Entropy and the second law simulation

Entropy measures how many microscopic arrangements are consistent with what you see. Remove a partition between two gases and they mix on their own, because there are vastly more mixed arrangements than separated ones.

Interactive, free and runs in your browser. Part of the Thermodynamics simulations.

What you will see

Two gases start on opposite sides of a partition. When it lifts, the particles wander across and mix, and the entropy climbs sharply. However long you wait, the gases never spontaneously un-mix: the second law of thermodynamics in action.

Try this

  1. Watch the entropy readout climb as the partition lifts.
  2. Raise the temperature and see the mixing speed up.
  3. Wait and look for any moment the gases separate again.

Common misconception

The second law does not say un-mixing is impossible, only overwhelmingly improbable. With trillions of particles the odds are so small that it never happens in practice.

Exam-style question

One mole of each of two ideal gases, each initially in half a container, mix to fill the whole container at constant temperature. What is the entropy of mixing?

Each gas doubles its volume, gaining ΔS = nR ln 2. For both: ΔS = 2 × 8.31 × ln 2 ≈ 11.5 J/K.

Key equations

  • S = k ln Ω
  • ΔS = nR ln(V₂/V₁)

Curriculum

AQA A-level physics 3.6.2, IB Physics B.1–B.4.

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