Calculation of absorptivities from emissivities

The equality resulting from Kirchhoff s law between the directional spectral absorptivity and the emissivity, aA = eA, suggests that investigation of whether the other three (integrated) absorptivities aA, a and a can be calculated from the corresponding emissivities sx, s and e should be carried out. This will be impossible without additional assumptions, as the absorptivities ax, a and a are not alone material properties of the absorbing body, they also depend on the incident spectral intensity Kx of the incident radiation, see Table 5.1. The emissivities sx, s and s are, in contrast, purely material properties. An accurate test is therefore required to see whether, and under what conditions, the equations analogous to (5.69), ax = sx, a = s and a = e are valid. 

If the hemispherical spectral absorptivity and emissivity shall agree, ax X,T) = sx(X,T), then according to Table 5.1 and 5.4 the equation 

The body has a diffuse radiating surface (Lambert radiator) then eA = eA(A, T) is valid. 

If the directional total absorptivity a equals the directional total emissivity, a (/3,tp,T) = then according to Tables 5.1 and 5.4 

The directional spectral emissivity is independent of the wavelength A sA = s x(f3,cp,T). A body with this property is called a grey body or a grey radiator. 

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