# Sun energy production as a function of depth

I've heard a few times that the Sun's energy output per unit volume is less than that of a human, with the Sun's much higher power output being a result of its much greater size.

In a blog post, Phil Plait runs through the numbers and concludes that humans put out 60,000 times more energy per unit volume than the Sun. However, he also makes the counterargument that one shouldn't assume the energy generation density is uniform inside the Sun, since most of it takes place in the core.

I would like to know how heat generation is distributed inside the Sun. Is it more or less uniform inside the core? Is there any part of the Sun that generates substantially more energy per unit volume than a human?

Phil Plait seems to say that there is, but I think he makes an error in his reasoning: he seems to imply that because the temperature of the inside of the Sun is millions of Kelvin, it must be generating millions of times as much heat. But of course, the temperature isn't the same as the rate of heat generation. If the core of the Sun were thermally insulated, it could stay at millions of Kelvin without generating any heat at all. (Of course I know this isn't really the case.) So I would like to know the figure for the amount of heat generated per unit volume in each part of the Sun.

At the center of the core $276$ $Watts/m^3$

at 9% of Sun's radius $103$ $Watts/m^3$

12% of radius $56$ $Watts/m^3$

14% of radius $20$ $Watts/m^3$

19% of radius $7$ $Watts/m^3$

22% of radius $2.2$ $Watts/m^3$

24% of radius $0.7$ $Watts/m^3$

29% of radius $0.09$ $Watts/m^3$

Source: B. Stromgrew (1965) reprinted in D. Clayton Principles of Stellar Evolution and Nucleosynthesis. New York: McGraw-Hill, 1968, page 483.

So even at the most powerful point in the Sun, the center, the power per volume is much less than a light bulb. Some have compared the power per volume to a compost pile!

The power of a human is about 100 Watts or $1,000$ $Watts/m^3$, so the power of a human per volume is indeed greater than any part of the Sun.