Winston Blake wrote:Well, 14.6e21 J per day is only equivalent to 18 Acclamator 200 gigaton TL shots per day. As the Hoth ion cannon showed, planetary installations have much greater power resources than ship-based weaponry, so it's plausible that a single installation periodically sends enough energy into space (say, into the sun) to make Coruscant a significantly open system.
My problem with that explanation is that we're
not talking about the well-behaved energy from a reactor here, but
heat, and heat is an unruly beast. I don't care how advanced the SW galaxy is; I expect thermodynamics to apply there as it does here.
The lowest entropy that 14.6e21 J can be at is evenly spread about the planet (a quick calculation shows that, and given a nearly even spread of population about Coruscant, the actual state would be near that). It takes five-star energy (which has to be generated) to shove it to one spot to be radiated to space.
If we concentrate the heat produced by the planet into a concentrated area, say a one-kilometer radius disk on Coruscant (3.141e6 m^2), then to radiate 169.531250e15 W over this area, we need an irradiancy of 53.963e9 W/m^2. Stefan-Boltzmann gives the necessary temperature as 31,233 K. To transfer 169.531250e15 W of heat into this area requires at least 18.279840e18 W of power. If your power generation efficiency is any less than 99.08%, then you're right back where you started or worse. I can see the Coruscantians looking at each other and thinking, "There's gotta be a better way than this!"
Notice that I didn't specify the nature of the radiator. This also applies to the snazzy neutrino radiators; they would work by dispersing heat into the (much colder) neutrino shower of space. The radiators still have a temperature, just that its thermal conductivity with ordinary matter is poor with respect to the neutrino shower.
If the neutrino radiators are scattered about the planet (say one major radiation facility per square kilometer), then the problem is much less pronounced, as we are not fighting heat's natural tendency to spread out (at least, not as badly). Thus, every square kilometer gets a (say) a dedicated 100 m square footprint building 2 km high neutrino radiator (1.2 km^2). Since each square meter of the planet has to radiate a net of 1,326.516 W/m^2, each neutrino radiator would have a heat dissipation rate of 1.326e9 W, which means that its neutrino temperature is a mere 373.66 K, which means that we minimum energy we need to consume to move heat to the radiators is a mere 51.19e15 J each day. That's much nicer, but this is not including the heat produced making the energy we need to run the radiators. A little dithering will find the correct neutrino temperature for the population.
On the other hand, if your food-growing farming planets are going to continue providing food for Coruscant for a long time, you'd better be exporting your waste to those planets to fertilize them. (It also makes good business sense, since you're selling back the farming planets' own nutrients!
) In this case, you're spending a lot of energy to lift a bunch of matter to orbit
anyway, so this cost is already paid. Thus, when you export the waste, it could also be worth your while to export heat along with it.
EDIT: The work figures were actually total amount of heat pushed into the radiators.
(For the thermodynamically impared, when you pump heat out of a cool place into a warm place, the energy you need to drive the heat pump goes into the hot resivour as more heat. My previous figures were the total heat pumped into the radiators, not the power you need to drive that heat to the radiators) This has been corrected.
EDIT 2: Miscelleneous clarification. Feh.