Particle Motion and Gas Pressure

Blow up a balloon and it pushes back against your fingers; leave a sealed can of fizzy drink in a hot car and it can burst. Both happen because a gas exerts a pressure on the walls of its container — and that pressure comes from countless tiny particles, in constant random motion, drumming against those walls. Heat the gas and the particles move faster, hitting the walls harder and more often, so the pressure climbs. This lesson, part of Topic P1 (Matter) of OCR Gateway Combined Science A, explains gas pressure using the particle model, links temperature to the mean kinetic energy of the particles, introduces the kelvin scale and absolute zero, and looks qualitatively at how heating a fixed volume of gas raises its pressure.

By the end of this lesson you should be able to explain gas pressure using the particle model, relate temperature to the mean kinetic energy of particles, describe qualitatively how the pressure of a gas changes with temperature at constant volume, and convert between °C and kelvin.

This lesson is AO1 for recalling the link between temperature and mean kinetic energy, AO2 for applying the particle model to explain gas pressure and for converting between °C and kelvin, and AO3 when you interpret or predict how a pressure reading changes as the temperature of a fixed volume of gas is varied.

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How a Gas Exerts Pressure

The particles in a gas are in constant, random motion, moving quickly in all directions. As they move they collide with the walls of their container. Each collision gives the wall a tiny push (a small force). With an enormous number of particles colliding every second, these pushes add up to a steady, outward force on the walls. The pressure of the gas is this force spread over the area of the wall:

$\text{pressure} = \dfrac{\text{force}}{\text{area}}$pressure=areaforce​

So gas pressure is caused by the particles of the gas colliding with the walls of the container. The more frequent and the harder these collisions are, the greater the pressure. This is why a gas pushes outward equally in all directions — its particles are striking every wall from inside.

Exam Tip: The cause of gas pressure is always collisions of the gas particles with the container walls. A complete answer says the particles are in constant random motion and that each collision exerts a force on the wall; many collisions per second produce the pressure.

Exam Tip: A common misconception is that gas pressure is the particles pushing on each other. The pressure on the walls comes from the particles colliding with the walls, not mainly with one another.

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Temperature and the Mean Kinetic Energy of Particles

The temperature of a gas is a measure of the mean (average) kinetic energy of its particles. The hotter the gas, the faster its particles move on average, and the more kinetic energy they have. This is the crucial link between what you can measure (temperature) and what the particles are doing (moving):

• higher temperature → particles have more kinetic energy → particles move faster (on average);
• lower temperature → particles have less kinetic energy → particles move more slowly.

This relationship is the key to understanding how a gas behaves when it is heated or cooled, because changing the temperature changes how fast the particles are moving, and that changes how they collide with the walls.

Exam Tip: Temperature is the average kinetic energy of the particles. Note "average" (or "mean") — at any instant some particles move faster and some slower, but the average rises with temperature.

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The Pressure–Temperature Relationship (Constant Volume)

Consider a gas in a sealed, rigid container so its volume cannot change. What happens to the pressure if you heat the gas?

As the temperature rises:

1. the particles gain kinetic energy and move faster;
2. faster particles hit the walls harder (each collision exerts a bigger force) and more often (they reach the walls more frequently);
3. so the total force on the walls increases, and since the area is unchanged, the pressure increases.

So, at constant volume, increasing the temperature of a gas increases its pressure, and cooling it decreases the pressure. This is why an aerosol can carries a warning never to heat it: the gas inside would reach a pressure high enough to burst the can.

Exam Tip: To explain why heating a fixed volume of gas raises its pressure, give the full chain: hotter → particles move faster → hit the walls harder and more often → more force on the walls → higher pressure. Examiners look for both "harder" and "more often".

Worked Example — Reasoning about a sealed container

A sealed, rigid tin of gas is taken from a cold room at $5\,°\text{C}$5°C and placed next to a radiator, where it warms to $45\,°\text{C}$45°C. The volume of the tin cannot change. State what happens to the pressure of the gas, and explain your answer using the particle model.

Step 1 — decide what changes: the temperature rises while the volume stays fixed, so this is a pressure–temperature at constant volume situation.

Step 2 — link temperature to the particles: a higher temperature means the particles have a greater average kinetic energy, so they move faster.

Step 3 — link the faster particles to the walls: faster particles collide with the walls harder and more often, so the total force on the walls increases.

Step 4 — link the force to the pressure: since the volume (and so the wall area) is unchanged, a greater force means a greater pressure.

Answer: the pressure increases, because the warmer particles move faster and collide with the walls harder and more often, giving a greater force — and so a greater pressure — on the fixed area of the walls.

This everyday reasoning is why manufacturers print "do not store above a stated temperature" on sealed pressurised containers, and why a car's tyre pressure reads a little higher after a long, fast drive: the air inside has warmed up, so its particles push harder on the tyre walls.

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Changing the Volume of a Gas (Qualitative)

The volume can also change the pressure. Keep the temperature constant but change the volume of a fixed mass of gas — for example, by pushing in a syringe plunger.

If you squeeze the gas into a smaller volume (at constant temperature):

• the same number of particles are now in a smaller space;
• they hit the walls more often (there is less distance to travel between collisions, and the wall area is smaller);
• so the pressure increases.

If you let the gas expand into a larger volume, the particles hit the walls less often, so the pressure decreases. In words: at constant temperature, decreasing the volume increases the pressure, and increasing the volume decreases the pressure — pressure and volume change in opposite directions. (Notice the particles themselves do not change size; there are simply the same particles in a bigger or smaller space.)