Think about pumping up a bike tyre. The more air you push in, the harder the tyre gets. If you hold your finger over the end of the pump and push the handle, it also gets hard to push, and the barrel warms up.
Now think about a can of spray deodorant. The label says do not leave it in a hot car or near a fire. Something inside the can changes when it gets hot, and it can be dangerous. That something is gas pressure.
Here is a picture to hold on to. Imagine a small box with hundreds of tiny bouncy balls flying around inside it. The balls keep hitting the walls, and every hit gives the wall a tiny push. A gas is like that, with the particles as the bouncy balls.
A gas is a state of matter, and its particles are far apart and moving fast. They are so small and so quick that you cannot see them. But you can feel what they do, because their collisions are what hold up a tyre or a balloon.
By the end of this lesson you will be able to do three things. First, explain gas pressure using particles. Second, explain what happens to the pressure when a gas is heated or squashed. Third, at Higher tier, use pressure × volume = constant and explain why a pump gets warm.
Particles in a gas
All matter is made of tiny particles. In a solid, the particles are packed tightly in fixed positions and only vibrate. In a liquid, they are close together but can slide past each other. In a gas, they are far apart and free to move.
The molecules of a gas are in constant random motion. They move quickly in random directions. They travel in straight lines until they hit another particle or the wall of the container, and then they bounce off in a new direction. There is mostly empty space between them. Check this against the picture below.
Because the particles are so far apart, a gas has no fixed shape and no fixed volume. It spreads out to fill any container. That is why the smell of cooking drifts all through a house, and why a gas can be squashed into a smaller space.
A sealed container of gas has a fixed number of particles. If you heat it or squash it, the number does not change. Only the speed of the particles, or the space they have, changes. Keep that in mind, because it helps with every question in this topic.
The temperature of a gas is related to the average kinetic energy of its molecules. The hotter the gas, the more kinetic energy its particles have on average. Kinetic energy is the energy of movement, so a higher temperature means the particles move faster on average.
Particles in a solid, a liquid and a gas. In the solid they are packed in a regular pattern and vibrate. In the liquid they touch and slide. In the gas they are far apart and move fast.
How gas particles make pressure
Each time a gas particle hits a wall, it bounces back and gives the wall a tiny push. One push is far too small to notice. But there are billions of billions of particles, and they hit the wall many times every second.
All those tiny pushes add up to a steady force on the wall. Pressure is force divided by area, so the force on each square metre of the wall is the gas pressure. The force acts at right angles to the wall.
Inside a gas, the pressure is the same in all directions. This is why a balloon is round and not lopsided. The air pushes outwards equally on every part of the rubber.
A balloon stays blown up because the particles inside keep hitting the rubber from the inside. Air outside hits it from the outside. If the pressure inside is bigger, the balloon is pushed out until the two balance.
So a bigger pressure means the particles are hitting the wall harder, or more often, or both. Keep that sentence in your head. It is the answer to nearly every question about gas pressure. A tyre pumped up hard has more particles inside, so they hit the inner wall more often.
Four boxes in order: a particle hits the wall, a tiny force acts on the wall, billions of hits happen every second, and together they give a steady force on the wall, which is the pressure.
Temperature and pressure
Imagine the gas is in a sealed container that cannot change size. The volume is fixed, and so is the number of particles. Now heat the gas. The particles gain kinetic energy and move faster.
Faster particles hit the walls harder, and they hit them more often because they cover the distance quicker. Think of a crowd of people running instead of walking. They bump into the walls harder and more often. Both effects push up the pressure. So heating a sealed gas of fixed volume increases its pressure.
Cooling does the opposite. The particles move slower, so they hit the walls less hard and less often. The pressure falls. That is why a car tyre can look a little flat on a frosty morning.
This explains why a sealed aerosol can is dangerous in a fire. The heat makes the gas inside the can push harder and harder on the metal. If it gets too hot, the can can burst. This is why gas cylinders and aerosols carry warnings about heat.
Scientists use the kelvin scale for temperatures in gas work. Nothing can be colder than absolute zero, which is 0 K, or −273 °C. To change from degrees Celsius to kelvin, add 273, so 27 °C is 300 K.
Bars showing the pressure of a sealed gas in kilopascals rising as the gas goes from cold to warm to hot.
Pressure and volume (Higher tier)
Now keep the temperature the same and change the volume. Push in the plunger of a sealed syringe. The same number of particles now have less room. They hit the walls more often, so the pressure goes up.
Pull the plunger out and the opposite happens. The particles have more room, so they hit the walls less often. The pressure falls. The temperature is unchanged, so the particles are moving at the same speed. Put your finger over the end of a bicycle pump and squash the air, and you can feel it pushing back harder.
At Higher tier you also put numbers on it. For a fixed mass of gas at constant temperature, pressure × volume is constant. If the volume halves, the pressure doubles. If the volume doubles, the pressure halves.
When pressure goes up as volume goes down, with their product staying the same, we say the two are inversely proportional. On a graph this gives a curve that falls steeply and then flattens. It is not a straight line.
Remember the two conditions. The temperature must stay constant, and the mass of gas must stay the same. If the gas is heated at the same time, or can leak out, the rule no longer works.
A graph of pressure against volume for a fixed mass of gas at constant temperature. The pressure falls from 120 kilopascals at 1 cubic metre to 20 kilopascals at 6 cubic metres, in a curve that gets flatter.
Using p₁ × V₁ = p₂ × V₂ (Higher tier)
For two states of the same gas at constant temperature, p₁ × V₁ = p₂ × V₂. The first pressure times the first volume equals the second pressure times the second volume. Here p is pressure and V is volume.
Pressure can be in kPa or Pa, and volume can be in m³, cm³ or litres. The only rule is to use the same units on both sides. You do not need to change the units if they already match.
Here is the method. Write the equation. Put in the three numbers you know. Multiply the two on the side that is complete, then divide by the number you have on the other side. That gives the missing value. Setting out your working in clear lines also earns method marks in an exam.
Try it with a syringe. It holds 60 cm³ of air at 100 kPa. The plunger is pushed in until the volume is 40 cm³. Then 100 × 60 = p₂ × 40, so p₂ = 6000 ÷ 40 = 150 kPa.
Always check the answer. A smaller volume should give a bigger pressure. If your answer shows the pressure falling when the gas is squashed, you have divided the wrong way round.
Four boxes in order: write the equation p1 times V1 equals p2 times V2, put in the three numbers you know, multiply one side then divide by the number on the other, and check that a smaller volume gives a bigger pressure.
Work done on a gas (Higher tier)
Push the plunger of a bicycle pump and you do work on the air. Work is energy transferred by a force. Rubbing your hands together is the same idea, because you do work and they warm up. The air is squashed, and that energy has to go somewhere.
If the gas is compressed quickly, there is no time for the energy to escape to the surroundings. The work done increases the internal energy of the gas. Internal energy is the total energy of all the particles in it.
A big part of that extra energy goes into the kinetic energy of the particles. They move faster, so the temperature of the gas goes up. That is why the barrel of a bicycle pump warms up when you pump hard.
If you compress the gas slowly, some of the energy has time to leak out as heat, so it warms up less. Speed matters. The quicker the compression, the bigger the temperature rise.
Notice the pattern. Do work on a gas and it gains energy, so it heats up. In the other direction, a gas that does work on its surroundings, such as pushing a piston outwards, loses energy and cools.
Four boxes in order: work is done pushing the piston, energy is transferred to the gas particles, the particles move faster, and the temperature of the gas rises.
Recap
A gas is made of particles that are far apart and moving fast in random directions. Gas pressure is caused by particles colliding with the walls. It acts at right angles to the wall.
Heating a sealed gas makes the particles move faster, so they hit the walls harder and more often, and the pressure rises. Cooling lowers the pressure. The number of particles in a sealed container never changes, so do not say that more particles appear.
At constant temperature, squashing a gas makes the pressure rise, because the particles hit the walls more often. At Higher tier, p₁ × V₁ = p₂ × V₂, and halving the volume doubles the pressure.
At Higher tier, compressing a gas quickly does work on it. The energy cannot escape, so the internal energy and the temperature rise. The energy is transferred to the gas, not created.
How this is asked in an exam: an explain question wants the chain in order, such as the particles move faster, so they hit the walls harder and more often, so the pressure increases. A calculation wants the equation, the numbers and the answer with its unit.
Key points
Gas particles move fast in random directions and are far apart.
Gas pressure is caused by particles colliding with the walls.
Heating a sealed gas makes the particles faster, so the pressure rises.
Higher tier: at constant temperature, pressure × volume is constant.
Higher tier: compressing a gas quickly does work on it, so its temperature rises.
The number of particles in a sealed gas does not change.
Worked examples
Example 1
Explain why the pressure of a sealed gas increases when it is heated.
Heating gives the particles more kinetic energy, so they move faster.
Faster particles hit the walls harder.
They also hit the walls more often, so the pressure increases.
Answer: The particles move faster, so they hit the walls harder and more often, and the pressure increases.
Common slips
Slip: The particles get bigger when they are heated. Particles do not change size. They move faster.
Slip: The particles move slower when they are heated. Heating makes the particles move faster, not slower.
Slip: There are more particles in the container. The container is sealed, so the number of particles stays the same.
Example 2
A gas at 100 kPa has a volume of 2 m³. It is compressed at constant temperature until the volume is 0.5 m³. Work out the new pressure.
Write the equation: p₁ × V₁ = p₂ × V₂.
Substitute the numbers: 100 × 2 = p₂ × 0.5.
Work it out: 200 = p₂ × 0.5, so p₂ = 200 ÷ 0.5 = 400 kPa.
Answer: 400 kPa
Common slips
Slip: p₁ ÷ V₁ = p₂ ÷ V₂ Pressure multiplied by volume is constant. The two are multiplied, not divided.
Slip: 100 × 0.5 = 50, so the pressure is 50 kPa. The original numbers are p₁ = 100 and V₁ = 2. Multiply those, then divide by the new volume.
Slip: The pressure falls to 25 kPa. Squashing a gas raises its pressure. The volume went down, so the pressure must go up.
Example 3
A syringe holds 60 cm³ of air at 100 kPa. The plunger is pushed in until the volume is 40 cm³. The temperature stays constant. Work out the new pressure.
Write the equation: p₁ × V₁ = p₂ × V₂.
Substitute the numbers: 100 × 60 = p₂ × 40.
Work it out: 6000 = p₂ × 40, so p₂ = 6000 ÷ 40 = 150 kPa.
Answer: 150 kPa
Common slips
Slip: 100 × 40 ÷ 60 = 67 kPa. Multiply the original pressure and volume, then divide by the new volume.
Slip: 100 + 20 = 120 kPa. Pressure and volume are multiplied, not added.
Slip: The pressure is 40 kPa. The pressure rises when the volume falls. 40 is the new volume.
Questions and answers
Gas pressure and volume practice questions for GCSE Combined Science Physics. Try each one, then open the answer. Easy questions come first.
Question 1 Easy
Name what causes the pressure of a gas on a container wall.
Show answer
Answer: particles colliding with the wall
Particles move randomly.
They collide with the wall.
Question 2 Easy
What happens to the pressure of a sealed gas when it is cooled?
Show answer
Answer: It decreases.
The particles slow down.
They hit the walls less hard and less often, so the pressure falls.
Question 3 Easy
The volume of a gas is halved at constant temperature. State what happens to the pressure.
Show answer
Answer: It doubles.
Pressure × volume is constant.
Halving the volume doubles the pressure.
Question 4 Easy
State the condition needed for pressure × volume to stay constant.
Show answer
Answer: constant temperature
The relationship only holds for a fixed mass of gas.
The temperature must stay constant.
Question 5 Medium
A gas at 200 kPa has a volume of 3 m³. It expands to 6 m³ at constant temperature. Work out the new pressure.
Show answer
Answer: 100 kPa
p₁ × V₁ = p₂ × V₂
200 × 3 ÷ 6 = 100 kPa
Question 6 Medium
A gas at 50 kPa has a volume of 6 m³. It is compressed to 2 m³ at constant temperature. Work out the new pressure.
Show answer
Answer: 150 kPa
p₁ × V₁ = p₂ × V₂
50 × 6 ÷ 2 = 150 kPa
Question 7 Medium
Explain why the pressure of a gas increases when its volume is reduced at constant temperature.
Show answer
Answer: The particles are closer together, so they hit the walls more often and the pressure increases.
The particles have less space.
They hit the walls more often, so the pressure rises.
Question 8 Medium
State what happens to the average speed of the particles when a gas is cooled.
Show answer
Answer: It decreases.
Cooling lowers the average kinetic energy.
The particles move slower.
Exam-style questions
Longer questions in the style of a written paper, with the marking points. These are Yumio practice questions.
Exam-style question 14 marks
A syringe contains 60 cm³ of air at a pressure of 100 kPa. The end is sealed and the plunger is pushed in until the volume is 40 cm³. The temperature stays constant.
(a) Work out the new pressure. [2 marks]
(b) Explain, in terms of particles, why the pressure increases. [2 marks]
Show answer and marking points
Answer: (a) 150 kPa (b) The same particles are in a smaller volume, so they hit the walls more often.
(a) p₁V₁ = p₂V₂, 100 × 60 ÷ 40 (1)
(a) 150 kPa (1)
(b) the same particles are in a smaller volume (1)
(b) they hit the walls more often (1)
Exam-style question 24 marks
A sealed container of gas is heated. The volume cannot change.
(a) Explain, in terms of particles, why the pressure of the gas increases. [3 marks]
(b) A bicycle pump gets warm when the air is compressed quickly. Give the reason. [1 mark]
Show answer and marking points
Answer: (a) The particles move faster, so they hit the walls harder and more often, so the pressure increases. (b) Work is done on the air, increasing its internal energy.
(a) the particles move faster (1)
(a) they hit the walls harder (1)
(a) and more often (1)
(b) work is done on the air, so its internal energy rises (1)
Common mistakes
Saying gas pressure is caused by particles sticking to the walls
Pressure is caused by particles colliding with the walls and bouncing back.
Saying heating a sealed gas makes more particles
The number of particles stays the same. They move faster.
Saying the particles get bigger when a gas is heated
The particles do not change size. They gain kinetic energy and move faster.
Adding pressure and volume instead of multiplying
At constant temperature, pressure × volume is constant. Multiply them.
Using p₁ × V₁ = p₂ × V₂ when the temperature changes
The rule only works at constant temperature and for a fixed mass of gas.
Questions students ask
Is Gas pressure and volume on the Foundation or Higher tier?
Gas pressure and volume is on both Foundation and Higher papers for GCSE Combined Science Physics, aimed at around grade 7.
What is a common mistake on Gas pressure and volume?
Saying gas pressure is caused by particles sticking to the walls. Pressure is caused by particles colliding with the walls and bouncing back.
Where are the answers to the Gas pressure and volume questions?
Open Show answer under each question on this page. The questions are Yumio practice questions, not past exam questions.