14.12–14.15Particle motion in gases
The molecules of a gas are in constant random motion. The temperature of the gas is related to the average kinetic energy of the molecules.
Changing the temperature of a gas, held at constant volume, changes the pressure exerted by the gas.
You should be able to explain how the motion of the molecules in a gas is related to both its temperature and its pressure, and to explain qualitatively the relation between the temperature of a gas and its pressure at constant volume.
Pressure in terms of the particles: the molecules are in constant random motion, so they collide with the walls of the container. Each collision exerts a small force on the wall. Pressure is the result of all those collisions together.
So raising the temperature at constant volume raises the pressure, and the reasoning has two steps that must both be given:
1. Raising the temperature increases the average kinetic energy of the molecules, so they move faster. 2. Faster molecules hit the walls more often, and each collision exerts a greater force — so the total force on the walls, and therefore the pressure, increases.
Worked example
A sealed can of gas is left in the sun. Explain, in terms of the molecules, why the pressure inside rises.
- The can is sealed and rigid, so the volume is constant.
- Energy is transferred to the gas, so its temperature rises.
- Temperature is related to the average kinetic energy of the molecules, so the molecules move faster on average.
- Faster molecules collide with the walls more frequently, and each collision exerts a greater force.
- More frequent and harder collisions mean a greater total force on the walls, so the pressure rises.
Answer: The molecules gain kinetic energy and move faster, so they hit the walls more often and harder — and since the volume is fixed, the pressure rises.
Common mistake
Do not say the molecules "expand" or "get bigger" when heated. The molecules are unchanged; it is their speed, and therefore the frequency and force of their collisions, that changes.
- Absolute zero
- the temperature at which the particles have the least possible kinetic energy, 0 kelvin or −273 °C
- Internal energy
- the total kinetic and potential energy of all the particles in a system
14.16P–14.19PPressure in gases
Physics only — not on the Combined Science specification
A gas can be compressed or expanded by pressure changes. The pressure produces a net force at right angles to the wall of the gas container, or any surface.
"At right angles" matters: the collisions come from all directions, but the net effect on any surface is a force perpendicular to it.
You should be able to use the particle model to explain how increasing the volume in which a gas is contained, at constant temperature, can lead to a decrease in pressure.
The explanation: at constant temperature the molecules keep the same average speed, and there are still the same number of them. But in a larger volume each molecule travels further between collisions with the walls, so it hits the walls less often. Fewer collisions per second on each unit of wall area means a lower pressure.
For a fixed mass of gas held at a constant temperature:
pressure × volume = constant p V = constant
pressure, p, in pascals, Pa; volume, V, in metres cubed, m³. This equation is given on the Physics equation sheet.
You should be able to calculate the change in the pressure of a gas, or the volume of a gas — a fixed mass held at constant temperature — when either the pressure or volume is increased or decreased.
Because the product stays constant, the practical form to use is p₁V₁ = p₂V₂.
Worked example
A gas occupies 0.030 m³ at a pressure of 100 000 Pa. It is compressed at constant temperature to 0.012 m³. Calculate the new pressure.
- The mass and temperature are constant, so p V = constant applies: p₁V₁ = p₂V₂.
- Substitute what you know: 100 000 × 0.030 = p₂ × 0.012.
- Work out the left side: 3000.
- Rearrange: p₂ = 3000 ÷ 0.012.
- Check it is sensible: the volume went down, so the pressure should go up — and it has.
Answer: 250 000 Pa
Common mistake
Check the direction of your answer against common sense. Squeezing a gas into a smaller volume must raise its pressure. If your new pressure is lower than the old one after a compression, the equation has been rearranged the wrong way.
14.20PIncreasing the pressure of a gasHigher tier
Physics only, and Higher tier only — not on the Combined Science specification
Work is the transfer of energy by a force.
Doing work on a gas increases the internal energy of the gas, and can cause an increase in the temperature of the gas.
You should be able to explain how, in a given situation such as a bicycle pump, doing work on an enclosed gas leads to an increase in the temperature of the gas.
Worked example
Explain why the barrel of a bicycle pump becomes warm when a tyre is inflated.
- Pushing the handle applies a force that moves the piston through a distance, so work is done on the gas.
- Work is the transfer of energy by a force, so energy is transferred to the gas.
- That energy increases the internal energy of the gas.
- The increase in internal energy raises the average kinetic energy of the molecules, so the temperature of the gas rises.
- Energy is then transferred from the hot gas to the barrel, which is why the barrel feels warm.
Answer: Work is done on the gas as it is compressed, increasing its internal energy and so its temperature; energy then transfers to the barrel, warming it.
Common mistake
The pump does not warm up mainly because of friction between the piston and the barrel. The examinable explanation is that work is done on the gas, raising its internal energy and its temperature.
- Work
- the transfer of energy by a force; doing work on an enclosed gas increases its internal energy and can raise its temperature
Before you practise
- Gas pressure comes from particles colliding with the walls of the container, and each collision exerts a force at right angles to the surface.
- Raising the temperature raises the average kinetic energy, so the particles move faster and hit harder and more often — the pressure rises.
- Absolute zero is −273 °C, where particle motion is at a minimum.
- Convert Celsius to kelvin by adding 273.
- At constant temperature, pressure × volume is constant: P₁V₁ = P₂V₂.
- Reducing the volume packs the particles closer, so collisions with the walls are more frequent and the pressure rises.
- Doing work on a gas by compressing it quickly raises its internal energy, and so its temperature — which is why a bicycle pump gets warm.