The total radiant intensity B(T ) of a blackbody at the absolute temperature T can be derived by integrating the Planck function over the entire wavelength domain from 0 to∞. Since blackbody radiation is isotropic, the flux density emitted by a blackbody is therefore F = π B(T ) which is proportional to the fourth power of the absolute temperature T through the Stefan-Boltzmann constant σ = 5.67 × 10−8 J m−2 sec−1 deg−4. Kirchoff's law establishes that for a medium at the thermodynamic equilibrium, the emissivity ε of a given wavelength λ (defined as the ratio of its emitting intensity IE to the Planck function B), is equal to the its absorptivity, A at the same wavelength λ (defined as the ratio of its absorbed intensity IA to the Planck function B). Hence ε=A at each fixed λ, for a blackbody ε=A=1 at whatever λ. Kirchoff's law is valid also in Local Thermodynamic Equilibrium (LTE) conditions as the ones usually occurring in (small volumes of) the Earth's atmosphere even in the most turbulent conditions.
Derive the Stefan-Boltzman Law from the Planck's one
Explain the impact of Kirchoff's Law on the measurements of spectral emissivity of opaque bodies
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