Advanced #61

The heat capacity Cv has a maximum

The isochoric heat capacity shows a maximum at a certain temperature.

Scientific Explanation

The isochoric heat capacity Cv measures how much heat a substance can absorb at constant volume. In most liquids, Cv changes only slightly with temperature. Water, however, shows a distinct maximum in the supercooled range — the heat capacity rises as temperature falls, reaches a peak, and then declines.

This maximum is closely related to the Cp maximum (anomaly 59) but has a somewhat different physical meaning. While Cp includes both the energy change upon heating and the contribution from thermal expansion, Cv captures only the pure energy change at fixed volume. The Cv maximum therefore directly reflects entropy fluctuations: near the second critical point, the local ordering pattern fluctuates so strongly that an extraordinary amount of energy is needed to raise the temperature at constant volume.

The fact that both Cp and Cv diverge is a strong theoretical argument for the existence of a genuine thermodynamic singularity — a critical point in supercooled water.

Cv of Water vs Temperature Showing Maximum Line chart showing the isochoric heat capacity Cv of water versus temperature. The curve rises with decreasing temperature, reaching a maximum in the supercooled region, consistent with growing structural fluctuations as water approaches its second critical point. Temperature (°C) Cv (J g⁻¹ K⁻¹) -50 -20 0 50 Cv Maximum Typical Isochoric Heat Capacity Cv of Water
Cv maximum in supercooled water. The divergence points toward a critical point.

Everyday Relevance

The Cv maximum itself lies outside the everyday temperature range. Yet its effects shape water’s behavior at room temperature: the exceptionally high heat capacity that makes water the most effective natural heat buffer is a direct legacy of this deeper thermodynamic anomaly. Without it, the oceans would be less effective climate regulators and biological systems would be less thermally stable.