Illustrated Physics
physics, drawn
Concept

Triple point — where it appears

The single pressure and temperature at which three phases of a substance coexist in equilibrium. Water's liquid meets its ices at four of them, and its ordinary triple point, 273.16 K, is where ice Ih, water and vapour meet.

Named by 3 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 line of water, through five ices. The pressure at which water freezes, in megapascals on a logarithmic axis, against temperature, along each of the five solid phases that meet the liquid, from the international standard equations. Along ordinary ice, Ih, the melting pressure rises as the temperature falls, from 611 Pa at 273.16 K to 209 MPa at 251.165 K — the backwards slope of the familiar melting line. There the liquid meets ice III, and from then on every ice melts at a higher pressure as the temperature rises: ice V, ice VI, and ice VII, which reaches 20.6 GPa at 715 K. The dots are the four triple points where two ices and the liquid coexist. The lowest temperature at which liquid water can exist in equilibrium, 251.165 K, is at the first of them.

The melting line that turns round

Squeeze water and it freezes at a lower temperature — the backwards slope of its melting line, and the reason ice floats. Keep squeezing and the slope reverses. Past two thousand atmospheres ordinary ice gives way to a denser ice, then another, and from there on every ice melts at a higher temperature under more pressure, exactly as a normal substance's does. At twenty thousand atmospheres water freezes into an ice that is still solid at a hundred degrees Celsius; at two hundred thousand, one still solid at four hundred. The famous anomaly belongs to one ice out of five, and the same relation that explained it explains its end.

thermodynamics · Phase change How a sphere of gas rings. The acoustic pressure against distance from the centre of a spherical cavity, for its three lowest radial modes, in which the gas breathes in and out in spherical shells: sin(zr/a)/(zr/a), with z = 4.4934, 7.7253, 10.9041 the roots of tan z = z that make the gas's motion vanish at the wall. Filled with argon at the triple point of water, 273.16 K, a sphere 62 mm in radius rings in these modes at 3551, 6104, 8616 Hz. Radial modes are the ones precision work uses: they have no motion along the wall, so the wall's roughness and the gas's viscosity there barely touch them, and their frequencies are set by the volume rather than the shape — a slightly imperfect sphere shifts them only at second order.

The note that fixed the kelvin

A sphere of argon, struck, rings at a pitch set by the speed of sound in it, and the speed of sound in argon contains only one quantity nobody could compute: the constant that converts a temperature into an energy. Argon's atoms can hold energy in exactly three ways, so its heat capacity is a count rather than a measurement, and its speed of sound is (5/3)kT/m with nothing left over. Ring the sphere at the temperature of melting ice, measure its size with radio waves in the same cavity, and Boltzmann's constant comes out to a part in a million. In 2019 that number stopped being measured and became the definition.

thermodynamics · Equipartition

Named alongside it

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

Clausius clapeyronPhase diagramAdiabatic indexBoltzmann constantChemical potentialCoexistenceComponentDegrees of freedomDensityEquilibriumEquipartitionFixed point

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