Where gas pressure comes from

Definition

Gas pressure

Gas pressure is the force per unit area that gas particles exert on a surface as a result of their collisions with it.

The particles of a gas move rapidly and randomly in all directions, and they have a wide spread of speeds rather than all moving at one speed.
Between collisions each particle travels in a straight line, because the forces between widely separated gas particles are very weak.
When a particle reaches a wall it collides with it and rebounds, so the direction of its motion is reversed.
Changing the direction of a moving particle requires a force from the wall, and the particle exerts an equal and opposite force back on the wall.
One collision gives an extremely small force lasting an extremely short time, so a single particle produces no measurable effect.
A gas contains an enormous number of particles, so an enormous number of collisions happen on every part of the wall every second.
Those separate impacts add up to a steady total force on the wall rather than a series of noticeable jolts.
The pressure of the gas is that total force spread over the area of the surface it acts on.

A diagram of gas molecules moving randomly inside a container. The molecules are shown colliding with the walls, which exerts a force and produces gas pressure.

What the pressure depends on

Two features of the collisions set the pressure: how often particles hit the wall, and how hard each one hits it.
Faster particles hit the wall harder and rebound more forcefully, so each collision contributes more to the total force.
Adding more particles to the same container increases the number of collisions each second, which is why a bicycle tyre becomes harder as it is pumped up.
Removing particles has the opposite effect, so a gas at low pressure produces fewer collisions each second on the same area of wall.
Because the motion is random, particles reach every part of the container, so the pressure acts on the whole inner surface and not only on the base.
The pressure inside a small container of gas is effectively the same at every point in it, unlike the pressure in a liquid, which increases with depth.
Atmospheric pressure at sea level is about $Pa1.0\times10^{5}\ \text{Pa}$ , produced by air particles colliding with every exposed surface.

Pressure, force and area

Pressure is defined by $p=FAp=\dfrac{F}{A}$ , where $p$ is the pressure, $F$ is the force acting on the surface and $A$ is the area of that surface.
The units are pascals for pressure, newtons for force and square metres for area, and $N/m21\ \text{Pa}=1\ \text{N/m}^{2}$ .
Rearranging gives $F=p×AF=p\times A$ , which is how the force on a piston, a window or a wall is worked out from the pressure.
The same pressure produces a larger force on a larger area, so a wide door in a pressurised cabin experiences a very large total force.
Convert areas into square metres before substituting, because $m21\ \text{cm}^{2}=1\times10^{-4}\ \text{m}^{2}$ .

Example

Force produced by a gas on a piston

A gas at a pressure of $Pa1.5\times10^{5}\ \text{Pa}$ acts on a piston of area $m22.0\times10^{-3}\ \text{m}^{2}$ .
Rearranging $p=FAp=\dfrac{F}{A}$ gives $F=p×AF=p\times A$ .
Substituting gives $F=1.5×105×2.0×10−3F=1.5\times10^{5}\times2.0\times10^{-3}$ .
The force on the piston is $NF=300\ \text{N}$ .
That force is the combined effect of countless particle collisions with the piston every second.

Exam technique

Explaining gas pressure

Build the answer as a chain: random motion, collisions with the wall, a force on the wall, then force divided by area.
Use the word collisions explicitly, because an answer that only says the particles push on the wall misses the mechanism mark.
Say that there are very many collisions each second, since the step from one tiny force to a steady pressure depends on that number.
Mention both how often and how hard the particles hit when a question asks what the pressure depends on.
Write $p=FAp=\dfrac{F}{A}$ before substituting, and convert any area given in square centimetres into square metres.

Common Mistake

Do not write that gas particles push on the walls all the time, because the force comes from separate collisions.
Do not write that particles repel one another to create the pressure, because the forces between widely separated gas particles are negligible.
Do not confuse force with pressure, because the same force spread over a larger area gives a smaller pressure.
Do not say the gas pushes hardest on the bottom of the container, because the random motion sends particles to every wall equally.

Self review

Describe how the particles of a gas move.
Explain how the collisions of gas particles produce a force on a container wall.
State the two features of the collisions that decide the pressure.
State the equation that links pressure, force and area, with the unit of each quantity.
Calculate the force produced by a pressure of $Pa2.0\times10^{5}\ \text{Pa}$ on an area of $m20.010\ \text{m}^{2}$ .
Explain why the pressure on a container wall is steady rather than jerky.

Where gas pressure comes from

Definition

Gas pressure

Gas pressure is the force per unit area that gas particles exert on a surface as a result of their collisions with it.

The particles of a gas move rapidly and randomly in all directions, and they have a wide spread of speeds rather than all moving at one speed.
Between collisions each particle travels in a straight line, because the forces between widely separated gas particles are very weak.
When a particle reaches a wall it collides with it and rebounds, so the direction of its motion is reversed.
Changing the direction of a moving particle requires a force from the wall, and the particle exerts an equal and opposite force back on the wall.
One collision gives an extremely small force lasting an extremely short time, so a single particle produces no measurable effect.
A gas contains an enormous number of particles, so an enormous number of collisions happen on every part of the wall every second.
Those separate impacts add up to a steady total force on the wall rather than a series of noticeable jolts.
The pressure of the gas is that total force spread over the area of the surface it acts on.

A diagram of gas molecules moving randomly inside a container. The molecules are shown colliding with the walls, which exerts a force and produces gas pressure.

What the pressure depends on

Two features of the collisions set the pressure: how often particles hit the wall, and how hard each one hits it.
Faster particles hit the wall harder and rebound more forcefully, so each collision contributes more to the total force.
Adding more particles to the same container increases the number of collisions each second, which is why a bicycle tyre becomes harder as it is pumped up.
Removing particles has the opposite effect, so a gas at low pressure produces fewer collisions each second on the same area of wall.
Because the motion is random, particles reach every part of the container, so the pressure acts on the whole inner surface and not only on the base.
The pressure inside a small container of gas is effectively the same at every point in it, unlike the pressure in a liquid, which increases with depth.
Atmospheric pressure at sea level is about $Pa1.0\times10^{5}\ \text{Pa}$ , produced by air particles colliding with every exposed surface.

Pressure, force and area

Pressure is defined by $p=FAp=\dfrac{F}{A}$ , where $p$ is the pressure, $F$ is the force acting on the surface and $A$ is the area of that surface.
The units are pascals for pressure, newtons for force and square metres for area, and $N/m21\ \text{Pa}=1\ \text{N/m}^{2}$ .
Rearranging gives $F=p×AF=p\times A$ , which is how the force on a piston, a window or a wall is worked out from the pressure.
The same pressure produces a larger force on a larger area, so a wide door in a pressurised cabin experiences a very large total force.
Convert areas into square metres before substituting, because $m21\ \text{cm}^{2}=1\times10^{-4}\ \text{m}^{2}$ .

Example

Force produced by a gas on a piston

A gas at a pressure of $Pa1.5\times10^{5}\ \text{Pa}$ acts on a piston of area $m22.0\times10^{-3}\ \text{m}^{2}$ .
Rearranging $p=FAp=\dfrac{F}{A}$ gives $F=p×AF=p\times A$ .
Substituting gives $F=1.5×105×2.0×10−3F=1.5\times10^{5}\times2.0\times10^{-3}$ .
The force on the piston is $NF=300\ \text{N}$ .
That force is the combined effect of countless particle collisions with the piston every second.

Exam technique

Explaining gas pressure

Build the answer as a chain: random motion, collisions with the wall, a force on the wall, then force divided by area.
Use the word collisions explicitly, because an answer that only says the particles push on the wall misses the mechanism mark.
Say that there are very many collisions each second, since the step from one tiny force to a steady pressure depends on that number.
Mention both how often and how hard the particles hit when a question asks what the pressure depends on.
Write $p=FAp=\dfrac{F}{A}$ before substituting, and convert any area given in square centimetres into square metres.

Common Mistake

Do not write that gas particles push on the walls all the time, because the force comes from separate collisions.
Do not write that particles repel one another to create the pressure, because the forces between widely separated gas particles are negligible.
Do not confuse force with pressure, because the same force spread over a larger area gives a smaller pressure.
Do not say the gas pushes hardest on the bottom of the container, because the random motion sends particles to every wall equally.

Self review

Describe how the particles of a gas move.
Explain how the collisions of gas particles produce a force on a container wall.
State the two features of the collisions that decide the pressure.
State the equation that links pressure, force and area, with the unit of each quantity.
Calculate the force produced by a pressure of $Pa2.0\times10^{5}\ \text{Pa}$ on an area of $m20.010\ \text{m}^{2}$ .
Explain why the pressure on a container wall is steady rather than jerky.

14.3.1 Gas pressure and particle motion

Where gas pressure comes from

What the pressure depends on

Pressure, force and area

Force produced by a gas on a piston

Explaining gas pressure

Review 14.3.1 Gas pressure and particle motion by teaching Genie

14.3.1 Gas pressure and particle motion

Where gas pressure comes from

What the pressure depends on

Pressure, force and area

Force produced by a gas on a piston

Explaining gas pressure

Review 14.3.1 Gas pressure and particle motion by teaching Genie

14.3.1 Gas pressure and particle motion

Where gas pressure comes from

What the pressure depends on

Pressure, force and area

Force produced by a gas on a piston

Explaining gas pressure

Review 14.3.1 Gas pressure and particle motion by teaching Genie

14.3.1 Gas pressure and particle motion Revision Guide

14.3.1 Gas pressure and particle motion

Where gas pressure comes from

What the pressure depends on

Pressure, force and area

Force produced by a gas on a piston

Explaining gas pressure

Review 14.3.1 Gas pressure and particle motion by teaching Genie

14.3.1 Gas pressure and particle motion Revision Guide