Sweating to cool down

Question

I want to understand in depth how sweating cools down the body. When we sweat the body is cooled down by evaporative cooling; however, there seems to be a few different scenarios/mechanisms that are possible:

Scenario (1)

The ambient air temperature is hotter than the bodies core temperature. A layer of sweat forms on the surface of the skin. This acts an insulating layer so that the surrounding air heats up the sweat, and this "layer" is then evaporated and replaced.

In this case the sweat is not really "cooling" the body, but it is just preventing it from heating up. A more direct example of sweating actually lowering the core body temperature is the next example.

Scenario (2)

The ambient air temperature is colder than the bodies core temperature. The bodies core temperature, however, is higher than desired (because of exercise, for example). If there were no sweat, cooling would still happen, but sweat can help to increase the rate of cooling. Hot water in the body is transferred to the surface of the skin where it evaporates.

(Given that the bodies core temperature is typically higher than the temperature at the surface, cooling can be made even more efficient by dilating blood vessels near the surface of the skin so that heat from the bodies core is transferred closer to the surface.)

Because water has a higher thermal conductivity than air, and because water evaporates away from the skin as opposed to air which remains in an insulating bubble near the skin, there is another mechanism at play here. This leads us to consider the next scenario:

Scenario (3)

Somebody gets into a swimming pool at $80^{\circ}$F when the temperature outside is $70^{\circ}$F. Immediately upon exiting the swimming pool the person feels much colder than before. Energy from the surface of the skin transfers more rapidly to the $80^{\circ}$F water than the $70^{\circ}$F air.

Scenario (3) suggests another potential mechanism which could be at play in scenarios (1) and (2). If the body were able to get sweat on the surface of the skin and have this sweat be colder than the skin, then the skin could dump heat into the sweat. It is not clear to me though if this is possible. Where would the water which is colder than the surface of the skin come from?

My main question though comes from the observation than in none of these examples can sweating/evaporative cooling ever be used to cool the body to a temperature that is lower than the ambient air. In other words, is it possible for the body to use evaporative cooling like a refrigerator? Can the body dump heat into ambient air which is hotter than the bodies core temperature? For example, suppose you were exercising in $101^{\circ}$F weather, and your bodies core temperature had risen to $100^{\circ}$F. Can sweating help get you down to the usual $98.6^{\circ}$F?

Answer 1

The reason sweating works to cool the body is that it absorbs a ton of energy when it evaporates, called latent heat. This heat is so much more than the energy required to change the temperature of the liquid sweat by a few degrees (about two orders of magnitude for a change of about 5 degrees) that for all practical purposes the heat that goes into warming or cooling the sweat can be neglected entirely.

Sweating can absolutely lower your temperature to below ambient--as long as the latent heat is larger in magnitude than the heat generated internally and the heat transferred to the body by conduction from the warmer air, (and the radiant heat you're absorbing if you're, say, in the sunshine) temperature will go down. The evaporation rate of the sweat depends on the humidity, which is why it feels so much hotter when it's humid: sweat doesn't do any good if it doesn't evaporate.

One way of understanding the origin of latent heat is to imagine the molecules in a drop of water (or sweat). They are jiggling around, some faster, some slower, and the average jiggling speed is related to the temperature. All the time, there are molecules at the surface of the drop that break free and drift away into the air, and similarly water molecules in the air that settle onto the surface and become part of the drop. As long as more are breaking free than landing (which is what happens when the relative humidity of the surrounding air is less than 100%) evaporation is taking place. The reason this evaporation causes cooling is that not all molecules at the surface are equally likely to escape--faster moving molecules are much more likely to fly away than slower ones. As faster molecules leave, the average speed of the ones left behind is slower: that means the temperature is less.

Answer 2

My main question though comes from the observation than in none of these examples can sweating/evaporative cooling ever be used to cool the body to a temperature that is lower than the ambient air.

The aspect being missed here is that Nature acts to minimize free-energy gradients, and these incorporate gradients in both temperature and concentration—here, the water concentration at and around our skin.

When evaporation isn't present, the simplest result is that bodies tend to equilibrate to the same temperature, agreed? The predominant gradient is simply the temperature gradient, which tends to even out.

The situation is more complicated when mass transfer is possible. When the humidity is less than 100%, water spontaneously evaporates to equilibrate its chemical potential. This forces heat transfer as mediated by the latent heat of evaporation; the spontaneous evaporation essentially sucks heat from the regions adjacent to the evaporating water. In this way, a wet object (including our skin) tends to cool below the ambient temperature. (In fact, this is the only way we can survive when the surrounding temperature exceeds our skin temperature; a heat transfer balance alone would tend to raise our core temperature, so copious sweating is required to dump our metabolic output via latent heat.)

Answer 3

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I don't have much time to answer this PHD question. So I'll just leave some thought experiments:

1. Boiling a pot of water on a stove stays at 212F even when the burner on the stove is red hot. It cools the pot sitting on the burner to almost 212F. The steam coming off the top is at 212F but mixes and cools to room temperature.

2. Put that all metal pot in a 500F oven, it still stays at 212F. The boiling water cools the pot, the steam, and the air around it, to 212F.

3. A wet bulb thermometer reads colder than a dry bulb thermometer by a few degrees, unless relative humidity is 100%.

4. A bucket of water in a room would be subject to evaporative cooling and room temperature heating. It is difficult to determine it's temperature, but would be colder than the room. Assuming a constant humidity and temperature air exchange.

5. A shallow/low, wide, and long, tray sitting on foam, would have little room air heating, and lots of evaporative cooling. It would be closer to the wet bulb temperature.

This reduces the opening question to why does evaporation cool water colder than the boiling temperature at sea level?

The answer becomes 'partial pressure'. Water boils at a lower temperature when at a lower pressure. Dry air has a lower partial pressure than humid air. So the temperature of evaporation is lower than the dry air temperature.

Why are there no steam bubbles in water that is evaporating? Because, for steam bubbles to form the temperature of the steam must be high enough to have a high enough pressure to form bubbles at the total atmospheric pressure. That is at 212F sea level. So evaporation becomes only a surface phenomenon, no bubbles.

As in all boiling, evaporation cools the liquid water, and the air around it. Cooling it to the boiling/evaporation point, which happens to be lower than ambient at low humidity.

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