# Which puts out more energy, a human body or the sun?

Asked by 6rant6 (13672) January 27th, 2011

I read somewhere today that if the human body were as massive as the sun, we would be hotter than the sun. I related this to a friend who insisted that was poppycock. The sun was nuclear, we are chemical. And nuclear is C^2 better.

I pointed out that the sun is taking billions of years to die out and we have enough fuel for maybe a couple of months. Certainly at some point, a fast chemical reaction overtakes a nuclear one, but where?

Anyone have a smart way to analyze this? Obviously it can be done on a via brute force – using calories in and out for the human, converting that to energy, figuring out the energy generated by the carbon cycle in the sun… yada, yada… Anyone have an elegant idea?

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Consider which puts out more energy: a chemical bomb or a nuclear bomb.

phaedryx (6118)

@phaedryx The question isn’t which puts out more energy, but which is hotter. That is, which puts out more energy per unit of time. For example, in a given day, maybe 1% of the fuel in a human body is converted to energy. Whereas for the sun, which burns for 5 billion years, maybe one part in 1.8*10^14 is expended each day.

6rant6 (13672)
Response moderated (Off-Topic)

The human body cannot approach the E=mc^2 of a fusion reaction. Also, we have quite a bit of waste products that wind up in the toilet while the Sun uses it’s fuel more efficiently.

It is worth noting that c is a large number by itself and thus c^2 is huge. Just a microscopic amount of matter converted to energy yields a lot of energy. If a human being put out the same energy density, just a few micrograms would melt us from the inside. I eat quite a bit of food (at least a couple of pounds) but I have yet to level a city with the energy released from that amount of mass.

How many calories worth of food would it take to release the same amount of heat as an H-bomb? Considering that H-bombs are much smaller than a buffet table, I would say that the Sun wins the energy density contest.

jerv (31034)

@jerv, you’re still not getting the time element. If you had a huge pile of dynamite, it could deliver more energy than a nuclear bomb. So the question isn’t can a chemical reaction deliver more energy than a nuclear one – it can – but rather will it release more in a shorter time. In the actual problem posed the “human star” would use up all the energy in a couple of months; the sun in 5 billion years. Granted, if the sun took only ten times as long it would release more energy per unit of time. Also for one hundred times. For a million times? A billion? A trillion? At some point the chemical reaction burn hotter.

Look at it this way. Take a gram of human. Now take 1 one billionth of a gram of sun. Which will emit more energy during their life cycle? I don’t know and just saying e=mc^2 doesn’t mean you do either. (BTW not all of the matter is converted into energy during the star’s life cycle. Much of it is releases at the time it goes nova. So mc^2 is just an upper bound.)

6rant6 (13672)

@6rant6

okay, let’s get more specific. Given a chemical bomb and nuclear bomb of equal mass, detonated at the same time, which will give off more energy per second?

I’m going to do another answer once I work through the math.

phaedryx (6118)

Fusion is the most efficient energy producing reaction known to man. It is many, MANY times better than fission, which is itself several orders of magnitude times better than chemical reactions. A human would have to be several times larger than a nuke to produce a nuke’s worth of energy, so a human must be much larger than the sun to produce a sun’s worth of energy.

PhiNotPi (12670)

@phaedryx But you can’t say, “Of equal mass” because the nuclear reaction takes billions of times longer. Again, it’s not which generates more energy, but which is hotter – or which is releasing more energy per unit of time.

6rant6 (13672)

Hmm, I guess I’ll do the math:

Googling tells me that the sun produces 3.8×10^26 joules per second (9.1×10^25 calories/second) and that its mass is 1.9891×10^30 kg

(9.1×10^25 calories/second)/(1.9891×10^30 kg) = 0.000046 for the sun

Now a human body:

Let’s say 300 calories/second and, I dunno, 75 kgs of weight

(300 calories/second)/(75 kg) = 4 for a human body

yeah, I’m fudging a lot of stuff here, calories consumed doesn’t translate directly to heat, etc. etc. but the magnitude is such that I’m going to change my vote to: the human body is producing more energy per second per mass.

phaedryx (6118)

The principle of Occam’s Razor may be of help here.

First of all the human body is made up of atoms that are mostly open space. So if you (or God) were to some how make a human body as big as the Sum you would have a very unstable and structurally very weak mega planet. The huge force applied on it by the space-time-continum alone would quickly smash it into a sphere. Then the weak and hollow nature of the resulting thing would then likely collapse into it’s self down into a singularity of a black hole.

Now ask yourself “How much energy is radiated out from a black hole”? Certainly not as much as the Sun.

gondwanalon (16740)

@phaedryx First off, I followed your first link and then went to “weight” and got a page which gives different numbers for some stuff. But the calorie figures are close enough to matching for my purposes, as you will soon see. You did do the right math with the right numbers regarding the Sun though.

Given the range presented for a basal metabolic rate in your first link, I think we can agree for purposes of illustration to use the number 1500 dietary calories per day. It takes 1,000 heat calories to equal 1 food calorie, so the human metabolic rate is 1.5*10^6 heat calories per day.

1 day = 24 hours = 1440 minutes = 86,400 seconds

(1.5*10^6 calories / day) / ( 86,400 seconds / day )
(1.5*10^6 calories / day) * ( day / 86,400 seconds )
(1.5*10^6 calories / day) * ( day / 86,400 seconds )
(1.5*10^6 calories / 86,400 seconds )
( 17.361… calories/sec )

Where did that 300 come from?

Okay, I looked up the weight of the average human and got 155 pounds (70kg), so you were not far off there; close enough that I would call it a decent guess.

( 17.361… calories/sec ) / 70kg = 0.248…

Since 0.248 > 4.57*10^-5, I hae to say that I stand corrected.

jerv (31034)

I must say that the phraseology on this one is tricky though. Are we talking total energy, energy density, and where did time enter into this? It seems almost like the rules kept changing with every answer.

So, which is hotter? The higher temperature; the Sun.
Which puts out more energy? Beyond all doubt, the Sun wins here too. Same with energy per unit time.
As for energy density, humans win there whether time enters into it or not.

Now, you also expressed interest in when (as in under what circumstances, I assume?) a fast chemical reaction overtakes a nuclear reaction. You should be a bit more specific there. What are you looking for? What definition of “hotter” are we using here? What criteria are we using; time, mass, density, volume, or some combination?

In other words, I would like a little more detail before I even think of attempting to answer the rest of this question. I want to help you, but I am also a bit confused.

jerv (31034)

Something I forgot is that things change with scale. Have you heard those things comparing the strength of an insect? “If a human had the same muscles as an ant, he could lift a Mack truck!” Well, the Square/Cube law begs to differ. Doubling size will increase strength by the correctional area of muscle, or 2^2 or four times as strong, but the body will be eight times heavier ( 2^3 ). Therefore, doubling size will effectively halve strength.

Whenever you scale things, it isn’t always linear.

jerv (31034)

@jerv On the human body link, I just clicked on the calories for human male. It showed a high of 0.0299 Calories/second: http://www.wolframalpha.com/input/?i=(268+to+2574)+dietary+calories+per+day

I realized I was looking at capital ‘C’ calories and did a quick conversion in my head. It should have been a high value of 29.9 calories/sec. Yeah, I was playing a little loose with the numbers.

phaedryx (6118)

jerv (31034)

I’ve come up with a way you can intuit this: Imagine you have a kilo of human flesh, metabolizing just as we do. Now imagine that you have a rock of the same mass. I tell you that the rock is one percent radioactive and the half life of the material is 500 million years (I’m not sure exactly how to scale this mental experiment, but I think most people have trouble intuiting anything over a million anyway). Intuitively, which do you think will be hotter?

To me, this is like comparing granite – which always has some radioactivity in it – to human flesh. And in that comparison, granite loses cold.

6rant6 (13672)

My friend did his own calculations. Here are his results.
[Spoiler alert, he’s within an order of magnitude of everyone else.]
—-

The power output of the sun is about 5×10^23 horsepower. http://helios.gsfc.nasa.gov/qa_sun.html#power

The solar mass is about 2×10^30 kg
http://helios.gsfc.nasa.gov/qa_sun.html#smas

Mass of a 190 lb man is about 86 kg

A man can produce about 1 hp for a brief amount of time.
http://en.wikipedia.org/wiki/Horsepower

To get the equivalent of a human with the mass of the sun, find out how many humans it would take to equal the mass of the sun. Divide the mass of the sun by the mass of a human to get that number. It’s 2.3×10^28.

Now to find out how much power such a massive human being would produce, all we have to do is multiply the number of humans equal to a solar mass by the amount of horsepower a person can produce. That number is 2.3×10^28 horsepower which is about 46,000 times bigger than the output of the sun (5×10^23 horsepower). So as surprising as it seems, the human would be hotter than the sun.

Of course, if you used somebody other than a 190 lb man, say Angelina Jolie, the human would be even hotter. On the other hand, if the person used was my ex, it’s very possible the sun could be hotter than the human.

On another thermal topic, how long would it take for my refrigerator to make hell to freeze over? I need to know because that’s when my boss said I would get my next raise.

6rant6 (13672)

The problem there is that you have two opposing forces, and Hell has a lot of fuel that it can (and will) use to generate heat. I’m not saying it will never happen, but I suspect that the answer is longer than your lifespan.

You could tell him to go to Hell to check on it’s progress though.

jerv (31034)

The weirdest question I have seen here. My mind is boggled but I’m going to agree with @6rant6 Angelina Jolie is hot.

flutherother (29282)

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