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I was looking into the following problem:
Who would win? 1 trillion lions or the sun? Obviously, the solution lies in how much energy either can output per unit of time.
The total energy output of the sun is $3.8×10^{26} \frac{J}{s}$.
The number of lions alone pales in comparison ($10^{12}$).

However, I'm now trying to figure out how many lions it would take to have an output equal to the sun, but I seem to be having a hard time finding good data.

What's the peak energy output of a lion per second (or where/how can I find such information)?

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    $\begingroup$ How do you define energy output? Its capacity to move an object, like horsepower? How much energy its cells produce? How much energy it would produce if completely combusted? $\endgroup$ – MattDMo Jan 13 '15 at 18:19
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    $\begingroup$ According tho this websote, a lion needs to eat from 5 to 7 kg of meat per day (with lots of variance from day to day going up to 50kg per meal). How much energy can a lion take up per kg of red meat? If someone find out this information we can easily answer the question by equating energy uptake and energy output (which totally makes sense for adults). $\endgroup$ – Remi.b Jan 13 '15 at 18:21
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    $\begingroup$ Speaking of hypothetical scenarios - did you see the excellent and somewhat related A mole of moles from "what if?"? $\endgroup$ – fileunderwater Jan 13 '15 at 21:20
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    $\begingroup$ If you burn the lions they're no longer lions, are they? $\endgroup$ – Nit Jan 14 '15 at 1:12
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    $\begingroup$ This question appears to be off-topic because it is about physics, not biology. It just happens to use a living organism as an example. $\endgroup$ – terdon Jan 14 '15 at 15:09
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Wow, as an astrophysicist who has just logged into biology SE for the first time, I didn't think I'd have a question I could immediately answer.

You are correct about the Sun's output, so what about the lion.

If the lion is in its usual passive state, i.e. lying around as shown in your picture, then you would not go far wrong in treating them as black body radiators (well this will give you an upper limit, though the emissivity of human skin is quite high, so it should be a reasonable approximation.). To estimate a power I need a lion's temperature and its surface area.

According to this site the body temperature of a lion is 311.33 Kelvin.

I found a calculator that used the DuBois formula for surface area (for humans) and put in 440 pounds and 7 feet 10 for the weight and "height" of a (male, adult) lion - this returned a surface area of $3.6\ m^2$ (about twice a, male human, so sounds roughly ok).

Now using the Stefan-Boltzmann formula $P = \sigma A T^4$, I get the power output of a "black body" lion to be about 2 kW.

Thus $10^{12}$ lions have a power output of $2\times 10^{15}\ W$, which is 11 orders of magnitude less than the Sun.

But now take the question at its most basic. Compared to the Sun, the lion is a pretty effective power generation unit. The Sun only generates $2\times 10^{-4}\ W/kg$, whereas a lion-based power source weighs in with a massive $10\ W/kg$!

EDIT: Note that the calculation just assumes the Lion can produce this kind of power output whatever environment it is in. In practice a Lion absorbs a large fraction of this power from its surroundings and its internal metabolism does not need (and probably cannot) supply 2kW. Thus the 2kW should be reduced to some extent, though I'm not sure a simplistic $T^4 - T_{\rm env}^{4}$ calculation can be correct, unless one of you biologists tells me that a Lion's metabolism shuts down once the ambient (African) temperature approaches 311K (I guess in a human a lot of it goes in evaporating sweat?) Whatever, the order of magnitude of the answer is unchanged.

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    $\begingroup$ This offers some interesting insight, thank you very much for your answer. $\endgroup$ – Nit Jan 13 '15 at 21:36
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    $\begingroup$ But it probably wouldn't a useful power source, remember that those lions need 10W/kg worth of food. $\endgroup$ – user137 Jan 13 '15 at 23:46
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    $\begingroup$ You've accounted for the heat radiated by the lion, but not for the heat absorbed by radiation from its environment. So unless the lion is floating in deep space, you've dramatically overestimated its power output. Assuming an environment at 295K gives a much more modest power output of ~370W. $\endgroup$ – David Jan 14 '15 at 2:10
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    $\begingroup$ @David As lion is a warm blooded animal, regardless of external radiation, the surface temperature will more or less be constant $\endgroup$ – One Face Jan 14 '15 at 12:59
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    $\begingroup$ @CRags I doubt that a lion can hold its body temperature in a 0K environment. Unlike the sun, that can hold its body temperature in a 0K environment, the lion will just die. $\endgroup$ – Alexander Jan 14 '15 at 14:31
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The sun will win until you have enough lions to form a star sized mass.

Assuming that your lions have an average mass of 200kg, which is probably pretty close, 1 trillion lions has a mass of 2×1014 kg, which is pretty close to the mass of Remus, a moon around the asteroid Sylvia. The mass of the sun is about 2×1030 kg.

So your lions would have enough mass to become gravitationally crushed into an object, but probably not enough to become rounded. Once crushed they won't be able to carry out any metabolism.

Even if we considered the sum of 2 trillion individual lions the sun would still win because nuclear fusion completely outclasses chemical reactions in terms of energy released, and the mass of the sun is still much much much larger.

However, if we somehow converted the lions into energy by E=mc2, we get about 1.8×1031 J. So if you managed that you could release more energy than the sun for a very short time.

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    $\begingroup$ I am not sure this was what the OP was after. He may have meant "energy consumption / metabolism" of a lion rather than the actual energy stored in its matter. But I missunderstand the OP's question. $\endgroup$ – Remi.b Jan 13 '15 at 19:38
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    $\begingroup$ @Remi.b It really doesn't matter, by the time you have enough lions for their normal metabolism to compete with the sun, you have more than enough mass to make a sun. $\endgroup$ – user137 Jan 13 '15 at 19:40
  • $\begingroup$ Ha ha yes I got this point. Well... but still I guess he would expect to know what is the ratio of the lion metabolism over the sun energy output. But the question might be better suited of worldbuilding.SE I guess $\endgroup$ – Remi.b Jan 13 '15 at 19:46
  • $\begingroup$ Relevant: what-if.xkcd.com/4 $\endgroup$ – agweber Jan 14 '15 at 18:29
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I'm going to work this from the angle of power the animals could produce for an extended (e.g. 1 hour) time. I'll assume that a lion produces power somewhere between that of a human and a horse, since the typical weight of a lion (180 kg/400 lb-ish for males) is between that of a human (80 kg/180 lb-ish for males) and a horse (850 kg/1800 lb-ish for draft horses).

  • Human: 100 W
  • Horse: 746 W ("1 horsepower", or 746 W, is based off of how much work a draft horse can do for an extended period of time)
  • Lion: 200 W?

So you would need 3.8×1026/200, or 1.9×1024 lions. That's not a trillion, but about 2 trillion trillion lions. The exact amount of power produced won't change this too drastically, e.g. if our lions produce 800 W instead, it'd be 475 billion trillion lions.

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  • $\begingroup$ Just a side note: this is an international website on science. Please use the SI system, i.e. kg instead of lb. $\endgroup$ – Shahbaz Jan 14 '15 at 10:31
  • $\begingroup$ Just as another side note: the definition of a horsepower was taken off James Watt's marketing materials and is not a good guide to how much work a real draft horse can do even over a period of a few hours. Also: feel free to use lbs; this is an international site after all. $\endgroup$ – Nagora Jan 14 '15 at 14:05

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