Particle Motion, Gas Pressure and Temperature
The molecules of a gas are in constant random motion, and the temperature of a gas is related to the average kinetic energy of those molecules, so raising the temperature raises their average speed. Gas pressure is caused by molecules colliding with the walls of the container, and heating a gas in a sealed rigid container, or reducing its volume at constant temperature, increases that pressure, since for a fixed mass of gas at constant temperature pressure x volume is constant.
Before you start
Make sure you're comfortable with these topics first:
Method
- Always explain pressure through collisions: molecules collide with the container walls, each collision exerts a force, and pressure is force per unit area. Any explanation that does not mention collisions will not gain the marks.
- For a temperature change at constant volume, use a three-step chain: higher temperature means greater average kinetic energy, so molecules move faster, so they collide with the walls more often and with greater force, so the pressure increases.
- For a volume change at constant temperature, use a different chain: a smaller volume means the molecules travel less distance between collisions with the walls, so they collide more frequently with a smaller total wall area, so the pressure increases. The average speed does not change, because the temperature has not changed.
- Use pressure x volume = constant for a fixed mass of gas at constant temperature, in the form p1 x V1 = p2 x V2, keeping the units consistent on both sides rather than converting to SI units.
- Remember that this relationship only holds at constant temperature, and say so when a question mentions a rapid compression, where the gas also warms up.
- For work done on a gas, link the mechanics to the particles: the force applied moves the piston, doing work and transferring energy to the internal energy store of the gas, which increases the temperature, as felt in the warm barrel of a bicycle pump.
Worked example
A sealed syringe contains 0.50 cubic metres of gas at a pressure of 100 kPa. The plunger is pushed in slowly until the volume is 0.20 cubic metres, with no change in temperature. Calculate the new pressure.
- Identify the condition: the temperature is constant and the mass of gas is fixed, so pressure x volume is constant.
- Write the relationship: p1 x V1 = p2 x V2.
- Substitute the known values: 100 x 0.50 = p2 x 0.20.
- Evaluate the left-hand side: 100 x 0.50 = 50.
- Rearrange and calculate: p2 = 50 / 0.20 = 250 kPa.
- Sense check and explain: the volume has been reduced to two fifths, so the pressure rises by a factor of two and a half, because the same molecules now hit the walls more frequently. Note that the compression must be slow, or the gas would also warm and the pressure would be higher still.
Practice questions
Try each question, then tap to reveal the answer.
Q1What causes the pressure of a gas on the walls of its container?Show answer
Answer: Collisions of the gas molecules with the walls; each collision exerts a force, and pressure is the total force per unit area.
Q2How is the temperature of a gas related to the motion of its molecules?Show answer
Answer: Temperature is related to the average kinetic energy of the molecules, so a higher temperature means a higher average speed.
Q3A gas is heated in a sealed rigid container. Explain what happens to the pressure.Show answer
Answer: It increases: the molecules move faster, so they collide with the walls more often and with greater force.
Q4State the relationship between pressure and volume for a fixed mass of gas at constant temperature.Show answer
Answer: Pressure x volume is constant, so p1V1 = p2V2.
Q5A gas at 200 kPa occupies 3.0 cubic metres. It is compressed to 1.5 cubic metres at constant temperature. Calculate the new pressure.Show answer
Answer: 200 x 3.0 = 600, so p2 = 600 / 1.5 = 400 kPa.
Q6Why does a bicycle pump get warm when used?Show answer
Answer: Work is done on the gas as it is compressed, transferring energy to its internal energy store, which raises its temperature; the pump barrel then warms by conduction.
Q7Why does reducing the volume of a gas increase the pressure even though the molecules do not speed up?Show answer
Answer: The molecules travel a shorter distance between collisions with the walls, so collisions happen more frequently over a smaller area, even though each collision transfers the same force on average.
Exam-style questions
Written in the style of a GCSE Science exam paper, with a full mark scheme.
Explain, in terms of particles, why the pressure inside a car tyre increases after the car has been driven for a long distance.
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A balloon of volume 2.4 cubic decimetres at a pressure of 101 kPa is taken underwater, where the pressure is 303 kPa. Assuming the temperature does not change, calculate the new volume and state one assumption you have made.
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Free printable worksheet
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This topic is chapter 21 of GCSE Physics Workbook, the whole course as one free printable PDF.
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