Spec links: 4.3.3.1 Particle motion in gases; 4.3.3.2 Pressure in gases (Physics only); 4.3.3.3 Increasing the pressure of a gas (Physics only) (HT) · Reading time: about 4 minutes
A warning light on a frosty morning
It is the first cold morning of winter. A driver starts the car and an orange light appears on the dashboard. It is the tyre pressure warning. Nobody has driven over a nail. So why have the tyres gone soft?
Particles on the move
The air inside a tyre is a gas. Its particles are far apart and move quickly in random directions. They keep hitting the inside walls of the tyre. Each collision exerts a small force on the wall. Huge numbers of collisions every second add up to a steady force. The force per unit area is the gas pressure. It acts at right angles to the walls.
The temperature of a gas is related to the average kinetic energy of its particles. The hotter the gas, the faster the particles move.
Cold air, lower pressure
Think about a gas kept at constant volume. If the temperature falls, the particles slow down. They hit the walls less often and with less force. So the pressure goes down.
A tyre is not a perfectly rigid container, but its volume does not change much. On a cold night the air inside cools, and the pressure drops. A fall of about 10 °C lowers the pressure by a few per cent. If a tyre was already a little low, that can be enough to set off the warning light. In summer, or after a long drive, the opposite happens and the pressure rises.
Squeezing a gas
Now think about a gas kept at constant temperature. If you squash it into a smaller volume, the particles have less space. They hit the walls more often, so the pressure rises.
For a fixed mass of gas at constant temperature, pressure × volume stays the same. The equation is p V = constant, where p is pressure in pascals (Pa) and V is volume in m3. This means p1 V1 = p2 V2.
Here is an example. A syringe holds 0.00006 m3 of air at 100 000 Pa. A finger blocks the end and the plunger is pushed in until the volume is 0.00002 m3. The new pressure is p2 = (100 000 × 0.00006) ÷ 0.00002 = 300 000 Pa. The volume became three times smaller, so the pressure became three times bigger.
Why the pump gets hot
Pump up a bicycle tyre quickly and feel the end of the pump. It gets warm. When you push the handle, you exert a force on the gas and move it through a distance. This is work done on the gas. Work done is energy transferred.
The work done increases the internal energy of the gas. The particles speed up, so the temperature of the gas increases. Some of that energy is then transferred to the pump.
So, check your tyres when it turns cold. A few minutes with a pump can put the pressure right, and you will feel the physics in your hands.
Key words
- Gas pressure: the force per unit area exerted by gas particles colliding with the walls of their container; it acts at right angles to the walls.
- Kinetic energy: the energy an object has because it is moving; the temperature of a gas is related to the average kinetic energy of its particles.
- Constant volume: a condition in which the gas cannot expand or contract, so its volume stays the same.
- pV = constant: for a fixed mass of gas at constant temperature, pressure multiplied by volume stays the same.
- Work done: energy transferred when a force moves an object through a distance; doing work on a gas increases its internal energy.
- Internal energy: the total kinetic energy and potential energy of all the particles in a system.
Questions
- What causes the pressure of the gas inside a tyre? [1 mark]
- In which direction does gas pressure act on the walls of a container? [1 mark]
- What is the temperature of a gas related to? [1 mark]
- Explain why the pressure in a car tyre falls on a cold night. Assume the volume stays the same. [3 marks]
- A bicycle pump gets warm when it is used quickly. Explain why. [3 marks]
- A fixed mass of gas has a volume of 0.004 m3 at a pressure of 150 000 Pa. It is compressed at constant temperature to a volume of 0.0015 m3. Calculate the new pressure. Give the unit. [3 marks]
- A weather balloon holds 2.0 m3 of helium at 100 000 Pa. As it rises, the pressure falls to 40 000 Pa. Assume the temperature stays the same. Calculate the new volume of the balloon. Give the unit. [3 marks]
- A student pushes in the plunger of a sealed syringe slowly, then pushes another sealed syringe in very quickly. Explain, using the particle model, what happens to the pressure and temperature of the air in each case. [6 marks]
Show answers
- (Gas) particles colliding with the walls (of the tyre) (1)
- At right angles to the walls (1)
- The average kinetic energy of its particles (1)
- Temperature decreases so the particles move more slowly / have less kinetic energy (1); particles collide with the walls less often (1); and with less force, so the pressure decreases (1)
- Work is done on the gas (by pushing the handle) (1); this increases the internal energy of the gas (1); so the temperature of the gas increases (1)
- p1V1 = p2V2 so p2 = (150 000 × 0.004) ÷ 0.0015 (1); p2 = 600 ÷ 0.0015 (1); p2 = 400 000 Pa (1)
- V2 = (p1 × V1) ÷ p2 = (100 000 × 2.0) ÷ 40 000 (1); V2 = 200 000 ÷ 40 000 (1); V2 = 5.0 m3 (1)
- Indicative content:
- in both cases the volume of the air decreases
- particles collide with the walls more often, so the pressure increases
- slow push: energy has time to be transferred to the surroundings, so the temperature stays about the same
- slow push: pV = constant applies, so pressure increases as volume decreases
- fast push: work is done on the gas
- fast push: the internal energy of the gas increases and particles move faster
- so the temperature rises
- faster particles also hit the walls harder, so the pressure rises even more than for the slow push
- Level 3 (5–6 marks): a detailed, coherent explanation of both cases, linking volume, collision rate, work done, internal energy, temperature and pressure; Level 2 (3–4 marks): explains the pressure increase and some link between work done and temperature, with some gaps; Level 1 (1–2 marks): simple relevant statements, e.g. the pressure increases or the syringe gets warm
More reading: See all 30 GCSE Physics comprehension articles