Free (Joule) expansion: a rigid, thermally insulated box is split by a partition. Gas fills only the left compartment (volume V₁); the right side is vacuum. The container exchanges no heat (Q = 0) and does no work on anything outside it (W = 0, there is nothing to push against) even after the partition is removed.
First law: ΔU = Q − W = 0 − 0 = 0
Ideal gas: U = U(T) only ⇒ ΔU = 0 ⇒ ΔT = 0
Entropy: ΔS = N k_B ln(V₂ / V₁) (V₂ = full box volume)
Because internal energy of an ideal gas depends only on temperature, zero net work and zero heat exchange force the temperature to end up exactly where it started — the live "mean speed" readout stays flat through the whole expansion, confirming ΔT = 0 directly from the particle speeds rather than assuming it.
Yet the process is irreversible: nothing forces the gas to spontaneously crowd back into the left half. The occupied-volume readout tracks the measured spread of molecules along the long axis of the box; entropy is estimated live from that spread with ΔS(t) = N kB ln(V(t)/V₁), converging to the textbook result once the gas is uniformly spread through the full volume V₂.
- Molecule count — more particles fill the vacuum more smoothly and make the volume/pressure readouts less noisy.
- Initial fill fraction — sets V₁ as a fraction of the total box (also sets the theoretical ΔS via ln(V₂/V₁)).
- Initial speed — scales starting molecular speed; only changes how fast equilibrium is reached, never the final entropy.
- Remove partition — deletes the wall; molecules that reach the open boundary are now free to cross into the vacuum side.
This experiment (Joule, 1845; refined by Joule–Thomson later for real gases) is the classical proof that an ideal gas's energy is a function of temperature alone — a real gas, by contrast, shows a small temperature change here because intermolecular attraction does internal work as the molecules separate.