Pressure

What you'll learn

What pressure means, and why it depends on both force and area.
How moving gas molecules create pressure in a closed container.
How changing temperature or volume changes gas pressure.
Why liquid pressure increases with depth, and how pressure differences cause upthrust.

Pressure: force spread over an area

Pressure is about how concentrated a force is. The same force can have a very different effect depending on the area it acts over: a drawing pin is easy to push into a board because the force is concentrated over a tiny tip.

Definition

Pressure

Pressure, $p$ , is the force per unit area acting normal to a surface. “Normal” means at right angles to the surface.

\frac{F}{A}

$F$ is the force in newtons (N).
$A$ is the area in square metres ( $m2\text{m}^2$ ).
$p$ is pressure in pascals (Pa), where $N/m21\ \text{Pa} = 1\ \text{N}/\text{m}^2$ .

Example

Finding pressure from force and area

A force of 80 N acts normally on an area of 0.0040 m². Calculate the pressure.

Choose the pressure equation because you know the force and area: $\frac{F}{A}$ .
Substitute the values with units: $\frac{80\ \text{N}}{0.0040\ \text{m}^2}$ .
Calculate the pressure: $20000\ \text{Pa}$ .

Gas pressure comes from particle collisions

A gas is made of tiny particles, often molecules, moving randomly in all directions. When these particles collide with the walls of a container, they exert tiny forces on the walls. Lots of tiny collisions add up to a measurable pressure.

A closed system is a system where no particles enter or leave. For GCSE gas pressure explanations, you usually describe what happens to a fixed amount of gas in a closed container.

Temperature is linked to the average kinetic energy of the particles. Kinetic energy is the energy an object has because it is moving. If a gas is hotter, its molecules move faster on average.

Gas particles in rigid containers showing higher temperature causing more frequent and forceful collisions with the walls

Key Idea

Gas pressure in a rigid container

In a closed, rigid container, increasing the temperature increases the pressure because gas molecules hit the walls more often and more forcefully.

Example

Heating a sealed gas container

A sealed rigid metal can is heated. Explain why the gas pressure inside increases.

The can is sealed, so the number of gas molecules stays the same, and it is rigid, so the volume cannot increase.
Heating transfers energy to the molecules, increasing their average kinetic energy, so they move faster.
Faster molecules collide with the walls more often and with greater force, so the force per unit area on the walls increases.

Tip

Use collision language

For gas pressure explanations, use phrases like molecules move faster, more frequent collisions, more forceful collisions, and greater force per unit area.

Changing gas volume at constant temperature

A gas can be compressed by decreasing its volume, or expanded by increasing its volume. This happens because gas particles are far apart, so there is space between them.

At constant temperature, the particles’ average speed stays the same. If the volume increases, the same particles have more space, so they collide with the container walls less often. This decreases the pressure.

For separate Physics J249, you should be able to use the gas pressure-volume relationship. Treat this as a relationship to know and recognise in questions, especially the conditions for using it.

\text{constant}

For two situations involving the same fixed mass of gas at constant temperature:

p_1V_1 = p_2V_2

Example

Compressing gas at constant temperature

A fixed mass of gas has a pressure of 120000 Pa and a volume of 0.050 m³. It is compressed at constant temperature to a volume of 0.020 m³. Calculate the new pressure.

The gas has a fixed mass and constant temperature, so use $p_1V_1 = p_2V_2$ .
Rearrange for the final pressure: $p2=p1V1V2p_2 = \frac{p_1V_1}{V_2}$ .
Substitute and calculate: $Pap_2 = \frac{120000\ \text{Pa} \times 0.050\ \text{m}^3}{0.020\ \text{m}^3} = 300000\ \text{Pa}$ .

Common Mistake

Constant temperature matters

Only use $p_1V_1 = p_2V_2$ when the temperature stays constant and the amount of gas is fixed. If the gas is heated, cooled, added, or allowed to escape, this relationship may not apply.

Doing work on a gas can heat it

This next idea is Higher Tier only. When you push on a gas and compress it, you do work on the gas. Doing work means transferring energy by a force moving through a distance.

In a bicycle pump, your hand pushes the piston, compressing the air. Some energy is transferred to the gas’s internal energy, so the gas temperature rises. That is why a pump can feel warm after use.

Example

Why a bicycle pump warms up

Explain why the air in a bicycle pump gets hotter when the pump is used quickly.

Your hand exerts a force on the piston and moves it, so work is done on the gas inside the pump.
The gas is compressed, so energy is transferred to the gas particles.
The particles have more kinetic energy on average, so the temperature of the gas increases.

Atmospheric pressure

The atmosphere is the layer of gases around the Earth. Atmospheric pressure is caused by the weight of air above a surface.

A simple GCSE model treats the atmosphere like a huge column of air pressing down. Near sea level, there is a lot of air above you, so atmospheric pressure is relatively high. Higher up a mountain, there is less air above you, so atmospheric pressure is lower.

You do not need to know named layers of the atmosphere for this section.

Common Mistake

Suction is not a pulling force

In GCSE Physics, avoid saying “suction pulls it in.” A better explanation is that a pressure difference causes a net force. For example, when the pressure inside a can is reduced, the larger atmospheric pressure outside can crush it.

Pressure in liquids

This liquid pressure section and the calculations below are Higher Tier only.

A liquid has weight. The deeper you go in a liquid, the more liquid there is above you, so the pressure is greater. A denser liquid also produces more pressure at the same depth because the liquid above has more mass.

Liquid tank showing pressure increasing with depth and a larger upward pressure on the bottom of a submerged block causing upthrust

For pressure due to a column of liquid:

h\rho g

$p$ is pressure due to the liquid column in pascals (Pa).
$h$ is the depth below the surface in metres (m).
$ρ\rho$ is the density of the liquid in kilograms per cubic metre (kg/m³).
$g$ is gravitational field strength, taken as 10 N/kg near the Earth’s surface unless the question gives another value.

This equation is for separate Physics J249 Higher Tier content. Learn when to use it, and make sure all quantities are in SI units.

Example

Pressure difference between two depths

Two points in water are at depths of 0.25 m and 0.80 m. The density of water is 1000 kg/m³. Calculate the pressure difference between the two points.

Find the difference in depth: $m\Delta h = 0.80\ \text{m} - 0.25\ \text{m} = 0.55\ \text{m}$ .
Use the liquid pressure relationship for a difference in depth: $Δp=Δhρg\Delta p = \Delta h \rho g$ .
Substitute and calculate: $Pa\Delta p = 0.55\ \text{m} \times 1000\ \text{kg/m}^3 \times 10\ \text{N/kg} = 5500\ \text{Pa}$ .

Common Mistake

Pressure due to liquid is not always total pressure

In an open liquid, the total pressure at a depth includes atmospheric pressure plus the pressure due to the liquid. If a question asks for a difference in pressure, the atmospheric pressure usually cancels out.

Floating, sinking, and upthrust

This is also Higher Tier only.

An object in a liquid experiences its weight downward. It may also experience upthrust, an upward force caused by the pressure difference between the bottom and top of the object.

The bottom of the object is deeper than the top, so the liquid pressure on the bottom is greater. This creates a larger upward force than the downward force from liquid pressure on the top, giving a resultant upward force: upthrust.

Key Idea

Floating and sinking

An object floats if the upthrust can balance its weight. It sinks if its weight is greater than the maximum upthrust the liquid can provide.

Example

Deciding whether an object floats

A block has a weight of 12 N. When fully submerged in water, the maximum upthrust on it would be 15 N. Decide what happens.

Compare the maximum upthrust with the weight: 15 N is greater than 12 N.
If the block were fully submerged, the resultant force would be upward, so it would rise.
The block settles partly submerged, where the upthrust becomes 12 N and balances its weight, so it floats.

Common Mistake

Small does not mean floats

Floating is not decided just by whether something is small or light. A small steel ball can sink, while a huge ship can float, because floating depends on weight, upthrust, density, and the volume of liquid displaced.

Exam technique

In the exam

Before using $p_1V_1 = p_2V_2$ , check the gas has a fixed mass and constant temperature.
For liquid pressure, use SI units: depth in metres, density in kg/m³, and $10\ \text{N/kg}$ near Earth.
In explanations, write about particle collisions or pressure differences — not vague “suction” or “air pulling”.

Self review

Check yourself

Why does heating a gas in a sealed rigid container increase its pressure?
A gas at 80000 Pa and 0.030 m³ is compressed to 0.010 m³ at constant temperature. What is its new pressure?
Why is the pressure force on the bottom of a submerged object larger than the pressure force on the top?

Pressure

What you'll learn

What pressure means, and why it depends on both force and area.
How moving gas molecules create pressure in a closed container.
How changing temperature or volume changes gas pressure.
Why liquid pressure increases with depth, and how pressure differences cause upthrust.

Pressure: force spread over an area

Definition

Pressure

Pressure, $p$ , is the force per unit area acting normal to a surface. “Normal” means at right angles to the surface.

\frac{F}{A}

$F$ is the force in newtons (N).
$A$ is the area in square metres ( $m2\text{m}^2$ ).
$p$ is pressure in pascals (Pa), where $N/m21\ \text{Pa} = 1\ \text{N}/\text{m}^2$ .

Example

Finding pressure from force and area

A force of 80 N acts normally on an area of 0.0040 m². Calculate the pressure.

Choose the pressure equation because you know the force and area: $\frac{F}{A}$ .
Substitute the values with units: $\frac{80\ \text{N}}{0.0040\ \text{m}^2}$ .
Calculate the pressure: $20000\ \text{Pa}$ .

Gas pressure comes from particle collisions

A closed system is a system where no particles enter or leave. For GCSE gas pressure explanations, you usually describe what happens to a fixed amount of gas in a closed container.

Temperature is linked to the average kinetic energy of the particles. Kinetic energy is the energy an object has because it is moving. If a gas is hotter, its molecules move faster on average.

Gas particles in rigid containers showing higher temperature causing more frequent and forceful collisions with the walls

Key Idea

Gas pressure in a rigid container

In a closed, rigid container, increasing the temperature increases the pressure because gas molecules hit the walls more often and more forcefully.

Example

Heating a sealed gas container

A sealed rigid metal can is heated. Explain why the gas pressure inside increases.

The can is sealed, so the number of gas molecules stays the same, and it is rigid, so the volume cannot increase.
Heating transfers energy to the molecules, increasing their average kinetic energy, so they move faster.
Faster molecules collide with the walls more often and with greater force, so the force per unit area on the walls increases.

Tip

Use collision language

For gas pressure explanations, use phrases like molecules move faster, more frequent collisions, more forceful collisions, and greater force per unit area.

Changing gas volume at constant temperature

A gas can be compressed by decreasing its volume, or expanded by increasing its volume. This happens because gas particles are far apart, so there is space between them.

For separate Physics J249, you should be able to use the gas pressure-volume relationship. Treat this as a relationship to know and recognise in questions, especially the conditions for using it.

\text{constant}

For two situations involving the same fixed mass of gas at constant temperature:

p_1V_1 = p_2V_2

Example

Compressing gas at constant temperature

A fixed mass of gas has a pressure of 120000 Pa and a volume of 0.050 m³. It is compressed at constant temperature to a volume of 0.020 m³. Calculate the new pressure.

The gas has a fixed mass and constant temperature, so use $p_1V_1 = p_2V_2$ .
Rearrange for the final pressure: $p2=p1V1V2p_2 = \frac{p_1V_1}{V_2}$ .
Substitute and calculate: $Pap_2 = \frac{120000\ \text{Pa} \times 0.050\ \text{m}^3}{0.020\ \text{m}^3} = 300000\ \text{Pa}$ .

Common Mistake

Constant temperature matters

Only use $p_1V_1 = p_2V_2$ when the temperature stays constant and the amount of gas is fixed. If the gas is heated, cooled, added, or allowed to escape, this relationship may not apply.

Doing work on a gas can heat it

This next idea is Higher Tier only. When you push on a gas and compress it, you do work on the gas. Doing work means transferring energy by a force moving through a distance.

Example

Why a bicycle pump warms up

Explain why the air in a bicycle pump gets hotter when the pump is used quickly.

Your hand exerts a force on the piston and moves it, so work is done on the gas inside the pump.
The gas is compressed, so energy is transferred to the gas particles.
The particles have more kinetic energy on average, so the temperature of the gas increases.

Atmospheric pressure

The atmosphere is the layer of gases around the Earth. Atmospheric pressure is caused by the weight of air above a surface.

You do not need to know named layers of the atmosphere for this section.

Common Mistake

Suction is not a pulling force

Pressure in liquids

This liquid pressure section and the calculations below are Higher Tier only.

Liquid tank showing pressure increasing with depth and a larger upward pressure on the bottom of a submerged block causing upthrust

For pressure due to a column of liquid:

h\rho g

$p$ is pressure due to the liquid column in pascals (Pa).
$h$ is the depth below the surface in metres (m).
$ρ\rho$ is the density of the liquid in kilograms per cubic metre (kg/m³).
$g$ is gravitational field strength, taken as 10 N/kg near the Earth’s surface unless the question gives another value.

This equation is for separate Physics J249 Higher Tier content. Learn when to use it, and make sure all quantities are in SI units.

Example

Pressure difference between two depths

Two points in water are at depths of 0.25 m and 0.80 m. The density of water is 1000 kg/m³. Calculate the pressure difference between the two points.

Find the difference in depth: $m\Delta h = 0.80\ \text{m} - 0.25\ \text{m} = 0.55\ \text{m}$ .
Use the liquid pressure relationship for a difference in depth: $Δp=Δhρg\Delta p = \Delta h \rho g$ .
Substitute and calculate: $Pa\Delta p = 0.55\ \text{m} \times 1000\ \text{kg/m}^3 \times 10\ \text{N/kg} = 5500\ \text{Pa}$ .

Common Mistake

Pressure due to liquid is not always total pressure

Floating, sinking, and upthrust

This is also Higher Tier only.

An object in a liquid experiences its weight downward. It may also experience upthrust, an upward force caused by the pressure difference between the bottom and top of the object.

Key Idea

Floating and sinking

An object floats if the upthrust can balance its weight. It sinks if its weight is greater than the maximum upthrust the liquid can provide.

Example

Deciding whether an object floats

A block has a weight of 12 N. When fully submerged in water, the maximum upthrust on it would be 15 N. Decide what happens.

Compare the maximum upthrust with the weight: 15 N is greater than 12 N.
If the block were fully submerged, the resultant force would be upward, so it would rise.
The block settles partly submerged, where the upthrust becomes 12 N and balances its weight, so it floats.

Common Mistake

Small does not mean floats

Exam technique

In the exam

Before using $p_1V_1 = p_2V_2$ , check the gas has a fixed mass and constant temperature.
For liquid pressure, use SI units: depth in metres, density in kg/m³, and $10\ \text{N/kg}$ near Earth.
In explanations, write about particle collisions or pressure differences — not vague “suction” or “air pulling”.

Self review

Check yourself

Why does heating a gas in a sealed rigid container increase its pressure?
A gas at 80000 Pa and 0.030 m³ is compressed to 0.010 m³ at constant temperature. What is its new pressure?
Why is the pressure force on the bottom of a submerged object larger than the pressure force on the top?

Pressure

What you'll learn

Pressure: force spread over an area

Gas pressure comes from particle collisions

Changing gas volume at constant temperature

Doing work on a gas can heat it

Atmospheric pressure

Pressure in liquids

Floating, sinking, and upthrust

Recap questions

You've reached the end

Pressure

What you'll learn

Pressure: force spread over an area

Gas pressure comes from particle collisions

Changing gas volume at constant temperature

Doing work on a gas can heat it

Atmospheric pressure

Pressure in liquids

Floating, sinking, and upthrust

Recap questions

You've reached the end

Pressure

What you'll learn

Pressure: force spread over an area

Gas pressure comes from particle collisions

Changing gas volume at constant temperature

Doing work on a gas can heat it

Atmospheric pressure

Pressure in liquids

Floating, sinking, and upthrust

Recap questions

You've reached the end

Pressure Revision Guide

Pressure

What you'll learn

Pressure: force spread over an area

Gas pressure comes from particle collisions

Changing gas volume at constant temperature

Doing work on a gas can heat it

Atmospheric pressure

Pressure in liquids

Floating, sinking, and upthrust

Recap questions

You've reached the end

Pressure Revision Guide