Blackbody radiation emissive power

Radiation that is emitted by the surface originates from the thermal energy of matter bounded by the surface. The rate at which energy is released per unit area Wjvr ) is determined by the surface emissive power E. For a blackbody the emissive power (representing a theoretical maximum rate) is prescribed by the Stefan-Boltzmann law ... 

Figure 7.3a represents the Planck distribution for blackbody spectral emissive power with E-i p / as a function of XT. The band fraction of emitted energy in the region from 0 to XT is equal to the shaded area, which is expressed as and shown in Figure 7.3b. About a quarter of the emitted energy is at wavelengths shorter than nd nearly 95% of the emitted energy is distributed between and The spectral distribution of solar radiation can be...

BLACKBODY RADIATION EMISSIVITY. As shown later [Eq. (14.10)], a black-body has the maximum attainable emissive power at any given temperature and is the standard to which all other radiators are referred. The ratio of the total emissive power IF of a body to that of a blackbody is by definition the emissivity s of the body. Thus,... 

E = hemispherical emissive power of a blackbody. f = fraction of blackbody radiation lying below X. 

At this point, we consider Equation (A3.1), which is only valid for pure monochromatic incident radiation. As we are dealing with blackbody radiation, we simulate the elemental density of radiation Paidco by monochromatic radiation that has the same power. According to Equation (A3.1), the corresponding probability of elemental transition (absorption or stimulated emission) dP is as follows ... 

In general, the emissivity of a solid is affected by the temperature as well as the wavelength of the radiation. The concept of monochromatic emissivity is related to the radiant emission by a solid at a specific wavelength. The monochromatic emissivity e is defined as the ratio of the monochromatic-emissive power of a solid Ex to the monochromatic-emissive power of a blackbody EbX at the same temperature and wavelength, i.e.,... 

Ebk Monochromatic-emissive power of blackbody radiation Po adsorbate Saturated vapor pressure... 

Blackbody Radiation Engineering calculations involving thermal radiation normally employ the hemispherical blackbody emissive power as the thermal driving force analogous to temperature in the cases of conduction and convection. A blackbody is a theoretical idealization for a perfect theoretical radiator i.e., it absorbs all incident radiation without reflection and emits isotropically. In practice, soot-covered surfaces sometimes approximate blackbody behavior. Let /.V, = /. A... 

The Stefan-Boltzmann law in Eq. 12-3 gives the total blackbody emissive power f. i, which is the sum of the radiation emitted over all wavelengths. Sometimes we need to know the spectral blackbody emissive power, which is the amount of radiation energy emitted by a blackbody at a thermodynamic temperature T per unit time, per unit surface area, and per unit wavelength about the wavelength X. For example, we are more interested in the amount of radiation an incandescent lighthulb emits in the visible wavelength spectrum than we are in the total amount emitted. 

Consider a 20-cm-dlameter spherical ball at 800 K suspended in air as shown in Fig. 12-12. Assuming the ball closely approximates a blackbody, determine a) the total blackbody emissive power, (h) the total amount of radiation emitted by the ball in 5 min, and (c) the spectral blackbody emissive power at a wavelength of. 3 (im. 

SOLUTION An isothermal sphere is suspended in air. The total blackbody emissive power, the total radiation emitted in 5 min, and the spectral blackbody emissive power at 3 p.m are to be determined. 

If all surfaces emitted radiation uniformly in all directions, the emissive power would be sufficient to quantify radiation, and we would not need to deal with intensity. The radiation emitted by a blackbody pet unit nonnal area is the same in all directions, and thus there is no directional dependence. But this is not the case for real surfaces. Before we define intensity, wc need to quantify the size of an opening in space. 

For a blackbody, radiosity J is equivalent to the emissive power j, since a blackbody a,bsorbs the entire radiation incident on it and there is no reflected component ih-Fadiosity. 

Consider a 20-cm X 20-cm X 20-cm cubical body at 750 K suspended in the air. Assuming the body closely approximates a blackbody, determine (a) the rate at which the cube emits radiation energy, in W and (h) the. spectral black-hody emissive power at a wavelength of 4 pm. 

That is, the radiosity of a blackbody is equal to its emissive power. This is expected, since a blackbody does not reflect any radiation, and thus radiation coming from a blackbody is due to emission only. 

The direction of the net radiation heat transfer depends on the relative magnitudes of 7, (the radiosity) and (, (the emissive power of a blackbody at the teinpeiature of the surface). It is from the surface if > 7,- and to the surface if 7f > ft),-. A negative value for ft indicates that heat transfer is to the surface. All of this radiation energy gained must be removed from the other side of the surface through some mechanism if the surface temperature is to remain constant. 

Each surface emits radiation based on its temperature. The ideal radiator is called a blackbody. The rate of energy emission per unit area, tf, is also termed blackbody emissive power, E, and is given by the Stefan-Boltzmann law. 

The blackbody is an ideal surface that absorbs all incident radiation regardless of wavelength and direction. Furthermore, a blackbody is a diffuse emitter and, at any prescribed wavelength and temperature, no surface can emit more energy than a blackbody. The total emissive power of a blackbody depends only on its temperature and is given by the Stefan-Boltzmann law. 

Blackbody radiation is achieved in an isothermal enclosure or cavity under thermodynamic equilibrium, as shown in Figure 7.4a. A uniform and isotropic radiation field is formed inside the enclosure. The total or spectral irradiation on any surface inside the enclosure is diffuse and identical to that of the blackbody emissive power. The spectral intensity is the same in all directions and is a function of X and T given by Planck s law. If there is an aperture with an area much smaller compared with that of the cavity (see Figure 7.4b), X the radiation field may be assumed unchanged and the outgoing radiation approximates that of blackbody emission. All radiation incident on the aperture is completely absorbed as a consequence of reflection within the enclosure. Blackbody cavities are used for measurements of radiant power and radiative properties, and for calibration of radiation thermometers (RTs) traceable to the International Temperature Scale of 1990 (ITS-90) [5]. 

LAWS OF BLACKBO YHRADIATION. A basic relationship for blackbody radiation is the Stefan-Boltzmann law, which states that the total emissive power of a blackbody is proportional to the fourth power of the absolute temperature, or... 

Plots of vs. X from Eq. (14.6) are shown as solid lines in Fig. 14.1 for blackbody radiation at temperatures of 1000, 1500, and 2000°F. The dotted line shows the monochromatic radiating power of a gray body of emissivity 0.9 at 2000. ... 

Thermal radiation emitted by a real body has an irregular wavelength dependence (see Ref. 47). The emissivity is defined to relate the emissive power of a real body, e or e, to that of a blackbody ... 

Measurements of the total emission from a small hole in a heated cavity showed thermal radiation to be proportional to the fourth power of the cavity temperature (Stefan, 1879) Boltzmaim (1884) derived this power law from thermodynamic considerations. Nine years later, Wien (1893) found that the product of the wavelength at the radiation maximum and the cavity temperature was the same for a wide range of temperatures he also proposed an exponential radiation law, which was in good agreement with available measurements at short wavelengths (Wien, 1896). Shortly thereafter, Lummer and Pringsheim (1897,1899) made fairly precise measurements of blackbody emission between 100 °C and 1300 °C. By the end of the nineteenth century an extensive set of experimental evidence was available on the spectral distribution and temperature dependence of blackbody radiation. 

---