Illustrated Physics
physics, drawn
Concept

Clausius clapeyron — where it appears

The relation giving the slope of a phase boundary in pressure and temperature as the entropy change of the transition divided by its volume change. It explains why boiling points rise with pressure, why ice melts under pressure, and why helium-3 freezes when heated.

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

Three curves that can only meet at a point. Water's phase diagram within a kelvin of its triple point, with each boundary drawn at the slope Clausius and Clapeyron give it from measured latent heats and densities: 44.4 Pa/K for boiling, 50.3 for sublimation, and -135 bar per kelvin for melting — negative, and so steep that it is drawn vertical here, because ice is the less dense phase and pressure therefore melts it. Two things follow that no amount of measurement could adjust. The three slopes are not independent: the sublimation and vaporisation curves differ in slope by 5.92 Pa/K, which is exactly what the fusion latent heat predicts, because going solid → gas directly and solid → liquid → gas must cost the same enthalpy. And the sublimation curve is the steeper of the two, so the two cross rather than touch — which is why the triple point is a crossing and not a tangency, and why ice sublimes below it and melts above it.

Why the triple point is a point

Three phases of one substance coexist at one temperature and one pressure and nowhere else, and the reason is arithmetic rather than chemistry: count the numbers that describe the state, count the conditions equilibrium imposes, and subtract. The same subtraction says four phases of one substance are impossible, and it says so without knowing what the substance is.

thermodynamics · Phase change The melting curve that turns back, then lies flat. The pressure at which liquid and solid helium-3 coexist, against temperature from 0.9 millikelvin to 1 kelvin on a logarithmic axis, from the international provisional low-temperature scale PLTS-2000, which is defined by this curve. Above 315.2 mK the curve behaves like any other: a higher temperature needs a higher pressure to freeze the liquid. Below it the curve turns back — at its minimum, 2.93113 MPa, it takes a higher pressure to freeze colder helium — and it rises to 3.4391 MPa at 1 mK, where it lies almost flat, as the third law requires of every coexistence line. The kinks that mark the liquid becoming superfluid and the solid's spins ordering sit on that flat end, at 2.444, 1.896 and 0.902 mK.

The melting curve that has to arrive flat

The slope of every line on which two phases coexist is their difference in entropy divided by their difference in volume. The third law says that entropy differences vanish at absolute zero, so every such line — melting, boiling, a superconductor's critical field — must reach the bottom of the temperature scale lying flat. Helium-3 reaches it in the strangest way available: below a third of a kelvin its solid is more disordered than its liquid, the melting curve runs backwards, and squeezing the liquid into solid absorbs heat. That backwards curve was the refrigerator in which superfluid helium-3 was found, and it is now the definition of temperature below one kelvin.

thermodynamics · Third law

Named alongside it

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

Chemical potentialCoexistenceComponentDegrees of freedomEntropyEquilibriumFermi liquidFixed pointHelium 3Intensive variableLatent heatMelting

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