Solve the following problem:
Q: An electrically heated sample is maintained at a surface temperature of Ts = 500 K. The sample coating is diffuse but spectrally selective, with the spectral emissivity distribution shown schematically. The sample is irradiated by a furnace located coaxially at a distance of Lsf = 750 mm. The furnace has isothermal walls with an emissivity of eA? = 0.7 and a uniform temperature of TA? = 3000 K. A radiation detector of area Ad = 8 X 10-5 m2 is positioned at a distance of Lsd = 1.0 m from the sample along a direction that is 45° from the sample normal. The detector is sensitive to spectral radiant power only in the spectral region from 3 to 5µm. The sample surface experiences convection with a gas for which T8 = 300 K and h = 20 W/m2. K. The surroundings of the sample mount are large and at a uniform temperature of Tsur = 300 K.
(a) Determine the electrical power, Pe, required to maintain the sample at Ts = 500 K.
(b) Considering both emission and reflected irradiation from the sample, determine the radiant power that is incident on the detector within the spectral region from 3 to 5µm.
