Illustrated Physics
physics, drawn
Concept

Superheating — where it appears

The heating of a liquid above its boiling point without boiling, possible because a vapour bubble must first reach a critical size against surface tension. A superheated liquid is metastable and boils explosively once a nucleus forms, which drives geysers and bumping in clean glassware.

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

The part of the curve no fluid follows. Van der Waals' isotherms in reduced units, at 5 temperatures either side of the critical one, so that nothing about any particular substance appears. Above the critical temperature the pressure falls monotonically as the volume grows, which is what a fluid does. Below it the curve develops a loop with a rising section in the middle, and that section says the pressure increases as the substance expands — a material with negative compressibility, which cannot exist, because any fluctuation would run away. What happens instead is drawn as the horizontal line: the substance separates into two phases at one pressure, and the volume moves along the line as the proportions change. Its height, 0.6470 of the critical pressure, is fixed by requiring the two areas the line cuts off to be equal, which is the condition that the two phases have the same Gibbs energy. It meets the curve at volumes 0.603 and 2.349, a ratio of 3.9, and those are the densities of the liquid and its vapour. The two turning points of the loop, at 0.72 and 1.53, bound the part that is not merely unobserved but impossible; between them and the construction the substance can be made to sit, superheated or supercooled, until something nucleates.

The part of the curve no fluid follows

One equation for a real gas produces isotherms with a rising middle section, which says a substance would expand as the pressure on it grows. Nothing does that. What replaces it is a horizontal line whose height is fixed by making two areas equal, and the condition is not a convenience.

thermodynamics · Phase change The boiling point in a column of water, and the depth heating reaches it first. The temperature at which water boils against depth in a geyser's conduit 2240 m above sea level, where the air's pressure is 77.6 kPa (solid): 92.7 °C at the surface, 103.6 °C at 4 m, 115.5 °C at 10 m and 131.8 °C at 22 m — rising steeply near the top and more gently below, because each extra metre adds the same pressure to water whose boiling point responds less as it gets hotter. Dashed: the water as it heats from beneath, cooled to 80 °C at the top by the pool and below that warming by only 0.8 °C per metre, mixed by convection; 6 °C and 3 °C short of the curve at 4 m, and then touching it. It touches at 4 m, not at the bottom: there the water is still 13.7 °C below boiling.

The column that boils from the middle

Water at the bottom of a geyser's tube is hotter than water anywhere else in it, and it is not the water that boils first. The weight of the column raises the boiling point with depth faster than the heat from below raises the temperature, so the column reaches its boiling curve partway down, under a cooler surface layer. A little boiling there lifts the water above. Everything beneath is then at a lower pressure than the one it was heated under, so it is superheated and flashes, and the eruption feeds itself: past about fourteen centimetres of water thrown out, each slug of steam makes more room than it was given.

thermodynamics · Phase change The wait after an eruption, against the eruption. For 400 simulated eruptions of the model geyser: the interval to the next eruption against the duration of the eruption just finished (dots), and the straight line through them, interval = 33.8 min + 10.5 × duration, with a correlation of 0.94. The eruptions fall in two clusters, short ones of about 2.2 minutes followed by waits near an hour and long ones of about 5.0 minutes followed by waits near an hour and a half, and the line runs through both. Its slope is the ratio of the discharge rate to the refill rate, 10.7: each minute of eruption throws out water that takes 10.7 minutes to replace. Plotted against the eruption that follows instead, the same intervals show a correlation of 0.05 — nothing. The interval is set by the past and tells nothing about the future.

The geyser that remembers one eruption

Old Faithful is famous for being predictable, and its predictability has an odd shape. Its eruptions come in two kinds, short and long, and the wait after each is short or long to match — about an hour after a short eruption, about an hour and a half after a long one. So the next eruption can be forecast from the last, to within about ten minutes, and from nothing else. The reason is a bookkeeping of water. An eruption throws out a volume of water that the geyser must take back from below before it can erupt again, and a long eruption throws out more. The geyser carries a memory of exactly one eruption: how much it has to refill.

thermodynamics · Phase change

Named alongside it

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

GeyserLatent heatNucleationBimodal distributionBoilingBoiling pointClausius clapeyronCompressibilityCritical pointEquation of stateEruption forecastingGibbs energy

All concepts