Question

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 T0 = 24.5°C (297.65 K). Suppose the engine generates 11.5 hp (8.58 kW) of power and, due to several deep surface fins, has a surface area of A = 0.540 m2. A shiny engine has an emissivity e = 0.0550, whereas an engine that is painted black has e = 0.950.

a) Determine the equilibrium temperature (in K) for the shiny engine. (Assume that radiation is the only mode by which heat is dissipated from the engine.)
b) And determine the equilibrium temperature (in K) for the black engine.