Equivalent temperature of air to feel as if it was in water

Question

I got interested in why, at the same temperature, water feels cooler than air. After a google search, I saw that this question got answered here: Why does water feel cooler than air. I understand the answer given there.; however, is there a formula which I could use to calculate the temperature at which the air should feel the same temperature as water? For example, at which temperature should the air feel the same temparature as water at 12ºC?

I myself have tried to get this formula working with Newton’s cooling law, but without any results.

Thank you in advance.

temperature thermodynamics

I myself have tried to get this formula working with Newton's cooling law, but without any results.

Thank you in advance.

JMLCarter · Answer

It can't be done to any accuracy really here's why.

You need to have the same heat-flow out of the body into the air (insulator) as into the water (conductor). We need to consider both conductive and convective losses through the medium.

At any given temperature, as air is an insulator, the ratio of conductive to convective loss is very much lower than water.

So if the thermal conductive losses are matched when the air/water is stationary, then if there is movement and convective loss occurs the air will convect much, much more energy than the water.

Conversely if the convective heat transfer is equalised, then the water will conduct much more heat energy and the air will feel warmer if it is stationary.

You can always feel the difference.

Equivalent temperature of air to feel as if it was in water

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