Explain, using the kinetic model of an ideal gas, why a fixed mass of ideal gas occupies a greater volume at constant pressure when its temperature is increased.

IB DP Physics Higher Level (2023 syllabus) — B.3 Gas laws · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (4 marks)

Increasing the temperature raises the average kinetic energy of the gas molecules, so they move faster.

Because the molecules are faster, each collision with the vessel walls exerts a larger force (or impulse) on the walls.

If the volume were unchanged, the increased force per collision would raise the pressure. To keep the pressure constant, the volume must therefore increase.

When the volume expands, the average distance between molecules grows, so collisions with the walls become less frequent. This reduction in collision frequency balances the higher force per collision, restoring the pressure to its original value.

Examiner tips

  • Use the kinetic theory terms: average kinetic energy, force per collision, collision frequency.
  • Show the logical chain: higher T → faster molecules → higher force → pressure would rise → volume must increase to keep P constant.
  • Mention that increased volume reduces collision frequency, which compensates for the higher force.

Common mistakes

  • Failing to link increased kinetic energy to increased force on the walls.
  • Not explaining how volume change restores the pressure.
  • Using vague language such as "more molecules" instead of "faster molecules".

Mark scheme (4 marks)

  1. Increasing temperature means the molecules have greater average kinetic energy / move faster on average.
  2. Faster-moving molecules strike the walls with greater force / impulse, so the pressure would tend to increase if the volume were unchanged.
  3. At constant pressure the volume must increase so that the force per unit area on the walls remains unchanged / to restore pressure to its original value.
  4. As volume increases, molecules travel farther between collisions / average separation increases, so collisions with the walls become less frequent, reducing pressure back to its original value.

Key terms in this question

kinetic model · ideal gas · pressure

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