Blackbody radiation spectral emissive power

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...

Other past studies of several radiant sources have yielded information on the variation of radiation intensity with monochromatic wavelength ". Figure 1 illustrates the emissive powers of solar, tungsten lamp, and hexane flame radiation. The manufacturer of the tungsten lamp indicated that the emissive power of the lamps is essentially that of a blackbody at 2500 K, it provides a maximum peak at 1.15 microns 12. The spectral emissive power of the hexane flame and other hydrocarbons was measured by Ryan,... 

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. 

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. 

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]. 

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. 

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