Radiant spectral emittance

According to the Planck theory of black-body radiation, the radiant spectral emittance is given by the formula... 

The spectral emittance is defined as the ratio of the radiant power per unit area leaving the surface of a body at some given wavelength to that leaving a blackbody at the same temperature. The spectral emittance can be determined practically by comparing the observed or apparent surface temperature of a material with that of a blackbody cavity existing in the same material. The normal spectral emittance is a special case in which the viewing direction is normal to the smooth, opaque surface of the crystalline material. Emissivity is a property of the surface of real specimens. 

The emissivity, S, is the ratio of the radiant emittance of a body to that of a blackbody at the same temperature. Kirchhoff s law requires that a = e for aH bodies at thermal equHibrium. For a blackbody, a = e = 1. Near room temperature, most clean metals have emissivities below 0.1, and most nonmetals have emissivities above 0.9. This description is of the spectraHy integrated (or total) absorptivity, reflectivity, transmissivity, and emissivity. These terms can also be defined as spectral properties, functions of wavelength or wavenumber, and the relations hold for the spectral properties as weH (71,74—76). 

The inclusion of radiative heat transfer effects can be accommodated by the stagnant layer model. However, this can only be done if a priori we can prescribe or calculate these effects. The complications of radiative heat transfer in flames is illustrated in Figure 9.12. This illustration is only schematic and does not represent the spectral and continuum effects fully. A more complete overview on radiative heat transfer in flame can be found in Tien, Lee and Stretton [12]. In Figure 9.12, the heat fluxes are presented as incident (to a sensor at T,, ) and absorbed (at TV) at the surface. Any attempt to discriminate further for the radiant heating would prove tedious and pedantic. It should be clear from heat transfer principles that we have effects of surface and gas phase radiative emittance, reflectance, absorptance and transmittance. These are complicated by the spectral character of the radiation, the soot and combustion product temperature and concentration distributions, and the decomposition of the surface. Reasonable approximations that serve to simplify are ... 

The heat generated heats up carbon black to a temperature -2200 K, yielding radiant emittance values comparable to a black body. Magnesium-rich formulations yield some extra energy by atmospheric oxidation or vaporized Mg in the gas phase. In addition, carbon oxidized to carbon dioxide provides additional radiant energy. Thus MTV spectral distribution displays the peak maximum at 2.0 p and strong emission bands at 4.3 p due to carbon dioxide. 

There is a maximum amount of radiant energy emitted by a body at a given absolute temperature T at a wavelength X. This maximum amount of radiant emission is the spectral blackbody radiation intensity Ixb(T) the emitter of such radiation is named a blackbody. This spectral blackbody radiation intensity is independent of direction. For a blackbody at an absolute temperature T and emitting radiative energy into a vacuum, I. b(T) is calculated from the relation given by Planck, 1959 [1], in the form... 

The emissive power E is the total radiant power exitent from the surface (per unit area) toward the hemisphere due to thermal emission, which may be obtained by integrating dq in Equation (7.3) over the hemisphere and over aU wavelengths. The spectral emissive power is the emissive power per unit wavelength interval about X. If the emitted intensity is the same in all directions, the surface is called a diffuse emitter, for which E = nl and Ex = nli. 

Table A4 Spectral and integrated radiant emittance for some metals and oxides [2, 3]...

The amount of energy emitted per wavelength, the spectral radiant emittance, Mx, is given by Planck s law,... 

The total radiant emittance (the spectral radiant emittance summed over all wavelengths) is equal to the area under the curve. The Stefan-Boltzmarm law is an empirical law that relates the total radiant emittance to the absolute temperature of the black body ... 

Planck was able to achieve agreement with experimental data by choosing a value of h approximately equal to the presently accepted value, 6.62608 x 10 Js. Planck s formula agrees with the Stefan-Boltzmann law and with Wien s law, which states that the wavelength at the maximum in the spectral radiant emittance curve is inversely proportional to the absolute temperature. 

Show that the wavelength of maximum spectral radiant emittance is inversely proportional to the absolute temperature and find the proportionality constant. 

Interstellar space is hlled with isotropic radiation that corresponds to black-body radiation with a temperature of 2.736 K. Find the wavelength of maximum spectral radiant emittance of black-body radiation at this temperature and construct a graph of the spectral radiant emittance as a function of wavelength for this temperature. 

Figure 5 Spectral characteristics of blackbody radiation. The spectral radiant emittance is plotted as a function of the wavelength for several values of the absolute temperature. The slartted, dashed line indicates Wien s displacement law.

---