K323 / 2027
Kinetic particle model of matter overview

Lesson 4 of 4

Gas pressure

  • I can explain gas pressure in terms of particle motion.Syllabus

    Syllabus K323, 7(e). Explain gas pressure in terms of particle motion.

Make a guess. You are not marked.

A fixed amount of gas is sealed in a rigid metal container. The container is warmed from 20 degrees C to 80 degrees C. What happens to the gas pressure?

  1. It increases, because the particles hit the walls harder and more often.
  2. It stays the same, because the rigid container cannot expand at all.
  3. It decreases, because the gas spreads out.
Show the answer

It increases, because the particles hit the walls harder and more often.

The particles move faster on average, so they hit the walls harder and more often. More force on the same wall area means a higher pressure.

Moving gas particles continually strike the container walls. Their collisions produce an average force per unit area: the gas pressure.

Pressure is force divided by area, measured in Pa. Temperature relates to average random particle kinetic energy. Use the conditions of the container before predicting a pressure change.

From a collision to a pressure

A gas particle approaching a wall changes its motion when it collides and rebounds. The wall exerts a force on the particle during the collision; the particle exerts an opposite force on the wall.

Many particles strike a wall at different times. Their combined effect is an average force acting perpendicular to its surface. Divide this force by the wall area to obtain the pressure.

Random motion takes particles towards every wall, including the sides and the top. Gas pressure is therefore not a downward force caused only by the gas's weight. A pressure force has the direction normal to the particular surface being considered.

A fixed amount of gas in the same rigid container

The container is sealed and its volume stays fixed. Warming the gas increases its average random kinetic energy and raises its pressure.

Blue arrows show particle motion. Lengths give a qualitative indication of speed; they do not give a numerical speed or temperature ratio.

20 °C

Gas at 20 degrees CelsiusTwelve equal-size particles are spread through a container of unchanged volume. Their blue motion arrows have varied directions and lengths. The particles at 20 degrees Celsius are already moving. Arrow lengths are qualitative; these are model snapshots, not measurements or tracked particles.

50 °C

Gas at 50 degrees CelsiusTwelve equal-size particles are spread through a container of unchanged volume. Their blue motion arrows have varied directions and lengths. At 50 degrees Celsius, the typical motion arrows are longer, although some are shorter. The warmer gas has greater average random kinetic energy, not a requirement that every particle always moves faster. Arrow lengths are qualitative; these are model snapshots, not measurements or tracked particles.

A gas particle collides with a wall

Particle motion reverses its component towards the wall, while the particle pushes on the wallOne particle is shown before, during and after a collision with the right-hand wall. The blue approach arrow points down and right; the blue departure arrow points down and left. The particle changes direction. The red arrow starts at the wall and points right, perpendicular to it. It represents the force the gas particle exerts on the wall during the collision. The blue arrows represent particle motion; they are not forces. The dashed path is a schematic guide between successive positions.WallBeforecollisionAftercollisionForce onthe wallOne particle at successive instants

Blue arrows: particle motion. Red arrow: force exerted on the wall. Collisions occur at every wall; their average force per unit area is the gas pressure.

At fixed volume, faster particles collide with a wall more frequently and give greater force contributions. The average force per unit area increases.

The two containers have the same volume and number of particles. The warmer gas has greater average kinetic energy. The collision inset separates arrows showing particle motion from the force exerted on the wall.

Warm a fixed amount in a rigid sealed container

Controlled comparison

The same gas at 20°C and 50°C

The container is rigid, so volume is unchanged. It is sealed, so the number of gas particles is unchanged. Warm the gas from 20°C to 50°C.

  1. The higher temperature means greater average random kinetic energy, with greater typical particle speeds.
  2. Particles reach a given wall more frequently, and their collisions make greater force contributions.
  3. The average force on a given wall area increases, so pressure increases.

The molecules do not become larger. There is no need to add particles to explain the increase. The Celsius readings do not give a pressure ratio of 50 / 20.

Put these in order

A sealed, rigid container of gas is warmed. Put the particle explanation of why the pressure rises in order.

Show the answer

1. The gas is warmed, so its particles gain kinetic energy and move faster on average. Faster particles reach the walls more often and strike them harder.

2. The particles hit the walls more often and with greater force at each collision. More frequent and harder collisions add up to a larger total force on the walls.

3. The total force on the walls each second increases. Pressure is force per unit area, and the wall area has not changed.

4. The pressure on the walls rises, since the area is unchanged.

The fixed conditions matter. If the gas can expand or escape, the volume or number of particles may change too, so warming does not justify the same pressure prediction by itself.

Compress the same gas while keeping its temperature unchanged

Now consider a sealed syringe containing a fixed amount of gas. Compress it slowly while keeping the temperature unchanged. The particles have the same average random kinetic energy, but occupy a smaller volume.

With particles closer together in the reduced space, the rate of collisions on each unit area of wall increases. The average force per unit area therefore increases. The explanation uses the changed volume and collision rate, without assuming that the molecules shrink or become faster.

Separate motion arrows from force arrows. An arrow showing a particle's velocity is not an extra force. The force on a wall comes from collisions and acts perpendicular to that wall.

Check your understanding

A sealed syringe contains a fixed amount of gas. It is compressed slowly while its temperature is kept unchanged. Why does its pressure increase?

  1. The molecules become smaller when squeezed, so each one hits the wall harder and more often than before.
  2. The same particles have less space, so they hit each unit area of wall more often.
  3. Compression makes each molecule move faster, even though the temperature is unchanged, so it hits harder.
Show the answer

The same particles have less space, so they hit each unit area of wall more often.

The particles have unchanged average random kinetic energy at the same temperature, but occupy a smaller volume. More frequent wall collisions per unit area produce a greater average pressure.

Practise an exam question

Write your answer first, then tick the mark points it makes.

Exam-style question

After a long journey, the air in a car tyre is warmer and its pressure is higher. The volume of the tyre has hardly changed. Explain, in terms of the air particles, why the pressure has increased. [3]

Saved on this browser only. Anyone using this browser can see it.