Suppose that your body is covered with a "perfect" blanket where the heat you release is 100 percent reflected back to you, it does not leak any temperature outside the environment and the blanket is indestructible and can not be deformed in any way. If your body continues to generate heat at 37 degree, and just like the blanket you are indestructible and no matter what will continue to radiate 37 degrees of heat, with enough time, can the temperature inside the blanket match that of the sun why or why not?
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$\begingroup$ You put out about 100W on average. But, you only have a finite amount of 'food' that can be turned in to heat. So, perhaps it depends how overweight the subject of such a horrible experiment is... $\endgroup$– Jon CusterCommented Dec 13, 2016 at 23:26
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2$\begingroup$ Temperature would rise to 41 or 42 degrees at most. Then death :( $\endgroup$– user137289Commented Dec 13, 2016 at 23:27
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$\begingroup$ Related, near duplicate : physics.stackexchange.com/questions/295653/… $\endgroup$– user108787Commented Dec 14, 2016 at 0:33
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3 Answers
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No, you could not reach the temperature of the sun.
First issue is what Pieter mentioned: we rapidly reach hyperthermia, pass out, and die. Once we're dead, our cells will stop metabolizing and generating heat.
Beyond that, the next issue is that you aren't adding any energy into the system. Thus, the maximum temperature achievable would be converting all of the energy stored in chemical bonds into heat. You can't get any hotter. If you take that energy and divide it evenly across all of the mass, you'll find your final resting temperature (see "Specific Heat" if you want to learn how to calculate this)
We don't have perfect blankets, so the closest you could get to this would be to heat the person up really quickly, using all of the chemical energy as fast as you can before the imperfectness of the blanket lets heat out.
In other words, if you set someone on fire and then covered them with a blanket, that'd be as close to the temperature of the sun as you're going to get.
Or maybe don't? I'm just saying, it's a rude thing to do. True, I intentionally omitted the fact that you'd run out of oxygen under the blanket, so the blanket would actually put the fire out, but just don't set people on fire. It's a good policy. =)
answered Dec 13, 2016 at 23:35
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$\begingroup$ I should have articulated my question better, so what if you are indestructible and can continuously generate 37 C of heat no matter what? Will that low heat of 37 C add up over time? @Cort Ammon $\endgroup$ Commented Dec 13, 2016 at 23:47
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$\begingroup$ I think you may be confused about units. 37C is a temperature, not a unit of heat (which would be joules -- energy). If the body is assumed to remain at the temperature of 37C, then it will reach the temperature of 37C, not the temperature of the sun. $\endgroup$ Commented Dec 13, 2016 at 23:59
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I think you're suggesting that human beings shouldn't be able to increase their temperature much higher than their original temperature, by some thermodynamic constraint.
It's true that if you put a hot, shining piece of metal at 1000 degrees under a perfectly insulated blanket, it wouldn't be able to raise the temperature of the air inside higher than 1000 degrees. This is true even if the insulation is perfect and the metal shines forever -- because once the air also reaches 1000 degrees, it'll shine too, and send energy back to the metal just as fast. This is guaranteed by the Second Law of Thermodynamics.
However, a human's temperature is different, because humans aren't in thermal equilibrium. Our bodies are constantly producing energy and expelling it to the environment; the Second Law argument doesn't apply because we're constantly producing entropy by these chemical processes. So thermodynamics doesn't really place constraints on the maximum temperature reached here.
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$\begingroup$ Sorry to have to ask to clarify, I don't see why humans and metals are different from one another, they are both forever radiating heat to their surroundings shouldn't they follow the same law?@knzhou $\endgroup$ Commented Dec 14, 2016 at 3:03
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$\begingroup$ @aimepie read carefully the answer. "humans are not in thermal equillibrium" metal is inert chemically, no metabolism! $\endgroup$– anna vCommented Dec 14, 2016 at 17:21
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So heat energy and temperature are two very different things. You are constantly burning chemical compounds to produce heat energy to maintain a constant temperature as you lose heat to your surroundings; your temperature is basically a measure of how much you are willing to "give out" heat to other people.
It's kind of like going to a sports game: the total heat energy has to do with the capacity of the stadium and how many people are in it, whereas the temperature has to do with how people flow into or out of the gates. It's very indirect. Now in our experience they are somewhat connected because when we're talking about a liquid or gas we're effectively talking about people milling around randomly and bumping into each other and there are people bumping around randomly outside the stadium too and people only go one way or another through the gates because they're bumping into each other more on one side or the other, so when you increase the heat energy contained in an object, you put more people in the stadium, people bump more into each other, and people are more likely to bump someone out of the doors, increasing the temperature. And that's also why temperature kills diseases; imagine a disease as being made out of little balloons spread through the stadium, if people bump into each other enough, naturally, they will pop the balloons. But they are fundamentally different phenomena, and technically one (temperature) is a "marginal" or "differential" version of the other (heat energy). (If you're more inclined to economic metaphors than sports metaphors, I can tell you about the difference between "total costs" and "marginal costs" in business.)
Now you want to put a body like mine into some sort of thermos that keeps in all of the matter and energy, but explore the idea of what would happen if that energy all became heat-energy. Well, of my 100kg body, there's about 50kg of water, 15kg of dry bone mass, and maybe 35kg of actual burnable stuff. Given that proteins and carbs yield 17 kJ/gram and fats yield 37 kJ/gram, we could split the difference by guessing that this averages to maybe 27 kJ/gram, meaning that in those 35kg there's about 1 GJ of chemical energy available. Vaporizing my water is a much lower cost of maybe 120 MJ or so: but in general people don't spontaneously combust because you still need to pay that 120 MJ to evaporate the water before the rest can burn. So it's a bit of a tradeoff.
It's very likely that if you just left me in a big thermos, my total heat as I rotted would not go much above boiling: my chemical decomposition is likely going to be done by other organisms feeding on my body, but most organisms can be killed by high enough temperatures and it would be very hard for them to survive in such a pressure-cooker.
But supposing you were willing to give my body a measured chunk of energy $E$ and then you would carefully remove an amount of $E$ energy later, so that the full 1GJ was liberated without increasing or decreasing my mass/energy in the balance: this would probably also require filling the thermos with a lot of raw oxygen gas. Then typical specific heats range from 1 to 5 kJ/(kg °C) so the remaining 850 MJ or so can raise my 100 kg somewhere between 1700 - 8500°C to somewhere in the 2000 K - 9000 K range. I would probably guess towards the lower end of that spectrum, maybe 3000 K or so, but the interval does include the Sun's surface which is at 5777 K.
So: you would probably be shy of glowing white-hot, but there's a decent chance you'd be glowing red-hot at least.
