Absorptivity hemispherical 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... 

Likewise, the spectral hemispherical absorptivity and. spectral hemispherical reflectivity of a surface arc defined as... 

Example 5.2 The hemispherical spectral absorptivity of a surface which appears bright to the eye is strongly simplified given by... 

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... 

By integrating Eq. 7.23 over all incident directions, the energy absorbed from all directions at a particular wavelength is obtained as hemispherical-spectral absorptivity. 

This relation is known as Kirchhoff s law. Equation 7.27 may be substituted into the various relationships for the integrated emissivity or absorptivity. However, it does not follow that such quantities as directional total, hemispherical-spectral, or hemispherical total emissivity and absorptivity are necessarily equal. In fact, the integrated properties are only equal if certain restrictions are met. These are given in Table 7.1. 

Figure 5 Schematic of experimental setup used to determine (A) the extinction coefficient Px from normal-normal spectral transmittance and (B) the absorption coefficient Kx from normal-hemispherical spectral transmittance.

For an opaque surface, the relationship between the spectral hemispherical reflectivity and the spectral hemispherical absorptivity is... 

Where n is the refractive index, a is the absorption coefficient from the Lambert-Beer law and JE is the Planck function specifying the spectral hemispherical em/ssivity of a black body ... 

Fig. 5.16 shows the spectral irradiance E according to (5.37) for T = 1000 K and T = 5777 K. Here, the proportionality constants c were each chosen so that for both temperatures the maximum of E, which appears at Amax = C2/5T, was the same. The hatched areas in Fig. 5.16 are proportional to the absorbed fraction of the incident radiation flow, whilst the areas under the E curves correspond to the irradiance E. The desired hemispherical total absorptivity a T) is, according to (5.28) and (5.36) the ratio of these areas. For T = 1000 K an absorptivity close to a 2 will be expected. In contrast the largest portion of the solar radiation (T = 5777 K) falls in the region of small wavelengths... 

The hemispherical total absorptivity is not only a property of the absorbing surface. Rather, it depends on the spectral distribution of the incident radiation energy. This is shown by the different values of a for the mainly short-wave solar radiation, in which the absorption properties at small wavelengths are decisive, and for the incident radiation from an earthly source, for which the long-wave portion of the absorption spectrum a (X,T) is of importance. 

Hendricks and Howell [253] measured the spectral normal transmittance and normal hemispherical reflectance of three sample thicknesses each of reticulated partially stabilized zirconia and silicon carbide at pore sizes of 10, 20, and 65 ppi. The measurements covered a spectral range of 400-500 nm. They used an inverse discrete ordinates method to find the spectrally dependent absorption and scattering coefficients as well as the constants appropri-... 

The average absorption and scattering cross-sections Cabs,x and Csca, i of microorganisms suspensions can be experimentally measured using a spectrometer equipped with an integrating sphere. Pint, the spectral normal-normal T j and normal—hemispherical T f, transmissions of several dilute suspensions with different known concentrations are measured, as illustrated in Fig. 5. Here, the scattering phase function Or (0) previously measured for the same suspension is used to correct for various optical effects. 

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