Advanced #58

The specific heat capacity Cp has a minimum at 36 degrees Celsius

The heat capacity at constant pressure passes through a minimum near body temperature.

Scientific Explanation

Although water’s specific heat capacity Cp is unusually high overall, it is not constant. Between 0 and 100 degrees Celsius, Cp passes through a minimum at approximately 36 degrees Celsius — remarkably close to human body temperature. At 0 degrees, Cp is 4.22 joules per gram per kelvin, drops to 4.178 at 36 degrees, and then rises again.

This minimum arises from the interplay of two contributions to heat capacity. At low temperatures, the hydrogen-bond network is largely intact and a significant fraction of added heat goes into breaking bonds — raising Cp. As temperature increases, more bonds break and fewer remain to be disrupted — Cp falls. Above 36 degrees, increasing thermal expansion begins to contribute a new term to heat capacity, and Cp rises once more.

The minimum is the point at which the declining bond contribution and the growing expansion contribution are exactly in balance.

Cp of Water vs Temperature Showing Minimum at 36 degrees Celsius Line chart showing the specific heat capacity Cp of water versus temperature. The curve decreases from 0 degrees Celsius, passes through a minimum at approximately 36 degrees Celsius, and then increases again at higher temperatures. Temperature (°C) Cp (J g⁻¹ K⁻¹) 0 20 36 60 100 4.18 4.22 Minimum at 36 °C Specific Heat Capacity Cp vs Temperature
Cp of water with a minimum at 36 degrees Celsius — close to human body temperature.

Everyday Relevance

The proximity of this minimum to body temperature may not be coincidental. Near the Cp minimum, water’s temperature responds most sensitively to heat input or removal, because less energy is buffered by the bond network. A body operating at 37 degrees Celsius benefits: small changes in heat production lead to measurable temperature shifts that the thermoregulation system can detect and correct.