Question: Consider a Carnot cycle heat engine operating in outer space. Heat can be rejected from this engine onl by thermal radiation, which is proportional to

Consider a Carnot cycle heat engine operating in outer space. Heat can be rejected from this engine onl by thermal radiation, which is proportional to the radiator area and the fourth power of absolut temperature, Qrad

= K A T^{4} .

Show that for a given engine work output and given

T_{H},

the radiator area wi be minimum when the ratio

\frac{T_{L}}{T_{H}} = \frac{3}{4} .

Consider a Carnot cycle heat engine operating in

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