# Q&BA: Pound for pound, are humans hotter than the Sun?

By Phil Plait | February 2, 2012 11:19 am

[Note: Every week I hold a live video chat on Google+ where I answer questions from readers. I call it Q&BA, and when I get a question that stands alone, I’ll make it its own video. ]

Every now and again, I hear this urban legend that pound for pound, the human body is actually hotter (or has more energy) than the Sun. I got this question in a recent Q&BA video chat session, so I tackled it. The answer is pretty interesting, and depends on how you ask the question!

I actually wrote about this legend on the blog a while back, and I show all the math. I really like this question, since it has a straightforward answer that makes it seem wrong, but then if you look at it more carefully the answer is a little trickier. And even in the video and that other post, it’s not really a complete answer; if you read the comments on the post you’ll see people arguing over it.

That’s really the best kind of question: the ones that keep on going! There’s always more stuff to figure out.

Visit the Q&BA Archive to see more videos like this one!

CATEGORIZED UNDER: Astronomy, Cool stuff, Q & BA, Science

1. Some human bodies are hotter than others… [rimshot!]

2. Chris

The math checks out. Just driving me crazy using cgs units. Actually as a suggestion it might be better for public outreach to use Watts instead of ergs. Everyone has heard of watts, but ergs are not as common.

3. TheDawgLives

But, if you took a human-sized chunk of the sun, then it wouldn’t have enough gravity to fuse hydrogen, and so it would be much cooler than a human…

4. Very nice, but the myth has tiny tiny truth in it. Did you try to average human temperature? 37C is the blood temperature but most of us are cooler (feet and bones for examples). While this will not affect the calculation much (the difference of few degrees is meaningless) it is still interesting.

5. The blog you posted earlier was about Energy per area or volume.

In this question, you are asked about Heat. May be the original question was vague, but how about I ask my own question.

Of course, I could probably solve this myself, but would be great to have your insight and explanation of it.

Q: Which gives off more heat per volume, the sun or a human being.
In other words, if you got enough human beings together such that their total volume equals the volume of the sun, what would be the temperature of that mass?

6. Bill3

@TheDawkLives Similarly, if you took a cubic centimeter of human, it also would die off and become much cooler.

7. alex

How many average sized human beings will fill the volume of the sun. Then average temperature of each body. Including if every human could survive the proximity, how the temperature will increase due to respiration, could be close?

8. Bill Nettles

It makes absolutely no sense to talk about “luminosity per volume” because luminosity is only important when looking at the power crossing the boundary of an object. The volume which is enclosed by the surface is completely irrelevant. Intensity (or Luminous flux) MEANS power per area CROSSING the area. If the Sun was a cube ( resistance is futile!) of surface area same as the Sun and same luminosity, its surface temperature would be the same despite the different volume.

Also, when you say “hotter” (outside the metasexual social meanings), you are necessarily talking about temperature and nothing else. It’s a disservice to people’s science education to accept incorrect definitions without correcting them. For the most part, Phil, you did this, but the whole luminosity per volume is a Bad Idea.

9. Gary Ansorge

,,,and from what I can recall, the human body runs on about 100 watts. That’s 100 watts radiated from about 2 m^2,,,times 7 billion,,,I don’t think the Matrix would be happy with that output,,,

I’ve seen this data before and can’t remember where(it was 40 years ago). Maybe Heinlien, Asimov or Clark pointed it out,,,

So, if we spread out all the humans in a very flat film,,,would that act as a self propelled photon rocket? To the Stars, Rambo,,,we don’t need no extra stinking rocket,,,it’s built in,,,

Gary 7

10. Chip

Stanley Kubrick probably got it right in 2001 – A Space Odyssey when the Frank Bowman character played by Keir Dullea had to cross about a foot of the vacuum of space without a space helmet after the HAL 9000 locked him out.

As you may recall before he entered the open airlock he grimaced, closed his eyes tightly shut and held his breath. This might actually be a wise move during a very short exposure to outer space because he’s making the ‘package’ of his body as tightly contained as possible. Once inside he was able to repressurize quickly while still holding his breath. Minimal time exposed is likely a key factor.

11. The correct statement of this mythical “myth” is that pound-for-pound (or ml-for-ml) the human body radiates more energy per second than the sun. Of course it’s not “hotter” nor does it *have* “more energy”, but it *loses* energy relatively more quickly because it has a relatively much larger surface area compared to its volume. This is just a consequence of the relative inefficiency of large spheres as radiators. The reason for this is because any old cc in the middle of the sun may be as hot as hell, but they all absorb almost as much radiation from their neighbours as they emit themselves, and it is only those near the surface which contribute photons which actually escape. So the idea of pulling them out to compare with us defeats the whole point of the exercise.

This is all part of the same theme which explains why elephants have big ears and why mice each day have to eat a much greater proportion of their body weight than we do. If I was as fat as the sun I’d be pretty hot in the middle too, and that’s precisely *because* I would then be getting rid of heat proportionately less rapidly than I was generating it.

12. Dragonchild

Basically, it’s a non-question in that it’s too ambiguous to give an answer.

That’s not a cop-out. Another example is, “which are larger, birds or cats”? Well, I’ve seen house cats hunt birds all the time, so — easy answer, right? Not quite. “Bird” and “cat” are vague terms in that the former include hummingbirds and ostriches, and the latter include housecats and lions. You can make any pairing of bird and cat to get any answer you want. If you want to compare populations, there are a number of ways to do it. The question’s just too vague.

One fundamental to science is learning how to ask the right questions!

13. My astrophysics professor used to phrase this conundrum as:

“A mouse running on a tradmill generates more power, gram-for-gram, than the sun does. Therefore, a one-solar-mass mouse would be hotter than the sun. Of course, then, you’d have to FEED it….”

This led me to create a Champions character named SOLARMOUSE:
http://www.rogermwilcox.com/Champions/solarmouse.html

14. @ Chip:

Dullea’s character was DAVE Bowman, not Frank Bowman. The other guy was Frank Poole. (Who comes back from the dead in _3001_, but that’s a different story.)

15. Off topic, but… nice mount and binocs! Can I assume that you a fan of open clusters?

… that misty glow; those lovely sparkles…

Scopes won’t give that.

16. I’ve been asked the same question a couple of times. The last time it was asked, I asked them for their ‘take’ on it. That was interesting.

It seems that there was some skerrick of knowledge that the *density* of the sun at the surface, compared to the density of a people, was considerably less, and somehow that got converted to a comparison of radiative units (my words, not theirs). The answer was still so bad “it wasn’t even wrong”, but it helped to understand what the questioner’s grasp of the concept was.

And yeah, “pound for pound” (why, oh why, do Americans still think in 17th century units of measure?) there are a couple of layers to the question, as mentioned above. For example, a pound of (mainly) hydrogen wouldn’t undergo fusion, so it would radiate less (be “cooler”) than a pound of a person.

My immediate response to pseudo-scientific comparisons like this is to ask the questioner to arrange for a “pound” of the sun… That usually breaks the spell.

17. Hypocee

So I had expected one more layer, to answer the actual question stated – taking equal volumes still plays into the unimaginable densities at the core. Gram-for-gram average, presumably mammalium wins again by orders of magnitude – but gram-for-gram at the core?

18. Matt B.

Why would someone even phrase the question with “pound for pound”? Temperature is a density, and is therefore already pound for pound (okay, it’s really particle for particle, but YKWIM). Of course, if you use pounds of weight, the calculation would be different, due to the high surface gravity of the Sun.

I thought maybe they should ask “liter for liter”, but the Sun’s average density is 1410 kg/m^3, and a human is about 1000.

Speaking of stellar density, I know a giant star expands by a huge factor and therefore has a much lower average density, but OTOH the Sun has its corona. So is there a qualitative way to define the difference between main-sequence and giant stars without knowing their histories?

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