Solar Engineering a Condensed Course

16Blackbody radiationAn ideal blackbody absorbs and emits the maximum amount of radiation: Cavity 100 %,"pitch black" 99 %, "black" paint 90-95 %.Planck's radiation lawThermal radiation has wavelengths between 0.2 µm (200 nm) and 1000 µm (1 mm). Thespectrum of blackbody radiation is, according to Planck:dEC1= Eλ b=(2.1.3)5∂A∂λλ [ exp( C2/ λT) −1]where C 1 = 3.74⋅10 -16 [m 2 W] and C 2 = 0.0144 [m⋅K].Wien's displacement lawDerivation of Planck's radiation law gives Wien's displacement law:λ max ⋅T = 2898 [µm⋅K]. (2.1.4)Stefan-Boltzmann's radiation lawIntegration of Planck's radiation law gives Stefan-Boltzmann's radiation law:dEdAσ4= Eb= T(2.1.5)where Stefan-Boltzmann's constant σ = 5.67⋅10 -8 [W/m 2 ,K 4 ].Radiation tablesThe blackbody spectrum is tabled in Appendix 1.Table 1 gives the fraction of blackbody radiant energy ∆f between previous λT and presentλT [µm K] for different λT-values.Table 2 gives the fraction of blackbody radiant energy ∆f between zero and λT [µm K] foreven fractional increments.Exercise 2.1.1Assume the sun is a blackbody at 5777 K. (a) What is the wavelength at which the maximummonochromatic emissive power occurs? (b) At what wavelength λ m is half of the emittedradiation below λ m and half above λ m (λ m = "median wavelength").