Artificial Wasteland · everyday physics, checked

The Densest Water Isn't the Coldest

Ice floats — every child knows it, and almost nobody is told the whole reason. Water is at its heaviest not at the freezing point but at 3.98 °C, and in the last four degrees before it freezes it does the opposite of nearly every other liquid: it expands. That backwards stretch is why the solid floats, and why a lake freezes from the top down instead of the bottom up. Drag the slider and feel it.

Cool almost any liquid and it shrinks: the molecules slow down and pack tighter, so it gets denser, all the way to the point where it freezes — and the solid, tighter still, sinks in its own melt. Drop a cube of solid argon into liquid argon and it goes straight to the bottom. Water refuses. Its solid floats, and the liquid itself has a hidden reversal on the way down. Here is the real curve.

1 · The curve that turns around

This is the measured density of pure water against temperature, computed live from the standard equation of state.¹ Drag the slider. Notice what happens as you cross 4 °C going down: the dot stops climbing and starts to fall. The coldest water, just above the ice, is lighter than the water a few degrees warmer.

The turnaround is small — from 4 °C down to 0 °C the density drops by only about 0.013% — but it is enough to change the world. It means the coldest water always wants to be on top.

2 · Why ice rides where it rides

When water finally freezes, the open crystal locks in even more empty space, and the solid ends up about 8% lighter than the liquid it came from — so it floats, with most of its bulk hidden. How much shows above the surface depends on what it is floating in. Denser water holds the berg higher. Slide from a mountain lake to the open sea to the Dead Sea.

In fresh water an ice cube sits with about 8.3% above the surface; in seawater a berg shows about 10.6% — the origin of "nine-tenths of an iceberg is underwater." The saltier and denser the water, the more of the ice you get to see.

3 · Why the lake freezes from the top

Now put the two facts together and a pond in winter becomes a small miracle. Because water is densest at 4 °C, the warmest-of-the-cold water sinks and pools at the bottom; the truly cold water floats up and freezes into a lid; and the lid, being ice, floats too and insulates everything beneath it. The fish overwinter in 4 °C liquid under the ice. Toggle to a make-believe "normal" liquid — one that just keeps getting denser to the freezing point — and see what would happen instead.

With real water, ice can never reach the bottom of a deep enough lake: the 4 °C floor stays liquid all winter. Were water "normal," the coldest, densest water would sink and freeze from the floor up, and a hard winter could turn the whole lake to a solid block — lethal to almost everything living in it. The anomaly in the last four degrees is, quite literally, a life-support system.

Where the strangeness comes from

Behind all three panels is one culprit: the hydrogen bond. Each water molecule can grip four neighbours — two through its own hydrogens, two through the lone pairs on its oxygen — and when it does, it holds them at arm's length in an open, four-cornered (tetrahedral) cage. Ice Ih is that cage made permanent: a wide hexagonal lattice with room to spare, which is exactly why the solid is so light and floats.

In the liquid, two effects fight. Ordinary thermal contraction wants to pull molecules closer as it cools. But cooling also lets more of those open, ice-like cages form, and cages take up room. Well above 4 °C, contraction wins and water behaves normally. Below 4 °C the cage-building wins, and the liquid expands as it chills toward freezing. The density maximum at 3.98 °C is simply the temperature where the two effects exactly cancel.