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Yes, you explained enough, but how is the organs endangered through a bikeride?
They are not. The heat was caused from the unusually heavy exercise. The only time danger to the organs comes into play is during heavy fevers.
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Enough heat must be generated to dry the blanket and it doesn't, as you said, have to be very high. But it does have to be high enough to be capable of causing evaporation and as far as i'm concerned water evaporates only at certain temperetures at certain speeds.
No...you are thinking of boiling. You are thinking of water transitioning to gas. That is not what happens with evaporation. In evaporation, the water from your sweat is diffusing into the air, not boiling off into it (water vapor, not water gas). Evaporation is more a product of the surface area and mass vs heat input. On the molecular level, water molecules are always moving around, on the surface, some molecules manage to escape from the rest and go off into the air. Eventually, all the molecules escape this way. If you add more energy to these molecules, such as with heat, then they move faster, and consequently escape at a higher rate.
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Wouldn't you have to start sweating if your body starts to cause evaprorarion?
You would only begin sweating if your body decided that it needed to get rid of heat at a faster rate, i.e. if it sensed that your organs were in danger.