"Now say you want to run some modest AI stuff. That's a bigger job, so let's scale up our cubical computer with edges twice as long as before. That would make the volume eight times larger (2 3), so we could have eight times as many processors, and we need eight times as much power input-2,400 watts. However, the surface area is only four times (2 2) larger, so the radiative power would be about 4,000 watts."
"OK, say you want to play Red Dead Redemption in space. Your computer is gonna get hot-maybe 200 F (366 Kelvin). To keep it simple, let's say this is a cube-shaped PC with a total surface area of 1 square meter, and it's a perfect radiator (ε = 1). The thermal radiation power would then be around 1,000 watts. Of course your computer is not a perfect radiator, but it looks like you'd be fine. As long as the output (1,000 watts) is greater than the input (300 watts), it'll cool down."
Radiative power follows the Stefan-Boltzmann relation: emissivity times area times the fourth power of temperature, so hotter objects radiate much more. A cube-shaped 1 m² perfect radiator at 366 K emits roughly 1,000 W, enough to dissipate a 300 W computer. Doubling edge length increases volume eightfold but surface area only fourfold, so heat generation scales faster than radiative capacity; an eight-times-packed system consuming 2,400 W would radiate about 4,000 W, narrowing the margin. Continued scaling makes very large space-based data centers impractical without extensive external radiators covering hundreds to thousands of square meters.
Read at WIRED
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