A gas has a volume of 0.50 m3 at a pressure of 200 kPa. It expands at constant temperature to a volume of 2.0 m3. What is the new pressure?
- Use p1 × V1 = p2 × V2: 200 × 0.50 = p2 × 2.0.
- 200 × 0.50 = 100.
- p2 = 100 ÷ 2.0 = 50 kPa.
Answer: 50 kPa
Particle model and pressure in gases
Physics · Particle model of matter. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
The molecules of a gas move all the time, in random directions and at a range of speeds. The temperature of the gas is related to the average kinetic energy of its molecules. A hotter gas has faster molecules.
Gas pressure is caused by molecules hitting the walls of the container. Each collision pushes on the wall. If a gas is heated at constant volume, the molecules hit the walls more often and harder, so the pressure rises.
If the volume is increased at constant temperature, the molecules are more spread out. They hit each unit area of the walls less often, so the pressure falls. Doing work on a gas, by compressing it quickly, raises its internal energy and its temperature.
Rules to remember
- Higher temperature means higher average kinetic energy and higher average speed of the molecules
- Constant volume: raising the temperature raises the pressure
- Fixed mass at constant temperature: pressure × volume = constant (pV = constant)
- So p1 × V1 = p2 × V2; pressure in Pa, volume in m3 (or the same units on both sides)
- Halving the volume doubles the pressure; doubling the volume halves the pressure
- Work done on a gas increases its internal energy, which can raise its temperature (a bicycle pump gets warm)
Common mistake
Students treat pressure and volume as directly proportional, so they multiply the pressure by the same factor as the volume. At constant temperature they are inversely proportional: a bigger volume gives a smaller pressure.
Worked example
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