Blackbody Displacement Laws

Blackbody Displacement Laws The blackbody energy spectrum 

Percentage of total blackbody energy found below XT, Fb (XT) 

5-9 Spectral dependence of monochromatic blackbody hemispherical emissive power. 

3140°F), wavelengths of engineering heat-transfer importance are bounded between 0.83 and 54.3 pm. 

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The Wien displacement law states that the wavelength of maximum emission, A , of a blackbody varies inversely with absolute temperature the product A T remains constant. When A is expressed in micrometers, the law becomes... 

Blackbody Emittance. Representative blackbody emittance (9,10), calculated as a power spectral density, is shown in Figure 2. The wavelength, X, of peak power density for a blackbody at temperature, T, is given by Wien s displacement law ... 

As seen in Eq. (17-1), the total radiation from a blackbody is dependent on the fourth power of ifs absolute temperature. The frequency of the maximum intensity of this radiation is also related to temperature through Wien s displacement law (derived from Planck s law) ... 

Wien displacement law Approximate formula for the wavelength, X, of maximum blackbody emission Xmax - T hc/5k — 2.878 X 10" 3 m K, where T is temperature in kelvins, h is Planck s constant, c is the speed of light, and k is Boltzmann s constant. Valid for T > 100 K. working electrode One at which the reaction of interest occurs. 

The sun s total radiation output is approximately equivalent to that of a blackbody at 10,350°R (5750 K). However, its maximum intensity occurs at a wavelength that corresponds to a temperature of 11,070°R (6150 K) as given hy Wien s displacement law. A figure plotting solar irradiance versus spectral distribution of solar energy is given in Fig. 9. See also Solar Energy. 

Figure 8.3 Spectral radiant power (per unit time per unit area) distribution of a blackbody at various temperatures. Note that the maximum intensity, even at 3500 K, is still in the infrared region of the spectrum. The displacement of the maximum of the radiant energy shifts linearly with absolute temperature (dotted lines) in accordance with Wein s displacement law.

It is quite apparent from Fig. 8-63 that solar radiation which arrives at the surface of the earth does not behave like the radiation from an ideal gray body, while outside the atmosphere the distribution of energy follows more of an ideal pattern. To determine an equivalent blackbody temperature for the solar radiation, we might employ the wavelength at which the maximum in the spectrum occurs (about 0.5 /im, according to Fig. 8-63) and Wien s displacement law [Eq. (8-13)]. This estimate gives... 

If we know the surface temperature of a blackbody, we can predict the wavelength for maximal radiation from it. To derive such an expression, we differentiate Planck s radiation distribution formula with respect to wavelength and set the derivative equal to zero.4 The relation obtained is known as Wien s displacement law ... 

We start this chapter with a discussion of eiectromaguetir. waves and the electromagnetic spectniiii, with particular emphasis on thermal radiation. Then we introduce the idealized blackhody, blackbody radiation, and black-body radiation ftinciion, together with the Sle/ati-Bolizniariii law, Planck s law, and Wien s displacement law. 

The Wien displacement law states that the wavelength maximum in micrometers for blackbody radiation is... 

Q.7.4 Show that (a) the Rayleigh-Jeans law is a special case of Planck distribution law for the blackbody spectrum. Show also that (b) the Wein displacement law can be derived from Planck s distribution law. 

The Wien displacement law for blackbody radiators states that the product of temperature in kelvin and the wavelength of maximum emission is a constant k k - T - Calculate the wavelength of maximum emission for a Globar infrared source operated at 18(X) K. Use the data In Figure 6-22 for the Nernst glower for the evaluation of the constant. 

I he Wien displacement law slates that the wavelength nia.xinilim in micromeiers tor blackbody radiation is given by Ihe relaiionship... 

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.

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