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How much energy in form of heat does a human body emit at rest level?

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2 Answers 2

That's easy. The energy requirement of an average man is 2,500 Calories per day, and one Calorie is 4184J. Therefore he emits about 10.5MJ/day or about 120W.

An average woman requires 2,000 Calories per day, so she emits about 97W.

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Does the human body emit as heat, all the energy it got from food? If yes, in typing this answer, you spent some energy - what is its energy source? –  New_new_newbie Jun 5 at 10:09
    
@New_new_newbie: assuming your weight stays the same you are emitting all the energy from your food as heat. If you're getting fatter it means you're retaining some of the energy and converting it to chemical energy (i.e. fat). Conversely if you're getting thinner it means you're converting chemical energy in fat to heat, so you're emitting more heat than you get from your food. I got the energy to type this from my body reacting glucose with oxygen to produce water, carbon dioxide and energy. –  John Rennie Jun 5 at 10:14
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Wrong. Energy gets stored in human body as ATPs (en.wikipedia.org/wiki/Adenosine_triphosphate). The chemical energy stored as a P-O bond gets released. Of course, some part of that will be lost as heat, but if picking up a 400g stone to 1m height required 4J of work, that 4J does come from the food you have consumed. Otherwise energy conservation would stand violated, if your ``input = output as heat'' conjecture was true. So, again, what is the energy source of typing this post if all the energy you got from food got EMITTED out as heat? –  New_new_newbie Jun 5 at 10:32
    
@New_new_newbie: the article you link has in its second paragraph: ATP is therefore continuously recycled in organisms. ATP is not used for long term storage. Medium term storage is as glycogen and long term storage is as fat. –  John Rennie Jun 5 at 10:38
    
@New_new_newbie: yes, if I lift a weight some of the energy I get from food has been converted to potential energy of the weight. So I suppose it would be more precise to say the energy from food ends as heat + any potential energy gain. In real life we are unlikely to make any long term potential energy changes to our environment (I suppose builders do, though their buildings will fall down eventually so the energy ends up as heat eventually). –  John Rennie Jun 5 at 10:42

I hesitate to contradict John, but: it's simplistic to assume caloric input equals caloric output, or that caloric output is purely heat, as opposed to moving from one place to another, lifting boxes, etc. A far better model IMHO is to set up the human body as a black-body source with $\epsilon = 0.98 $ (emissivity), temperature = 310K, and some reasonable estimate as to total body area. Then you compare the absorption of heat from, say an ambient environment of 294K to see the net outflow of heat.

That does ignore conductive and convective heat flow :-) .

See, for example, the excellent calculator at hyperphysics

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Yes, I recall that the result using Stefan-Boltzmann's law is close to that of John Rennie. In space, the power output is close to $1 kW$, quite impressive! –  auxsvr Jun 5 at 12:26
    
I expect that black body radiation losses are small compared to other heat losses of the human body in most ordinary circumstances. I haven't done the numbers, but I betcha the heat loss from inhaling gas at ambient temperature and exhaling it at body temperature is much greater than black body radiation when sitting behind a desk in a typical office. Add to that evaporative cooling since exhaled breath usually contains more moisture. –  Olin Lathrop Jun 5 at 12:47
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Unless you're building a ziggurat or otherwise storing lots of gravitational potential, don't you think all of that mechanical energy also ends up as heat? –  rob Jun 5 at 12:55
    
@rob, yeah, most of it does. But just think of the stored entropy that comes from learning a bunch of stuff (highly ordered :-) neuron structures). –  Carl Witthoft Jun 5 at 13:35
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@Carl Well, if I commit a terabyte of information to memory (seems unreasonably large), the minimum entropy change is $S=k\ln2^{40}\approx 1200\,\mathrm{K/eV}$. At my body temperature the minimum energy release is only about 1/4 eV. Even if the ratio of physical to information entropy is a billion to one I still have much less than a joule of heat associated with learning. I don't think it's a big correction. –  rob Jun 5 at 13:51

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