Illustrated Physics
physics, drawn
Concept

Phase change — where it appears

The passage of a substance between solid, liquid and gas, at a temperature and pressure where two phases can coexist. A first-order change absorbs a latent heat while the thermometer stands still; a continuous one absorbs none, and the two are separated by a critical point.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

A siphon's pressure, and the 10.09 m it cannot pass. The absolute pressure of the liquid along a siphon, from the upper surface, over the crown, and down to an outlet 1.2 m below the surface, for 4 crown heights. The profile is hydrostatic and depends on nothing but height: the tube's shape, its length and its bore do not appear. At the crown the liquid is below atmospheric pressure by ρg times the lift, and the whole question of how high a siphon can reach is whether that number stays above the liquid's vapour pressure — 2.34 kPa for water at 20 °C, which puts the ceiling at 10.09 m. a 2 m crown sits at 81.7 kPa and holds, a 6 m crown sits at 42.5 kPa and holds, a 9.5 m crown sits at 8.1 kPa and holds, a 11.5 m crown sits at -11.5 kPa and is below the vapour pressure, so it boils. The ceiling is a property of the liquid, not of the mechanism: a degassed liquid that can be pulled into tension has no such limit, and siphons in a vacuum.

The height a siphon cannot pass

A siphon will not lift water more than about ten metres, and the usual explanation for the limit is also given as the explanation for the mechanism. It cannot be both. A siphon runs in a vacuum, with degassed water, over a crown no atmosphere could support.

fluids · Hydrostatics Two straight lines that are not the same line. Half the difference between the liquid and vapour densities, in units of the critical density, against the distance from the critical temperature — both logarithmic, over 5 decades. The van der Waals curve is solved for the coexisting pair at each temperature and its slope in the last decade is 0.500, which is the mean-field ½. Real fluids give 0.326. The two differ by 11 per cent at t = 0.1 and by a factor of 7.9 at the bottom of the axis, which is why an equation with the wrong exponent in it looked right for eighty years.

The point at which the two become one

Heat a sealed tube of carbon dioxide and the meniscus inside it does not boil away — it fades, the two densities converging until there is nothing to separate. Twenty millikelvin before that happens the fluid turns milky, and the exponent describing the last approach is a number van der Waals got wrong and could not have got right.

thermodynamics · Phase change Melting curves, and the one that leans the wrong way. Melting temperature against pressure for water, benzene, naphthalene, each measured from its own melting point at one atmosphere, with pressure in bars. The slope of every coexistence line is the latent heat divided by the temperature and the change in volume, and the latent heat of melting is positive for everything — so the sign of the slope is the sign of the volume change, and nothing else. Almost everything expands on melting and its line leans forwards. Water's solid is less dense than its liquid, so its line leans backwards at 135 bars a kelvin: pressing on ice at just below zero melts it, and it takes 135 atmospheres to gain a single degree. The anomaly is not in the thermodynamics; it is in the fact that ice floats.

The melting curve that leans the wrong way

The slope of any coexistence line is the latent heat divided by the temperature and the change in volume. Latent heat is always positive, so the sign of the slope is the sign of the volume change — and for water the volume change is negative, which is the whole of why ice floats and why the melting curve leans backwards.

thermodynamics · Phase change

Named alongside it

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

Surface tensionPressureAtmospheric pressureBoundary conditionsCapillarityCavitationCompressibilityCorrelation lengthCritical exponentCritical pointDensityEquation of state

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