Absorptivity directional spectral

These definitions are for lolol hemispherical properties, since G represents the radiation flux incident on tlic surface from all directions over the hemi spherical space and over all wavelengths. Thus, a, p, and t are the average properties of a medium for all directions and all wavelengths. However, like einissivity, these properties can also be defined for a specific wavelength and/or direction. For example, the spectral directional absorptivity and spectral directional reflectivity of a surface are defined, respectively, as the absorbed and leflected fractions of the intensity of radiation incident at a specified wavelength in a specified direction as... 

The two material functions r x and a x of an opaque body are not independent of each other. The directional spectral reflectivity r x is determined by the directional spectral absorptivity a x. The similar relationship between the different absorptivities and reflectivities from Tables 5.1 and 5.2, respectively, mean that equations analogous to (5.41) are valid, with which the three other reflectivities can be found from the corresponding absorptivities. 

A small body is located in the enclosure that, once thermodynamic equilibrium has been reached, assumes the same temperature T as the walls, Fig. 5.20. This body shall have the special property that it completely absorbs all incident radiation from every direction at every wavelength. Its directional spectral absorptivity is (independent of A, / ,

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Fig. 5.21 Body with any directional spectral absorptivity a x in an adiabatic enclosure...

The directional spectral absorptivity of a any radiator agrees with its directional spectral emissivity. 

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. 

The equality of the three pairs of absorptivities and emissivities, namely ax(X,T) = ex(X,T), a (/3,ip,T) = j3,ip,T) and a(T) = e(T), is only given if the absorbing and emitting surfaces have particular properties, or if the incident spectral intensity Kx of the radiation satisfies certain conditions in terms of its directional and wavelength dependency. These conditions are satisfied by incident black body radiation, when the black body is at the same temperature as the absorbing body, which does not apply for heat transfer. In practice, the more important cases are those in which the directional spectral emissivity e x of the absorbing body at least approximately satisfies special conditions. We will once again summarise these conditions ... 

The enclosure schematically illustrated in Fig. 5.70 contains a homogeneous gas mixture with an absorbent component. The element dA on the surface of the gas volume, shown in Fig. 5.70, will be used for the definition and calculation of its directional spectral absorptivity a XG. The radiation emitted from dA, with the spectral intensity Lx, is weakened by absorption. Depending on the direction, the path through the gas is of different lengths, which according to (5.179) leads to varying reductions in Lx. 

The directional spectral absorptivity is a property (variable of state) of the absorbing gas. Its direction dependence manifests itself in the dependence on the beam length s, through which the radiation passes in the gas. 

The absorptivity is a property that determines the fraction of the irradiation that is absorbed by a surface. The directional spectral absorbtivity of a surface is defined as the fraction of the spectral intensity incident in the direction of 9 and that is absorbed by the surface ... 

Kirchhoff s Law. Through an energy balance at thermodynamic equilibrium, it can be shown that the directional-spectral emissivity is always equal to the directional-spectral absorptivity of a surface, or... 

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