Particle Motion and Pressure in Gases

A gas is made of molecules that are far apart and move freely. Understanding their motion explains both temperature and pressure.

The molecules of a gas are in constant random motion, moving quickly in all directions.

Because they move randomly, the molecules constantly collide with each other and with the walls of their container. They travel in straight lines between collisions and change direction each time they bounce off something.

The temperature of a gas is related to the average kinetic energy of its molecules. The higher the temperature, the greater the average kinetic energy, and so the faster the molecules move on average.

This is why heating a gas makes its molecules speed up: adding energy to the gas increases the kinetic energy of the molecules, which the thermometer reads as a rise in temperature. Not all molecules move at the same speed, so it is the average kinetic energy that matters.

Gas pressure is caused by molecules colliding with the walls of their container. Each collision exerts a tiny force on the wall; the countless collisions together produce a steady pressure.

The pressure of a gas is the force per unit area exerted by the molecules on the container walls, acting at right angles (90°) to each wall.

Two things increase the pressure by changing the collisions with the walls:

• Molecules hitting the wall harder — faster molecules deliver a bigger force per collision.
• Molecules hitting the wall more often — more collisions per second means more total force.

Because the molecules move randomly in all directions, the force is spread evenly over every wall and always acts perpendicular to the surface. This is why a sealed gas pushes outwards equally in all directions, inflating a balloon into a rounded shape.

If a fixed amount of gas is kept in a sealed rigid container so its volume cannot change, raising the temperature raises the pressure.

At constant volume, increasing the temperature of a gas increases its pressure.

The particle model explains this clearly. Raising the temperature increases the average kinetic energy of the molecules, so they move faster. Faster molecules:

• hit the walls harder (each collision transfers more force), and
• hit the walls more often (they cross the container more quickly).

Both effects increase the total force on the walls. Since the area of the walls has not changed, the force per unit area, the pressure, goes up.

This is why a sealed aerosol can warns against heating: the trapped gas's pressure rises with temperature and the can may burst. The volume is fixed, so all the extra molecular energy shows up as higher pressure.

(Physics only) This slide covers content in separate Physics, not in Combined Science.

For a fixed mass of gas held at constant temperature, the pressure and volume are linked by a simple rule.

$pV=\text{constant}$

• $p$ is the pressure, in pascals (Pa)
• $V$ is the volume, in cubic metres (m³)

This equation is given on the Physics equation sheet.

If the temperature and mass stay the same, then $p_1{V}_1=p_2{V}_2$. Squeezing a gas into a smaller volume raises its pressure; letting it expand lowers its pressure.

The particle model explains why: reducing the volume packs the same molecules into a smaller space, so they hit the walls more often, raising the pressure. Increasing the volume spreads the molecules out, so they hit the walls less often and the pressure falls.

Because $p_1{V}_1=p_2{V}_2$, you can find a new pressure or volume when a gas is compressed or expanded at constant temperature.

$p_2=\frac{p_1{V}_1}{V_2}$

Worked example — a sealed syringe holds 0.02 m³ of gas at a pressure of 100 000 Pa. The plunger is pushed in until the volume is 0.005 m³, keeping the temperature constant. Find the new pressure.

$p_2=\frac{p_1{V}_1}{V_2}=\frac{100000\times 0.02}{0.005}$

$p_2=\frac{2000}{0.005}=400000\text{Pa}$

The volume was reduced to a quarter, so the pressure rose to four times its original value, as $pV$ stays constant.

Always check the answer makes sense: a smaller volume must give a larger pressure. If your pressure went down when the gas was compressed, you have divided the wrong way round.

(Physics only) (Higher Tier only) This slide covers content in separate Physics and only at Higher Tier.

Work is the transfer of energy by a force. When a force compresses a gas, it does work on the gas and transfers energy to it.

Doing work on an enclosed gas increases its internal energy, which can raise its temperature.

A bicycle pump is the standard example. As you push the plunger, you exert a force through a distance, doing work on the trapped air. That energy is transferred to the gas molecules, increasing their kinetic energy and so raising the gas's temperature. This is why the pump and the valve feel warm after inflating a tyre.

The key idea is that heating is not the only way to raise a gas's temperature. Doing mechanical work on the gas raises its internal energy directly, and if that shows up as increased kinetic energy of the molecules, the temperature rises.

1. Saying molecules push the walls because they repel them

Gas pressure comes from molecules colliding with the walls, not from any repulsion. Each collision applies a small force; billions of collisions produce the pressure.

2. Forgetting the "constant volume" condition

The rule that pressure rises with temperature applies only when the volume is fixed. If the gas can expand, the volume changes too and the simple statement no longer holds.

3. Using pV = constant when the temperature changes

$pV=\text{constant}$ only applies to a fixed mass of gas at constant temperature. If the temperature changes, this relationship cannot be used on its own.

4. Not converting units in pV calculations

Pressure must be in pascals and volume in cubic metres for consistency. As long as both readings use the same units on each side, $p_1{V}_1=p_2{V}_2$ works, but mixing units gives a wrong answer.

5. Thinking only heating can raise a gas's temperature

Doing work on a gas, such as compressing it with a pump, also increases its internal energy and can raise its temperature, without any heating (Higher Tier, Physics only).