The specific heat capacity Cp has a minimum with respect to pressure

Scientific Explanation

When pressure on liquid water is increased at constant temperature, the specific heat capacity Cp exhibits anomalous behavior: instead of decreasing or increasing monotonically, Cp passes through a minimum at intermediate pressures before rising again at very high pressures. In a typical liquid, one would expect a smooth, modest decrease.

The minimum arises from the pressure-dependent restructuring of the hydrogen-bond network. At low pressure, an open, tetrahedral local ordering with significant void space exists. Moderate pressure compresses this structure and reduces the fluctuations that contribute to heat capacity — Cp drops. At still higher pressures, the water is so strongly compressed that new energetic degrees of freedom appear (such as hydrogen-bond distortions and changes in coordination number), which can absorb additional heat — Cp rises.

This pressure-dependent minimum is the counterpart of the temperature-dependent minimum at 36 degrees Celsius (anomaly 58) — both reflect the same structural conflict, just in different thermodynamic variables.

Everyday Relevance

In geochemistry and ocean science, pressure effects on water’s heat capacity play a role in modeling deep-sea currents and hydrothermal systems. When hot water rises in vents on the ocean floor under high pressure, its thermal properties change in ways that can only be correctly described by accounting for Cp’s anomalous pressure dependence.