Consider a Carnot-cycle heat engine operating in outer space. Heat can be rejected from this…

Consider a Carnot-cycle heat engine operating in outer space. Heat can be rejected from this engine only by thermal radiation. The rate at which heat is transferred by thermal radiation is proportional to the fourth power of the absolute temperature and to the area of the radiating surface. Show that for a given output of engine power and a given T H, the area of the radiator will be minimum when the ratio

 

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