5 ms·

So you have a supply of water at 50°F - that’s 10°C (an optimistic temperature in many places). And you are using it to try to maintain a body temperature aroun

So you have a supply of water at 50°F - that’s 10°C (an optimistic temperature in many places). And you are using it to try to maintain a body temperature around 37°C. Let’s assume you do so by transferring heat from your body into the water enough to raise its temperature by 25°C - that’s probably overly optimistic given that it will also be warmed by the environment and the rate of transfer will be reduced as the temperature increases, but it’s a working number. The specific heat capacity of water is about 4kJ/kg/°C so a liter of that cold water can absorb 100kJ of energy in the process of warming up. Once it’s warmed up it can’t do any more cooling. Your body, when not working hard, produces about 200W of heat. That’s 200J per second. So that liter of water can absorb your body’s heat output from about 500 seconds of being alive. That’s a little over eight minutes. So that means the cooling needs for one human for one day can be met by about 170 liters of cold, 50°F water. That’s about 44 US Gallons. If, however, that water can evaporate - well, the latent heat capacity of vaporization of water is over 2 thousand kJ per kg. That’s why the wet bulb temperature matters. If water can’t evaporate, that cold water can’t absorb body heat except by just warming up.

saalweachter 3y ago
> Your body, when not working hard, produces about 200W of heat. That’s 200J per second. Minor quibble, 2000 (kilo)calories / 1 day = ~100 Watts.
- jameshart 3y ago
  Fair - I took a number for an active, awake human. You don’t produce that wattage all the time; resting and sleeping have much lower heat output; average power over a day is probably more like 100W (hence that being a reasonable average ‘healthy calorie intake’ number which I assume is where your 2000kCal comes from.)
  - darkerside 3y ago
    Focused resting probably reduces it even further. You're not just "not working hard" in a situation like this, you are barely moving and probably slowing down your metabolism if anything.
Kon-Peki 3y ago
The Great Lakes region of the US and Canada is a truly special place when it comes to fresh water. The experiences in this area can't be extrapolated to elsewhere. You can get hypothermia in the middle of a summer heatwave if you spend too much time in the water more than 1km from the shore. Even if you stay at your local beach, most people would find the water uncomfortably cold. In Chicago today, the high temperature is going to be around 18° or 19° C. The surface temperature of the water at the beach is slightly less than 4° C.
jijijijij 3y ago
Thank you for doing the math! At least in my area in central Europe, 10°C would be wildly optimistic in summer. I also presume when submerged in cold water, your body will start heating up, at first. So there is probably only a narrow temperature window for effective cooling. Not to mention, you may have to work and be awake to exchange the water, and being constantly wet for a prolonged time may come with it's own set of health problems. I imagine there could be a situation with a deadly wet-bulb temperature, but below body temperature, where a large body of water may work to cool the body by convection, no?
- jameshart 3y ago
  A large body of cool water works great at moving heat way from you, obviously - an ‘acre foot’ of water is 1.2 million liters - 300,000 gallons. So a fairly small one acre lake that’s ten feet deep has 12 million kg of water, which can absorb 48GJ of heat before it rises in temperature by a single degree. The big question though is how long will that lake remain cooler than the air in the face of wet bulb temperatures around body temperature. Thermal equilibrium will win in the end.
  - jijijijij 3y ago
    Yeah, but the question rather is, would let's say 32°C water, 5°C temperature gradient, work to cool the body, if completely submerged? When ambient conditions are deadly wet-bulb 32°C, would it still cool the water to its original 32°C? So, my thinking would be, if the heat transfer from the body to the water and from water to air (through large surface) is sufficient. In a shaded pool, so all heat transfer from the outside is by convection and conduction. I guess, if it would be sufficient cooling, you could also "just" drink the water and remove hot sweat from the skin, or dispose urine, instead. In theory, never mind electrolytes.
saalweachter 3y ago
Hmm, taking this in the opposite direction, what if you stop relying on water for evaporative cooling? What if I cover myself in alcohol or gasoline some other easily-vaporized substance? Would that still evaporate at a satisfactory rate when the wet bulb temperature is high?
- jameshart 3y ago
  Depends. Are you a smoker?
  - saalweachter 3y ago
    It looks like Puron (the replacement for Freon) is non-toxic (and non-flammable), but it also wouldn't be a liquid at any temperature you'd need cooling at. I'm guessing there are other chemicals which have vaporization temperatures in the 150-200 degree range, and are neither toxic nor flammable, but assuming ethanol works it has the advantage of being fairly easy to come by in a pinch.

saalweachter 3y ago

> Your body, when not working hard, produces about 200W of heat. That’s 200J per second. Minor quibble, 2000 (kilo)calories / 1 day = ~100 Watts.

jameshart 3y ago
Fair - I took a number for an active, awake human. You don’t produce that wattage all the time; resting and sleeping have much lower heat output; average power over a day is probably more like 100W (hence that being a reasonable average ‘healthy calorie intake’ number which I assume is where your 2000kCal comes from.)
- darkerside 3y ago
  Focused resting probably reduces it even further. You're not just "not working hard" in a situation like this, you are barely moving and probably slowing down your metabolism if anything.

Kon-Peki 3y ago

The Great Lakes region of the US and Canada is a truly special place when it comes to fresh water. The experiences in this area can't be extrapolated to elsewhere. You can get hypothermia in the middle of a summer heatwave if you spend too much time in the water more than 1km from the shore. Even if you stay at your local beach, most people would find the water uncomfortably cold. In Chicago today, the high temperature is going to be around 18° or 19° C. The surface temperature of the water at the beach is slightly less than 4° C.

jijijijij 3y ago

Thank you for doing the math! At least in my area in central Europe, 10°C would be wildly optimistic in summer. I also presume when submerged in cold water, your body will start heating up, at first. So there is probably only a narrow temperature window for effective cooling. Not to mention, you may have to work and be awake to exchange the water, and being constantly wet for a prolonged time may come with it's own set of health problems. I imagine there could be a situation with a deadly wet-bulb temperature, but below body temperature, where a large body of water may work to cool the body by convection, no?

jameshart 3y ago
A large body of cool water works great at moving heat way from you, obviously - an ‘acre foot’ of water is 1.2 million liters - 300,000 gallons. So a fairly small one acre lake that’s ten feet deep has 12 million kg of water, which can absorb 48GJ of heat before it rises in temperature by a single degree. The big question though is how long will that lake remain cooler than the air in the face of wet bulb temperatures around body temperature. Thermal equilibrium will win in the end.
- jijijijij 3y ago
  Yeah, but the question rather is, would let's say 32°C water, 5°C temperature gradient, work to cool the body, if completely submerged? When ambient conditions are deadly wet-bulb 32°C, would it still cool the water to its original 32°C? So, my thinking would be, if the heat transfer from the body to the water and from water to air (through large surface) is sufficient. In a shaded pool, so all heat transfer from the outside is by convection and conduction. I guess, if it would be sufficient cooling, you could also "just" drink the water and remove hot sweat from the skin, or dispose urine, instead. In theory, never mind electrolytes.

saalweachter 3y ago

Hmm, taking this in the opposite direction, what if you stop relying on water for evaporative cooling? What if I cover myself in alcohol or gasoline some other easily-vaporized substance? Would that still evaporate at a satisfactory rate when the wet bulb temperature is high?

jameshart 3y ago
Depends. Are you a smoker?
- saalweachter 3y ago
  It looks like Puron (the replacement for Freon) is non-toxic (and non-flammable), but it also wouldn't be a liquid at any temperature you'd need cooling at. I'm guessing there are other chemicals which have vaporization temperatures in the 150-200 degree range, and are neither toxic nor flammable, but assuming ethanol works it has the advantage of being fairly easy to come by in a pinch.