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nineeyes

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Consider an engine in outer space which operates on the Carnot cycle. The only way in which heat can be transferred from the engine is by radiation. The rate at which heat is radiated is proportional to the fourth power of the absolute temperature and the area of the radiating surface ([tex]Q_L[/tex] is proportional to [tex] A(T_L)^4[/tex]). Show that for a given power output and a given [tex]T_H[/tex] the area of the radiator will be an minimum when [tex]T_L/T_H=3/4[/tex] .

I was guessing I need to try to show Q_L is a minimum using the given ratio. I can find the efficiency but after fooling around with it a few times in some equations I haven't come up with much, I generally have problems when few numbers are provided.

Any hints that can be provided would be great, Thanks!