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# How efficient can a Dyson sphere be?

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The shell variant of a Dyson sphere consists of an artificially-made shell of material about 1 AU in radius encircling a star. The sphere captures most of the star's energy and stores it for future use. Unfortunately, the megastructure will lose energy. It has a non-zero temperature, and therefore it will radiate energy in the form of black body radiation. As with any heat engine, we can assign an efficiency, $\eta$, to it: $$\eta\equiv1-\frac{T_{\text{DS}}}{T_*}$$ with $T_{\text{DS}}$ the temperature of the shell and $T_*$ the temperature of the star. An old paper I found thinks that a temperature of $T_{\text{DS}}=300\text{ K}$ might be realistic (giving an efficiency $\eta=0.95$), and that the ultimate lower-temperature limit is set by the cosmic microwave background, at $T_{\text{DS}}=2.7\text{ K}$ and $\eta=0.99955$, all assuming a Sun-like star.

I'd bet anything that the true limit is higher and depends on the composition of the shell, but I have no idea what that limit is. Assuming that the structure is built by a Type II civilization but that they don't have access to handwavium or any other magical material, what's the maximum efficiency of a Dyson sphere of this nature?

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#### 2 comments

You don't need this to be a full sphere to determine efficiency. The same would be true of a 1 square meter thermal panel in space receiving about 1.3 kW from the sun on one side and facing cold space on the other. ‭Olin Lathrop‭ 3 months ago

@OlinLathrop Structural requirements for a sphere are likely different than those for an array of panels, and that might impact materials choice. Plus, I figured I might as well keep it narrowed down to the structure I'm interested in. ‭HDE 226868‭ 3 months ago

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