Gas pressure and temperature

What you'll learn

Why a gas produces pressure on the walls of its container.
How changing temperature affects particle speed and gas pressure.
What absolute zero means, and how to convert between Celsius and kelvin.
For Separate Physics: how changing gas volume affects pressure, including using $P_1V_1 = P_2V_2$ .

Starting point: gases in the particle model

A gas is made of particles that are far apart compared with solids and liquids. The particles move quickly and randomly in all directions.

Because gas particles are spread out, a gas has no fixed shape or volume. It fills its container.

Definition

Pressure

Pressure is the force acting on each square metre of a surface. Its unit is the pascal (Pa), where $N/m21\ \text{Pa} = 1\ \text{N/m}^2$ .

For gases, the important idea is that pressure is not caused by one big push. It is caused by huge numbers of tiny particle collisions with the container walls.

Gas particles colliding with the walls of a container, producing pressure

Why gases produce pressure

Each gas particle moves in a straight line until it collides with another particle or the wall of the container.

When a particle hits the wall, it changes direction. During the collision, the particle exerts a tiny force on the wall. Many particles collide with the wall every second, so the total effect is a steady pressure.

Key Idea

Gas pressure from collisions

Gas pressure is caused by gas particles moving randomly and colliding with the walls of their container. More frequent or harder collisions produce a higher pressure.

What makes the pressure bigger?

Gas pressure increases if:

particles collide with the walls more often
particles collide with the walls at higher speed
the same particles are squeezed into a smaller volume

Example

Explaining pressure in a sealed container

A sealed metal can contains air. Explain why the air produces pressure on the inside walls.

The air is made of gas particles moving randomly in all directions.
When these particles collide with the inside walls, they exert forces on the walls.
The total force from many collisions over each square metre of wall produces gas pressure.

Common Mistake

Thinking pressure acts in one direction only

In a gas, particles move randomly, so gas pressure acts on all surfaces of the container. It does not only push downwards.

Temperature and particle speed

Definition

Temperature

Temperature is a measure of how hot or cold something is. In the particle model, a higher temperature means the particles have more energy and, in a gas, move faster on average.

When a gas is heated:

energy is transferred to the particles
the particles move faster on average
they hit the walls more often
they hit the walls harder because their speed is greater

If the gas is in a fixed container, its volume cannot change. So the increased particle motion causes the pressure to increase.

Definition

Constant volume

Constant volume means the gas stays in the same amount of space. For example, gas in a sealed rigid container has constant volume.

Key Idea

Heating a gas at constant volume

For a fixed mass of gas at constant volume, increasing the temperature increases the particles’ average speed, so the pressure increases.

Example

Heating gas in a rigid container

A sealed rigid flask of air is heated. Explain what happens to the pressure.

Heating transfers energy to the air particles, so their average speed increases.
The flask is rigid, so the volume stays the same and the particles cannot spread out into more space.
The faster particles collide with the walls more often and with greater force, so the pressure increases.

Tip

Use the collision chain

For explanation questions, link the ideas in order: higher temperature → faster particles → more frequent/harder wall collisions → higher pressure.

Absolute zero

As a gas is cooled, its particles move more slowly on average. If you keep imagining the particles getting slower and slower, you eventually reach a lowest possible temperature.

Definition

Absolute zero

Absolute zero is the lowest possible temperature, $−273∘C-273^\circ\text{C}$ . At this temperature, particles have the minimum possible energy and are described at GCSE as having no movement.

In real exams, you do not need a complicated quantum explanation. For GCSE, say that at absolute zero the particles have no movement / minimum possible kinetic energy.

Common Mistake

Do not go below absolute zero

The kelvin scale starts at absolute zero, so temperatures below 0 K are not physically possible.

Celsius and kelvin

You normally use degrees Celsius, °C, in everyday life. In physics, gas temperature often uses the kelvin scale.

Definition

Kelvin scale

The kelvin scale is an absolute temperature scale. It starts at absolute zero, so 0 K is the same temperature as $−273∘C-273^\circ\text{C}$ .

Kelvin temperatures use the unit K, not “degrees K”.

To convert:

TK=θC+273T_\text{K} = \theta_\text{C} + 273

θC=TK−273\theta_\text{C} = T_\text{K} - 273

where $TKT_\text{K}$ is temperature in kelvin and $θC\theta_\text{C}$ is temperature in degrees Celsius.

Example

Converting between Celsius and kelvin

Convert 27 °C into kelvin, then convert 250 K into degrees Celsius.

For 27 °C, add 273 because kelvin starts 273 degrees lower than Celsius: $TK=27+273T_\text{K} = 27 + 273$ .
Calculate the kelvin temperature: $KT_\text{K} = 300\ \text{K}$ .
For 250 K, subtract 273 to return to Celsius: $θC=250−273=−23∘C\theta_\text{C} = 250 - 273 = -23^\circ\text{C}$ .

Common Mistake

Writing degrees kelvin

Write 300 K, not 300 °K. Kelvin is not written with a degree symbol.

Separate Physics: compressing and expanding gases

The next ideas are for Separate Physics students.

A gas can be compressed by reducing its volume. For example, pushing down a syringe plunger squeezes the gas into less space.

A gas can be expanded by increasing its volume. For example, pulling the syringe plunger out gives the gas more space.

Definition

Fixed mass of gas

A fixed mass of gas means no gas particles are added or removed. The same amount of gas stays in the container.

If the mass of gas is fixed and the temperature is constant:

decreasing the volume increases the pressure
increasing the volume decreases the pressure

This happens because changing the volume changes how often particles collide with the container walls.

Compressing a fixed mass of gas increases collision rate and pressure; pressure-volume graph curves downward

Definition

Constant temperature

Constant temperature means the gas particles have the same average kinetic energy, so their average speed stays the same.

Why reducing volume increases pressure

If the gas is compressed:

the same number of particles is in a smaller space
the particles have less distance to travel before hitting a wall
collisions with the walls happen more often
pressure increases

Key Idea

Volume and pressure

For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume: if volume halves, pressure doubles.

Example

Explaining pressure change during compression

A syringe is sealed and the plunger is pushed in slowly. The temperature stays constant. Explain why the pressure increases.

Pushing in the plunger decreases the volume of gas in the syringe.
The same number of gas particles is now in a smaller space, so each particle travels a shorter distance before hitting a wall.
The particles collide with the walls more frequently, so the force per unit area increases and the pressure rises.

Separate Physics: pressure produces a force

Gas pressure acts at right angles to any surface it touches. “At right angles” means perpendicular to the surface.

If gas pressure acts on a surface area, it produces a force:

\times A

where $F$ is force in newtons (N), $P$ is pressure in pascals (Pa), and $A$ is area in square metres (m²).

This is why air pressure can push on a balloon, why tyres feel firm, and why a piston can be pushed by compressed gas.

Example

Finding the force from gas pressure

A gas has a pressure of 80,000 Pa and acts on a piston area of 0.020 m². Calculate the force on the piston.

Use the pressure-force relationship because pressure acts over an area: $\times A$ .
Substitute the values with SI units: $\times 0.020$ .
Calculate the force: $1600\ \text{N}$ .

Separate Physics: using $P_1V_1 = P_2V_2$

For a fixed mass of gas at constant temperature, the pressure-volume relationship is:

P_1V_1 = P_2V_2

You use this equation when a gas changes from one state to another:

$P_1$ = initial pressure
$V_1$ = initial volume
$P_2$ = final pressure
$V_2$ = final volume

This equation is for Separate Physics. It is normally provided on the Edexcel equation sheet as a “use” equation, but you must know when it applies.

Common Mistake

Only for constant temperature

Only use $P_1V_1 = P_2V_2$ when the mass of gas is fixed and the temperature stays constant. If the gas is heated or cooled, this equation on its own is not valid.

Example

Calculating the new pressure of a compressed gas

A gas has a volume of 0.50 m³ and a pressure of 100,000 Pa. It is compressed to a volume of 0.20 m³ at constant temperature. Calculate the new pressure.

Choose the pressure-volume equation because the gas has fixed mass and constant temperature: $P_1V_1 = P_2V_2$ .
Rearrange for the unknown final pressure: $P2=P1V1V2P_2 = \frac{P_1V_1}{V_2}$ .
Substitute the values: $P2=100000×0.500.20P_2 = \frac{100000 \times 0.50}{0.20}$ .
Calculate the result with units: $PaP_2 = 250000\ \text{Pa}$ .

Tip

Sanity check for Boyle’s law

If the volume gets smaller, the pressure should get bigger. If your calculation gives the opposite, check your rearranging.

Higher Tier Separate Physics: doing work on a gas

This final idea is Higher Tier and Separate Physics only.

When you do work on a gas, you transfer energy to it. For example, in a bicycle pump, your hand pushes the piston down. The piston does work on the trapped air.

That energy increases the internal energy of the gas, so the particles move faster on average. This means the temperature of the gas increases.

Key Idea

Bicycle pump heating

A bicycle pump can get warm because work is done on the air as it is compressed. Energy is transferred to the gas, increasing the particles’ average kinetic energy and therefore the temperature.

Example

Explaining why a bicycle pump warms up

Explain why the barrel of a bicycle pump may become warm when pumping up a tyre.

Your hand applies a force to move the piston, so work is done on the air inside the pump.
This transfers energy to the gas, increasing its internal energy.
The air particles move faster on average, so the temperature of the gas rises and energy is transferred to the pump barrel by heating.

Common Mistake

Saying compression always means constant temperature

Slow compression may allow energy to transfer away, so temperature can stay roughly constant. Fast compression, like in a bicycle pump, can increase the gas temperature because work is done on the gas faster than energy escapes.

Exam technique

In the exam

For explanation questions, always link particle motion to collisions with the container walls, then link collisions to pressure.
For temperature questions, state whether volume is constant: at constant volume, higher temperature means faster particles and higher pressure.
For $P_1V_1 = P_2V_2$ calculations, check the conditions first: fixed mass of gas and constant temperature.

Self review

Check yourself

Why does heating a gas in a sealed rigid container increase its pressure?
Convert 35 °C into kelvin, and convert 290 K into degrees Celsius.
A gas at constant temperature is compressed to half its original volume. What happens to its pressure?

Gas pressure and temperature

What you'll learn

Why a gas produces pressure on the walls of its container.
How changing temperature affects particle speed and gas pressure.
What absolute zero means, and how to convert between Celsius and kelvin.
For Separate Physics: how changing gas volume affects pressure, including using $P_1V_1 = P_2V_2$ .

Starting point: gases in the particle model

A gas is made of particles that are far apart compared with solids and liquids. The particles move quickly and randomly in all directions.

Because gas particles are spread out, a gas has no fixed shape or volume. It fills its container.

Definition

Pressure

Pressure is the force acting on each square metre of a surface. Its unit is the pascal (Pa), where $N/m21\ \text{Pa} = 1\ \text{N/m}^2$ .

For gases, the important idea is that pressure is not caused by one big push. It is caused by huge numbers of tiny particle collisions with the container walls.

Gas particles colliding with the walls of a container, producing pressure

Why gases produce pressure

Each gas particle moves in a straight line until it collides with another particle or the wall of the container.

Key Idea

Gas pressure from collisions

Gas pressure is caused by gas particles moving randomly and colliding with the walls of their container. More frequent or harder collisions produce a higher pressure.

What makes the pressure bigger?

Gas pressure increases if:

particles collide with the walls more often
particles collide with the walls at higher speed
the same particles are squeezed into a smaller volume

Example

Explaining pressure in a sealed container

A sealed metal can contains air. Explain why the air produces pressure on the inside walls.

The air is made of gas particles moving randomly in all directions.
When these particles collide with the inside walls, they exert forces on the walls.
The total force from many collisions over each square metre of wall produces gas pressure.

Common Mistake

Thinking pressure acts in one direction only

In a gas, particles move randomly, so gas pressure acts on all surfaces of the container. It does not only push downwards.

Temperature and particle speed

Definition

Temperature

Temperature is a measure of how hot or cold something is. In the particle model, a higher temperature means the particles have more energy and, in a gas, move faster on average.

When a gas is heated:

energy is transferred to the particles
the particles move faster on average
they hit the walls more often
they hit the walls harder because their speed is greater

If the gas is in a fixed container, its volume cannot change. So the increased particle motion causes the pressure to increase.

Definition

Constant volume

Constant volume means the gas stays in the same amount of space. For example, gas in a sealed rigid container has constant volume.

Key Idea

Heating a gas at constant volume

For a fixed mass of gas at constant volume, increasing the temperature increases the particles’ average speed, so the pressure increases.

Example

Heating gas in a rigid container

A sealed rigid flask of air is heated. Explain what happens to the pressure.

Heating transfers energy to the air particles, so their average speed increases.
The flask is rigid, so the volume stays the same and the particles cannot spread out into more space.
The faster particles collide with the walls more often and with greater force, so the pressure increases.

Tip

Use the collision chain

For explanation questions, link the ideas in order: higher temperature → faster particles → more frequent/harder wall collisions → higher pressure.

Absolute zero

As a gas is cooled, its particles move more slowly on average. If you keep imagining the particles getting slower and slower, you eventually reach a lowest possible temperature.

Definition

Absolute zero

Absolute zero is the lowest possible temperature, $−273∘C-273^\circ\text{C}$ . At this temperature, particles have the minimum possible energy and are described at GCSE as having no movement.

In real exams, you do not need a complicated quantum explanation. For GCSE, say that at absolute zero the particles have no movement / minimum possible kinetic energy.

Common Mistake

Do not go below absolute zero

The kelvin scale starts at absolute zero, so temperatures below 0 K are not physically possible.

Celsius and kelvin

You normally use degrees Celsius, °C, in everyday life. In physics, gas temperature often uses the kelvin scale.

Definition

Kelvin scale

The kelvin scale is an absolute temperature scale. It starts at absolute zero, so 0 K is the same temperature as $−273∘C-273^\circ\text{C}$ .

Kelvin temperatures use the unit K, not “degrees K”.

To convert:

TK=θC+273T_\text{K} = \theta_\text{C} + 273

θC=TK−273\theta_\text{C} = T_\text{K} - 273

where $TKT_\text{K}$ is temperature in kelvin and $θC\theta_\text{C}$ is temperature in degrees Celsius.

Example

Converting between Celsius and kelvin

Convert 27 °C into kelvin, then convert 250 K into degrees Celsius.

For 27 °C, add 273 because kelvin starts 273 degrees lower than Celsius: $TK=27+273T_\text{K} = 27 + 273$ .
Calculate the kelvin temperature: $KT_\text{K} = 300\ \text{K}$ .
For 250 K, subtract 273 to return to Celsius: $θC=250−273=−23∘C\theta_\text{C} = 250 - 273 = -23^\circ\text{C}$ .

Common Mistake

Writing degrees kelvin

Write 300 K, not 300 °K. Kelvin is not written with a degree symbol.

Separate Physics: compressing and expanding gases

The next ideas are for Separate Physics students.

A gas can be compressed by reducing its volume. For example, pushing down a syringe plunger squeezes the gas into less space.

A gas can be expanded by increasing its volume. For example, pulling the syringe plunger out gives the gas more space.

Definition

Fixed mass of gas

A fixed mass of gas means no gas particles are added or removed. The same amount of gas stays in the container.

If the mass of gas is fixed and the temperature is constant:

decreasing the volume increases the pressure
increasing the volume decreases the pressure

This happens because changing the volume changes how often particles collide with the container walls.

Compressing a fixed mass of gas increases collision rate and pressure; pressure-volume graph curves downward

Definition

Constant temperature

Constant temperature means the gas particles have the same average kinetic energy, so their average speed stays the same.

Why reducing volume increases pressure

If the gas is compressed:

the same number of particles is in a smaller space
the particles have less distance to travel before hitting a wall
collisions with the walls happen more often
pressure increases

Key Idea

Volume and pressure

For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume: if volume halves, pressure doubles.

Example

Explaining pressure change during compression

A syringe is sealed and the plunger is pushed in slowly. The temperature stays constant. Explain why the pressure increases.

Pushing in the plunger decreases the volume of gas in the syringe.
The same number of gas particles is now in a smaller space, so each particle travels a shorter distance before hitting a wall.
The particles collide with the walls more frequently, so the force per unit area increases and the pressure rises.

Separate Physics: pressure produces a force

Gas pressure acts at right angles to any surface it touches. “At right angles” means perpendicular to the surface.

If gas pressure acts on a surface area, it produces a force:

\times A

where $F$ is force in newtons (N), $P$ is pressure in pascals (Pa), and $A$ is area in square metres (m²).

This is why air pressure can push on a balloon, why tyres feel firm, and why a piston can be pushed by compressed gas.

Example

Finding the force from gas pressure

A gas has a pressure of 80,000 Pa and acts on a piston area of 0.020 m². Calculate the force on the piston.

Use the pressure-force relationship because pressure acts over an area: $\times A$ .
Substitute the values with SI units: $\times 0.020$ .
Calculate the force: $1600\ \text{N}$ .

Separate Physics: using $P_1V_1 = P_2V_2$

For a fixed mass of gas at constant temperature, the pressure-volume relationship is:

P_1V_1 = P_2V_2

You use this equation when a gas changes from one state to another:

$P_1$ = initial pressure
$V_1$ = initial volume
$P_2$ = final pressure
$V_2$ = final volume

This equation is for Separate Physics. It is normally provided on the Edexcel equation sheet as a “use” equation, but you must know when it applies.

Common Mistake

Only for constant temperature

Only use $P_1V_1 = P_2V_2$ when the mass of gas is fixed and the temperature stays constant. If the gas is heated or cooled, this equation on its own is not valid.

Example

Calculating the new pressure of a compressed gas

A gas has a volume of 0.50 m³ and a pressure of 100,000 Pa. It is compressed to a volume of 0.20 m³ at constant temperature. Calculate the new pressure.

Choose the pressure-volume equation because the gas has fixed mass and constant temperature: $P_1V_1 = P_2V_2$ .
Rearrange for the unknown final pressure: $P2=P1V1V2P_2 = \frac{P_1V_1}{V_2}$ .
Substitute the values: $P2=100000×0.500.20P_2 = \frac{100000 \times 0.50}{0.20}$ .
Calculate the result with units: $PaP_2 = 250000\ \text{Pa}$ .

Tip

Sanity check for Boyle’s law

If the volume gets smaller, the pressure should get bigger. If your calculation gives the opposite, check your rearranging.

Higher Tier Separate Physics: doing work on a gas

This final idea is Higher Tier and Separate Physics only.

When you do work on a gas, you transfer energy to it. For example, in a bicycle pump, your hand pushes the piston down. The piston does work on the trapped air.

That energy increases the internal energy of the gas, so the particles move faster on average. This means the temperature of the gas increases.

Key Idea

Bicycle pump heating

A bicycle pump can get warm because work is done on the air as it is compressed. Energy is transferred to the gas, increasing the particles’ average kinetic energy and therefore the temperature.

Example

Explaining why a bicycle pump warms up

Explain why the barrel of a bicycle pump may become warm when pumping up a tyre.

Your hand applies a force to move the piston, so work is done on the air inside the pump.
This transfers energy to the gas, increasing its internal energy.
The air particles move faster on average, so the temperature of the gas rises and energy is transferred to the pump barrel by heating.

Common Mistake

Saying compression always means constant temperature

Exam technique

In the exam

For explanation questions, always link particle motion to collisions with the container walls, then link collisions to pressure.
For temperature questions, state whether volume is constant: at constant volume, higher temperature means faster particles and higher pressure.
For $P_1V_1 = P_2V_2$ calculations, check the conditions first: fixed mass of gas and constant temperature.

Self review

Check yourself

Why does heating a gas in a sealed rigid container increase its pressure?
Convert 35 °C into kelvin, and convert 290 K into degrees Celsius.
A gas at constant temperature is compressed to half its original volume. What happens to its pressure?

Gas pressure and temperature

What you'll learn

Starting point: gases in the particle model

Why gases produce pressure

What makes the pressure bigger?

Temperature and particle speed

Absolute zero

Celsius and kelvin

Separate Physics: compressing and expanding gases

Why reducing volume increases pressure

Separate Physics: pressure produces a force

Separate Physics: using $P_1V_1 = P_2V_2$

Higher Tier Separate Physics: doing work on a gas

Recap questions

Gas pressure and temperature

What you'll learn

Starting point: gases in the particle model

Why gases produce pressure

What makes the pressure bigger?

Temperature and particle speed

Absolute zero

Celsius and kelvin

Separate Physics: compressing and expanding gases

Why reducing volume increases pressure

Separate Physics: pressure produces a force

Separate Physics: using $P_1V_1 = P_2V_2$

Higher Tier Separate Physics: doing work on a gas

Recap questions

Gas pressure and temperature

What you'll learn

Starting point: gases in the particle model

Why gases produce pressure

What makes the pressure bigger?

Temperature and particle speed

Absolute zero

Celsius and kelvin

Separate Physics: compressing and expanding gases

Why reducing volume increases pressure

Separate Physics: pressure produces a force

Separate Physics: using P1V1=P2V2P_1V_1 = P_2V_2P1​V1​=P2​V2​

Higher Tier Separate Physics: doing work on a gas

Recap questions

Gas pressure and temperature Revision Guide

Gas pressure and temperature

What you'll learn

Starting point: gases in the particle model

Why gases produce pressure

What makes the pressure bigger?

Temperature and particle speed

Absolute zero

Celsius and kelvin

Separate Physics: compressing and expanding gases

Why reducing volume increases pressure

Separate Physics: pressure produces a force

Separate Physics: using P1V1=P2V2P_1V_1 = P_2V_2P1​V1​=P2​V2​

Higher Tier Separate Physics: doing work on a gas

Recap questions

Gas pressure and temperature Revision Guide

Separate Physics: using $P_1V_1 = P_2V_2$

Separate Physics: using $P_1V_1 = P_2V_2$