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PARTICLE MODEL OF MATTER · CHAPTER 9 OF 10

Gas pressure and temperature

A sealed container can hold gas without changing shape. But if the gas gets hotter, its pressure increases. What changes inside when the container stays the same size?

By the end, you’ll be able to…

  • Describe the random motion of gas particles.
  • Explain how collisions with container walls produce pressure.
  • Relate gas temperature to average particle kinetic energy.
  • Explain how heating and cooling change pressure when mass and volume stay constant.

How can a gas push on a container?

Gas particles move continuously in random directions. They travel in straight lines between collisions with other particles or the container walls.

When particles collide with a wall, they exert forces on it. The combined effect of many collisions produces gas pressure: force per unit area, measured in pascals (Pa).

Follow one collision

The particle hits the wall and rebounds. During contact, it exerts a force on the wall.

The orange arrow points towards the wall, at right angles to its surface.

A gas particle pushes on a container wall A particle approaches a vertical wall from the left and rebounds. During contact, an orange arrow to the left of the wall points right, with its tip touching the contact point. It represents the force exerted by the particle on the wall. Force on wall Container wall

Collision slowed down and contact time exaggerated so the force arrow is visible.

The wall exerts an equal and opposite force on the particle, making it rebound.

A gas pushes on every wall of its container. Although individual collisions are brief, huge numbers of particles produce a steady average pressure.

What changes when the gas gets hotter?

Temperature is related to the particles’ average kinetic energy. At a higher temperature, particles of the same gas move faster on average. Individual particles still have different speeds.

Predict what happens to pressure when the gas is heated in a sealed, rigid container. Then compare the two temperatures below.

INTERACTIVE EXPLORER

Why does tyre pressure rise when the air warms?

The tyre is sealed. Assume its volume stays approximately constant. Compare the air inside at two temperatures.

A pink bicycle and its front tyre A pink bicycle with black tyres. A pink circle highlights a section of the front tyre. A straight dashed line extends upwards and to the right towards its magnified view. The sun is yellow at lower temperature and orange at higher temperature. Look inside

Same sealed tyre · No air added

Magnified section through the tyre

Air particles colliding with tyre walls Twelve pink particles move individually through an air-filled space surrounded by black rubber. They reach the inner walls and change direction there. Their motion becomes faster at higher temperature.

Black: rubber walls · Pink: air particles

Pressure
Lower temperature
Lower pressure
Higher temperature
Higher pressure

Cooler air particles have less average kinetic energy. Compared with the warmer air, they produce a smaller average force on the tyre walls, so the pressure is lower.

Warmer air particles move faster on average. Wall collisions are more frequent, with a greater momentum change per collision on average. The average force on the walls increases, so the pressure rises.

Simplified model: tyre volume is assumed approximately constant. Particle paths, sizes and gauge movement are illustrative; collisions between particles are not shown.

Why does the pressure increase?

At constant volume, faster particles collide with the walls more frequently. Their collisions also produce a greater change in momentum on average.

Together, these effects increase the average force on each wall. The wall area stays the same, so the pressure increases.

Cooling reverses this: average particle kinetic energy decreases, and the pressure falls.

Why must the container stay the same size?

The explanation above assumes a fixed mass of gas at constant volume. A sealed, rigid container keeps both conditions controlled.

A balloon behaves differently: its flexible walls allow it to expand as the gas warms. You cannot assume its volume stays constant.

Sealed rigid container

Same gas particles · Constant volume

A rigid container stays the same size as its gas warms Two straight-sided containers with sealed lids have the same volume. Both contain eight particles. The warmer particles move faster. Their speeds match those shown for the same temperature in the balloon panel. Cooler gas Warmer gas Warms Same volume Same volume
Constant-volume model applies

The gas cannot expand. Heating increases its pressure.

Sealed flexible balloon

Same gas particles · Volume can change

A flexible balloon can expand as its gas warms Two tied balloons with rounded tops and tapered bottoms. The warmer balloon is larger. Both contain eight equal-sized particles. At each temperature, particle speeds match those in the rigid-container panel. Cooler gas Warmer gas Warms Smaller volume Larger volume
Constant-volume model does not apply

The balloon can expand as its gas warms.

Same gas and matching temperatures across both panels. Speeds and paths are illustrative, not calculated. The balloon’s pressure also depends on the surrounding air and the tension in its rubber.

☆ Heating does not make the particles larger or create extra particles. In this model, their average kinetic energy increases.

A sealed container in a warm room

Imagine moving a sealed, rigid gas container from a cool room into a warmer room. As its gas warms, the pressure rises even though no extra gas enters.

Once the gas reaches a steady temperature, its average pressure becomes steady too. The particles keep moving and colliding with the walls.

INTERACTIVE QUICK CHECK
1

What causes a gas to exert pressure on its container?

Correct. Many collisions produce an average force on the walls. Pressure is force per unit area.
The particles do not expand to fill the gaps. They move through the space and collide with the container walls. These collisions produce pressure.
Gas particles move in random directions. They collide with all the walls, rather than moving together towards one.
2

A fixed mass of gas is heated at constant volume. Why does its pressure increase?

No extra particles are created in this model. Heating increases average kinetic energy, so the particles move faster on average.
Particle size stays the same. Faster motion increases the average force on the walls through collisions.
Correct. These effects increase the average force on the walls. With the same wall area, pressure increases.
3

Gas in a sealed, rigid container cools without changing state. What happens?

The same particles remain inside. Pressure decreases because they have less average kinetic energy and exert a smaller average force on the walls.
Correct. Slower particles produce less frequent wall collisions and a smaller momentum change per collision on average, reducing pressure.
Sealing keeps the mass of gas constant, not its pressure. Cooling lowers its pressure when volume stays constant.
CHALLENGE QUESTION

A sealed, rigid container of gas is moved into a warmer room. Its pressure rises, then becomes steady. A student says, “The particles must have stopped colliding with the walls once the pressure stopped rising.” Explain why this is wrong.

Explain both the initial pressure rise and the steady reading. Assume the gas does not change state.

As the gas warms, its particles gain average kinetic energy. They collide with the walls more frequently and with a greater momentum change per collision on average, increasing pressure at constant volume.

Once the gas reaches a steady temperature, its average kinetic energy and average pressure become steady. The particles continue moving and colliding with the walls. These continuing collisions maintain the pressure.

Chapter 9 summary

Gas pressure and temperature

  • Gas particles move continuously in random directions, travelling in straight lines between collisions.
  • Collisions with container walls exert forces on them. Pressure is force per unit area, measured in pascals (Pa).
  • Gas temperature is related to average particle kinetic energy. At higher temperature, particles of the same gas move faster on average.
  • For a fixed mass of gas at constant volume, heating increases pressure. Cooling decreases pressure, provided the gas does not change state.
  • Faster particles collide with the walls more frequently, with a greater momentum change per collision on average. This increases the average force on the walls.
  • A sealed, rigid container keeps gas mass and volume constant. Heating does not make its particles larger or create extra particles.
  • Steady pressure does not mean motion has stopped. Particles keep moving and colliding with the walls.