Say a person is put in a perfectly insulated box with a block of ice. The person’s body is producing heat and the block of ice is absorbing heat. How much ice would be necessary so that the cooling effect of the ice would exactly match the heat output of the person, thus keeping the temperature inside the box constant?
The answer doesn’t have to be perfect, so make any assumptions you need.
A resting adult puts out about 100 to 140 watts of heat. That’s 340 to 475 BTU/hour, or 86 to 120 kcal per hour.
It takes 79.8 kilocalories to melt 1 kg (1 liter) of ice..
So 1.1 to 1.5 kg of ice should be enough to keep the temperature of your box constant for about an hour.
Are we allowed to bring something to drink, being all that ice around… I think I’ll make a screwdriver.
The thing is, a person keeps producing heat (so long as they’re alive), whereas the ice can only absorb a fixed amount of heat before it melts completely (after which the temperature of the water will increase due to the human’s heat output). So eventually the human always wins, unless he suffocates, starves, or freezes to death – all of which strike me as reasonable worries for a person in a 100% thermally insolated box. Which one happens would probably depend on how big the box is (i.e., how much air), how well-fed the person is, how much ice there is, whether the ice is significantly colder than freezing to begin with, etc.
Even if the person melts the ice, he still needs to find a way out of the box before he heats the whole system up so much that he dies of heat stroke.
After the human is dead, the system will eventually achieve thermal equilibrium and stay at a constant temperature from there on out. So I guess in some sense the ice eventually wins, even if it’s completely melted by the time a constant temperature is permanently achieved.
If you want something that actually completely and permanently cancels the heat output of the human, then you can’t just use something that absorbs a limited amount of heat into itself. You need something that actually removes heat from the system (since the human’s metabolic processes are producing new heat in the system). Say, an air conditioner.
Hmm. . . I guess there’s another way the situation could end: the human dies of thirst. I guess he can drink the water after melting the ice, but that still will only sustain him so long. In the case where it’s a big box (so lots of air to breathe and absorb heat), but there isn’t that much ice (so water gets used up long before starvation becomes a consideration), then this seems like the most likely scenario.
But I seem to be interpreting this problem in the most morbid way possible. 