An air-cooled motorcycle engine loses a significant amount of heat through thermal radiation according to the Stefan-Boltzmann equation. Assume that the ambient temperature is T_{0}=27^{\circ} \mathrm{C}(300 \mathrm{~K}). Suppose the engine generates 15 \mathrm{hp}(11 \mathrm{~kW}) of power and, because there are several deep surface fins, has a surface area of A=0.50 \mathrm{~m}^{2}. A shiny engine has an emissivity e=0.050, whereas an engine that is painted black has e=0.95 . Determine the equilibrium temperatures for the black engine and the shiny engine. (Assume that radiation is the only mode by which heat is dissipated from the engine.)
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