Blackbody radiation function

H Calculate the fraction of radiation emitted in a specified wavelength band using Ihc blackbody radiation functions,... 

Therefore, we define a dimensionless quantity /x called the blackbody radiation function as... 

Analysis The visible range of the electromagnetic spectrum extends from A( = 0.4 pm to A2 = 0.76 pm. Noting that T = 2500 K. the blackbody radiation functions corresponding to A, T and Aj Tare determined from Table 12-2 to be... 

Pivovonsky, M. Nagel, M.R. Tables of Blackbody Radiation Functions. New York ... 

S. L. Chang and K. T. Rhee, Blackbody Radiation Functions, International Communications in Heat and Mass Transfer, vol. 11, p. 451,1984. 

If we think in terms of the particulate nature of light (wave-particle duality), the number of particles of light or other electi omagnetic radiation (photons) in a unit of frequency space constitutes a number density. The blackbody radiation curve in Fig. 1-1, a plot of radiation energy density p on the vertical axis as a function of frequency v on the horizontal axis, is essentially a plot of the number densities of light particles in small intervals of frequency space. 

Figure 1-1 The Blackbody Radiation Spectrum. The short curve on the left is a Rayleigh function of frequency.

Contrary to the impression that one might have from a traditional course in introductory calculus, well-behaved functions that cannot be integrated in closed form are not rare mathematical curiosities. Examples are the Gaussian or standard error function and the related function that gives the distribution of molecular or atomic speeds in spherical polar coordinates. The famous blackbody radiation cuiwe, which inspired Planck s quantum hypothesis, is not integrable in closed form over an arbitiar y inteiwal. 

Water Vapor The contribution to the emissivity of a gas containing H9O depends on Tc andp L and on total pressure P and partial pressure p . Table 5-8 gives constants for use in evaluating . Allowance for departure from the special pressure conditions is made by multiplying by a correction factor C read from Fig. 5-21 as a function of (p + P) and p ,L. The absorptivity 0t of water vapor for blackbody radiation is evaluated from Table 5-8 but at T instead of Tc and at p LT /Tc instead of p, h. Multiply by (Tc/Ti)° . ... 

Figure 4.24. The Planck distribution law spectral radiance of blackbody radiation as a function of temperature and wavelength. (After Touloukian and DeWitt (1972). Plenum Press.)...

Fig. 4.8. Efficiency rj, open-circuit voltage Voc, and short-circuit current density jsc as a function of the band gap a of a 2-band system illuminated by blackbody radiation at 5 800 K with an incident energy current density of 1.39 kW/m2...

The Planck theory of blackbody radiation provides a first approximation to the spectral distribution, or intensity as a function of wavelength, for the sun. The black-body theory is based upon a "perfect" radiator with a uniform composition, and states that the spectral distribution of energy is a strong function of wavelength and is pro portional to the temperature (in units of absolute temperature, or Kelvin), and several fundamental constants. Spectral radiant exitance (radiant flux per unit area) is de fined as ... 

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]. 

Figure 3.19 Spectral distribution ofthe intensity of blackbody radiation as a function of frequency for several temperatures. The dashed line is the prediction of classical physics. (Reprinted with permission from University Science Books.) °...

Figure 5.13 Emission intensity of blackbody radiation at various temperatures as a function of wavelength 3000 K is equivalent to a tungsten filament lamp (an incandescent lamp) 6000 K is equivalent to a xenon arc lamp.

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