Advanced #29

There is a maximum in the compressibility-temperature relationship

The isothermal compressibility shows a maximum at low temperatures.

Scientific Explanation

While water’s isothermal compressibility passes through a minimum between 0 and 46.5 degrees Celsius (anomaly 28), it displays a dramatic maximum in the opposite direction — when supercooled far below the freezing point. Near minus 46 degrees Celsius at atmospheric pressure, the compressibility rises steeply, as though the water were suddenly becoming soft.

This maximum is closely linked to the hypothesis of a second critical point. According to this theory, below a certain temperature and pressure, two distinct liquid phases of water exist: a low-density variant (LDL) and a high-density variant (HDL). At the critical point between these phases, density fluctuations diverge — and with them, the compressibility.

Experimental verification is difficult because water crystallizes extremely easily in this range. Nevertheless, both computer simulations and ultrafast experiments on tiny water droplets show that the compressibility does reach a sharp maximum before declining at even lower temperatures.

Compressibility-Temperature Maximum in Water Line chart showing isothermal compressibility of water at different pressures. At low pressures, a sharp maximum appears at supercooled temperatures around minus 46 degrees Celsius. As pressure increases, the maximum broadens and shifts. Temperature (°C) Compressibility κT -60 -30 0 30 Maximum 1 atm High pressure Compressibility Maximum in Supercooled Water
Compressibility maximum in supercooled water. At low pressure the maximum is sharp and prominent.

Everyday Relevance

This maximum is not directly perceptible in daily life, since the relevant temperatures lie far below the freezing point. But it indirectly explains many of the anomalies we observe at everyday temperatures: the density anomaly, the compressibility minimum, and the unusual speed-of-sound behavior. All of these phenomena are aftereffects of the same fundamental structural conflict between the two forms of liquid water.