15.3 Kinetic Theory of Gases

2026 📋 Syllabus Objectives

By the end of these notes, you should be able to:

  1. State the basic assumptions of the kinetic theory of gases.
  2. Explain how molecular movement causes the pressure exerted by a gas, and derive and use the relationship pV = ⅓Nm⟨c²⟩.
  3. Understand that the root-mean-square speed c_r.m.s. is given by √⟨c²⟩.
  4. Compare pV = ⅓Nm⟨c²⟩ with pV = NkT to deduce that the average translational kinetic energy of a molecule is ³⁄₂kT, and use this expression.

1. The Basic Assumptions of the Kinetic Theory of Gases

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The kinetic theory of gases is a model — a simplified picture — that scientists use to explain the behaviour of gases at the molecular level. It is built on a set of assumptions. Think of these as the "rules of the model". In a real exam, you may be asked to recall them precisely, so learn each one carefully.

💡 Examiner Tip: Memorise all the assumptions below. Examiners frequently ask you to state them.

Here are the assumptions:

  • All molecules are identical — every molecule of a given gas has the same mass.
  • Molecules are hard, perfectly elastic spheres — "elastic" here means that when they collide (with each other or with a wall), no kinetic energy is lost. They bounce off perfectly.
  • Molecules are in continuous random motion — they move in all directions at all times, constantly and unpredictably changing direction after collisions.
  • There are no forces between molecules — there is no attraction or repulsion between molecules except during actual collisions. Between collisions, they travel in straight lines.
  • External forces (such as gravity) are ignored — we assume gravity has no effect on the molecules.
  • Newton's laws of motion apply — the molecules obey the same laws of motion that govern everyday objects.
  • The volume of the molecules is negligible — the actual size of each molecule is so tiny compared to the volume of the container that we treat molecules as point particles.
  • Collisions with the container walls are perfectly elastic — molecules bounce off walls without losing any kinetic energy.
  • The time of a collision is negligible — the time a molecule spends actually hitting a wall is far, far shorter than the time it spends travelling freely between collisions.
  • There are a very large number of molecules — this means we can meaningfully talk about averages across all of them.

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