A simple question. In several places, including this very recent and already famous paper
http://www.sciencemag.org/content/348/6236/786.short
it is stated that bodies lose heat in water very fast due to the big heat capacity of water. I don't understand why heat capacity is relevant for the rate of heat loss. Why does it matter is the temperature of the air around me increases faster than that of water? Unless I am using clothes, that hot air is going away due to convection anyway and is being constantly replaced by new, cold air.
My naive explanation of this would be that we lose heat faster in water because we are essentially made of water and, when submerged, heat is transferred simply via conduction. We lose heat fast because the thermal conductivity of water is large.
So, does the heat capacity of a fluid influence significantly the heat loss rate of a body submerged in it?
Best Answer
The heat flow (per unit area) through some thin layer, e.g. a boundary layer of water, is given by:
$$ \frac{dQ}{dt} = \frac{K\Delta T}{d} $$
where $K$ is the thermal conductivity, $d$ is the thickness of the layer and $\Delta T$ is the temperature difference between the two sides of the layer.
So a high thermal conductivity does indeed mean a high heat flow rate. But as your body loses heat, that heat goes into heating up the water. If the water had a low specific heat then it would heat up fast and you'd quickly be surrounded by a layer of water at your body temperature. This layer of water would then act as an insulator.
In the context of the equation above, a low specific heat means $\Delta T$ quickly reduces with time and that reduces the heat flow. Conversely, a high specfic heat means it takes a lot of the heat from your body to heat the water, and that tends to maintain $\Delta T$ at a high value.
So while you are quite correct that high thermal conductivity is a major factor in the heat loss to water, so is the high specific heat of the water.