aerosol cans carry the warning "do not heat above 50 °C" — heating raises the internal pressure until the can could burst.

Worked example 2. A sealed canister of gas is at a pressure of 200 kPa at 27 °C. It is heated to 127 °C. What is the new pressure?

Step 1 — convert to kelvin. Add 273. T₁ = 27 + 273 = 300 K. T₂ = 127 + 273 = 400 K. Step 2 — apply the law. P₁ ÷ T₁ = P₂ ÷ T₂ → 200 ÷ 300 = P₂ ÷ 400. P₂ = (200 ÷ 300) × 400 = 266.7 kPa.

Notice that using Celsius (27 and 127) would have given a wildly wrong answer — the kelvin conversion is essential.

The kelvin scale and absolute zero

Why must temperature be in kelvin? The gas laws involve proportionality, and proportionality only makes sense measured from a true zero. The kelvin scale starts at absolute zero, the coldest possible temperature, where particles have the minimum possible energy and (in the simple model) stop moving altogether.

• Absolute zero = 0 K = −273 °C.
• To convert: K = °C + 273.
• A change of 1 °C is the same size as a change of 1 K; only the starting point differs.

At absolute zero, a gas would in theory exert no pressure at all, because its particles would no longer collide with the walls. You cannot actually reach it, but it anchors the whole scale.

Putting the three together

The two laws above are special cases of a single relationship for a fixed mass of gas:

(P₁ × V₁) ÷ T₁ = (P₂ × V₂) ÷ T₂

Hold temperature constant and it reduces to Boyle's law; hold volume constant and it reduces to the pressure law. This combined equation lets engineers predict what happens inside an engine cylinder, a refrigerator, or a weather balloon climbing into the cold upper atmosphere.

Why this matters

The gas laws are everywhere once you look:

• Car engines rely on compressing a fuel–air mixture (Boyle's law) and the pressure surge from the hot expanding gases after ignition (pressure law).
• Scuba diving safety depends entirely on how pressure changes with depth.
• Weather balloons are filled only partly at launch, because the gas expands enormously as the surrounding pressure drops at altitude.
• Aerosols, pressure cookers and tyres all behave the way they do because of these rules.

Try it yourself! 🧪

Demo — the temperature–pressure balloon (a pressure-law experiment). Stretch a balloon over the neck of an empty glass bottle so it seals the opening.

1. Stand the bottle in a bowl of hot tap water (an adult should handle very hot water). Watch the balloon: within a minute or two it begins to inflate, standing up off the bottle.
2. Now move the bottle into a bowl of iced water. The balloon deflates and may even get sucked partway down into the bottle.

What's happening? The air sealed inside the bottle is a fixed mass of gas in a (roughly) fixed space. Heating it makes the particles move faster, raising the pressure until they push the balloon outward. Cooling it slows the particles, lowering the pressure so the outside air pushes the balloon in. You have just demonstrated the pressure law with nothing but a bottle, a balloon and two bowls of water — watching invisible particles change their behaviour with temperature.