Changing the temperature of a gas, held at constant volume, changes the…

The idea

Gas pressure arises from particles colliding with the container walls. Each collision exerts a tiny force, and the total force per unit area is the pressure. If the volume is fixed, heating the gas transfers energy to the particles, so their mean kinetic energy and average speed increase. Faster particles hit the walls more often and each impact is harder, so the pressure rises. Cooling has the opposite effect: particles move more slowly, collide less often and less forcefully, so pressure falls. For a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature in kelvin, so doubling the kelvin temperature doubles the pressure. A sealed rigid container, such as an aerosol can left in a hot car, illustrates the effect and explains why such containers carry warnings.

What earns the marks

• Pressure is the force exerted by gas particles per unit area on the container walls.
• At constant volume, raising the temperature increases the average kinetic energy and average speed of the particles.
• Faster particles collide with the walls more frequently and each collision exerts a larger force, so pressure increases.
• Cooling a fixed volume of gas reduces particle speed, collision frequency and impact force, so pressure decreases.
• For a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature measured in kelvin.
• Kelvin temperature is calculated by adding 273 to the Celsius temperature, so 27 °C is about 300 K.

Common mistakes and how to put them right

• Saying that particles expand or get bigger when heated.

  Put it right by stating that the particles themselves do not change size; their average speed and kinetic energy increase.

• Using degrees Celsius in a pressure–temperature calculation.

  Put it right by converting to kelvin first, because the proportionality only holds for absolute temperature.

• Claiming that pressure increases because there are more particles.

  Put it right by explaining that the number of particles is unchanged at constant volume; the increase is due to more frequent and more forceful collisions.

Exam tips

• Link each change in pressure to both collision frequency and the force of each collision, since either alone gives an incomplete explanation.
• Convert temperatures to kelvin before comparing or calculating pressures, and show the conversion clearly.
• Use the particle model consistently: refer to particles, collisions, kinetic energy and wall force rather than saying the gas 'wants more space'.