Illustrated Physics
physics, drawn
Concept

Free expansion — where it appears

A gas expanding into a vacuum with nothing to push against and no heat entering, so that its internal energy is unchanged. An ideal gas therefore keeps its temperature; a real one cools slightly, and the effect is small enough that Joule's attempt to measure it found nothing and had to be replaced by the throttling experiment.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The entropy of mixing, and the entropy of not mixing. The entropy gained when two ideal gases at the same temperature and pressure are allowed to mix, per particle and in units of Boltzmann's constant, against the proportion of the mixture that is the first gas. The curve has no property of either gas in it — not their masses, not their sizes, not how strongly they interact, since ideal gases do not — and it is largest at 0.500, where it reaches ln 2 = 0.6931. Below it is the same quantity for two samples of the SAME gas, which is zero at every proportion: removing the partition between two halves of a box of nitrogen changes nothing that can be measured, and putting it back recovers the original state. The two results are correct and they do not join up. Make the two gases more and more alike — two isotopes, then two nuclear spin states, then nothing at all — and the upper curve does not descend to meet the lower one; it stays exactly where it is until the two species become identical, and then jumps. What the figure is really about is that the jump is in the counting and not in the gas.

Mixing what is already mixed

Let two different gases into each other's halves of a box and the entropy rises by a fixed amount that contains nothing about either gas. Do it with the same gas on both sides and it rises by nothing. Make the gases more and more alike and the answer does not converge — it jumps.

thermodynamics · Entropy Throttling a gas, and the curve that says which way it goes. Curves of constant enthalpy for a van der Waals gas, in temperature and pressure both measured against the critical values. A gas pushed slowly through a plug or a valve keeps its enthalpy, so it moves along one of these curves — from right to left, since the pressure falls. Where a curve slopes upward to the right the gas cools as it expands; where it slopes downward it warms. An ideal gas would give horizontal lines and no change at all, because its enthalpy depends on the temperature alone; every curve here is bent, and the bending is the attraction between molecules and the room they take up, fighting. The dashed line through the tops of the curves is the inversion curve, and the maxima were found on the drawn points rather than put there — they lie on the closed form to 0.65 per cent. Which side of it a gas starts on decides the sign of the effect, and that is the whole of why air can be liquefied by throttling at room temperature and hydrogen cannot: hydrogen has to be pre-cooled below its own inversion temperature first, which is why Dewar needed liquid air before he could get liquid hydrogen, and why Onnes needed liquid hydrogen before he could get helium.

The gas that cools by being let go

Push a gas through a plug and its temperature changes, although no work is done on anything and no heat goes anywhere. Which way it changes depends on where it starts: inside a dome in the pressure–temperature plane it cools, outside it warms, and hydrogen at room temperature is outside — which is why liquid hydrogen needed liquid air first.

thermodynamics · Phase change

Named alongside it

The objects these essays reach for when they reach for this one.

EnthalpyEntropyEntropy of mixingEquation of stateExtensivityGibbs paradoxIndistinguishabilityIntermolecular forcesInversion temperatureIrreversibilityJoule thomsonLiquefaction

All concepts