Built on Facts

Star Light, Star Bright

The power output of the sun is often talked about in awe-inspiring terms. You’ll be told that it’s like a continuous thermonuclear blast, or that a tiny fraction of the tiny fraction of power that happens to hit the earth would support humanity’s energy needs. It’s all true. The light and heat from a campfire can make you uncomfortable from a few feet away, while the light from the sun can scorch deserts from almost a hundred million miles distant.

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Let me quantify this, since it’s what we physicists compulsively do. The total power output of the sun is something in the vicinity of 3.8 x 1026 watts. For comparison, this is about ten trillion times the total power currently in use by the human species. It’s a hefty number.

On the other hand, the sun is a very large power plant. With a radius of about 7 x 108 meters, it has a total volume of 1.4 x 1027 cubic meters. Dividing the total power output by the total volume, I get an average power production of a little under 0.3 watts per cubic meter. Weak sauce, as they say. Standing on the surface of the sun though, you can imagine that you’re standing on a rather enormous tower of cubic meters stretching down to the sun’s center, and so the total effect is the blazing brightness we see.

Now really this isn’t a fair calculation. The entire volume of the sun isn’t producing energy, only the core is. I’ve seen figures that put per-volume power output near the center of the sun in the ~300 W/m^3 range, which is much larger but still unimpressive. Your average cow can do that, and so could your average compost heap. You do it too – you take up a lot less than a cubic meter and yet your 2000 calorie diet is the equivalent of about 100 watts.

So don’t be too hard on the scientists trying to develop practical fusion energy. Even if they came up with a reactor with the proportionate output of the sun it would be woefully inadequate.

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Comments

  1. #1 Chris
    January 26, 2009

    This is quite an interesting calculation. Thanks for sharing it!

  2. #2 Max Fagin
    January 26, 2009

    “Your average cow can do that, and so could your average compost heap. You do it too – you take up a lot less than a cubic meter and yet your 2000 calorie diet is the equivalent of about 100 watts.”

    Sure. But let’s see you, a cow, or a compost heap put out that much energy for 10 Billion sequential years.

  3. #3 Stefan
    January 26, 2009

    … power output near the center of the sun in the ~300 W/m³ range

    That’s a very interesting number! One can imagine filling a room with lightbulbs so to produce this energy output – it would look pretty light :-)

  4. #4 Dr. Pablito
    January 26, 2009

    I just returned from a meeting in which we discussed the so-called “Standard Solar Model” in which we reviewed the nuclear physics data which enter calculations of the main power output of the sun.
    Thanks for the interesting calculation — it is always cool to consider that the sun just barely burns, and that if it weren’t for quantum tunneling, it wouldn’t burn the way it does. It’s a huge engine for turning gravity into light via nuclear matter.

  5. #5 Carl Brannen
    January 26, 2009

    This does put the fusion problem in perspective.

    By the way, in comparing your audience to cows and compost heaps is there some sort of message here? It’s been 25 years or so but I recall that there was a certain time of year around which I’d pretty much had my fill of grad school. The worst was towards the end of the 3rd quarter of a 3 quarter year. About that time, the Santa Anna winds reverse. The result is a wanderlust breeze off the ocean.

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