An electrically heated sample is maintained at a surface temperature of T_s = 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 L_sf = 750 mm. The furnace has isothermal walls with an emissivity of ?_? = 0.7 and a uniform temperature of T_? = 3000 K. A radiation detector of area Ad = 8 X 10^-5 m² is positioned at a distance of L_sd = 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 5?m. The sample surface experiences convection with a gas for which T_? = 300 K and h = 20 W/m². K. The surroundings of the sample mount are large and at a uniform temperature of T_sur = 300 K.

(a) Determine the electrical power, Pe, required to maintain the sample at T_s = 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 5?m.

Furnace. isothermal walls 4 = 0.7 7= 300 K T,- 3000 K. D, = 25 mm ,= 8 x 10* m La= 750 mm L =1 m Inert Gas 0, = 45 0.8 T- 300 K A= 20 Wim-K! -T = 500 K D- 20 mm, E, 0.2 Sampie mount with electrical heater (um)