Black body radiation intensity

FIG. 53. Spectral absorption coefficients of sheet glass at various temperatures and spectral distribution of black body radiation intensity in terms of temperature (after Neuroth, 1952 from Garden, 1968),... 

Fractal dimension In gel networks or aggregates of nanoparticles in which the mass M inside any sphere of radius R, about a centre chosen at random in the gel network or aggregate, increases statistically with R as, M k Ef, the number/is usually a noninteger and is termed the fractal dimension. Aerogels are examples of fractal solids Fractional function of the first kind /o-a( ) Fraction of the total black-body radiation intensity having wavelengths between 0 and A... 

Two crucial pieces of experimental information about black-body radiation were discovered in the late nineteenth century. In 1879, Josef Stefan investigated the increasing brightness of a black body as it is heated and discovered that the total intensity of radiation emitted over all wavelengths increases as the fourth... 

For nineteenth-century scientists, the obvious way to account for the laws of black-body radiation was to use classical physics to derive its characteristics. However, much to their dismay, they found that the characteristics they deduced did not match their observations. Worst of all was the ultraviolet catastrophe classical physics predicted that any hot body should emit intense ultraviolet radiation and even x-rays and y-rays According to classical physics, a hot object would devastate the countryside with high-frequency radiation. Even a human body at 37°C would glow in the dark. There would, in fact, be no darkness. 

CANDELA a unit of luminous intensity, defined as 1/60 of the luminous intensity per square centimeter of a black-body radiator operating at the temperature of freezing platinum (1772 °C), Formerly known as a candle. The unit is abbreviated as Cd... 

The Stefan-Boltzmann Law and Wien s Law for black body radiation have been unified into Planck s Law for black body radiation, from which Planck s constant was first introduced. Planck s analysis of the spectral distribution of black body radiation led him to an understanding of the quantisation of energy and radiation and the role of the photon in the theory of radiation. The precise law relates the intensity of the radiation at all wavelengths with the temperature and has the form ... 

Visible astronomy does, however, provide most of the atomic and black body spectra of stars and astronomical objects and is of course appealing to us because the human eye is uniquely adapted to detection in the wavelength range 300-800 nm. The appeal of colour pictures has lead to the development of false colour scales used routinely by astronomers to visualise the intensity of radiation at other wavelengths. The concepts of temperature and colour are linked by the black body radiation and it... 

Figure 9.23 Wien s law and black-body radiation as the temperature T of the black body is raised, so the wavelength maximum of the emitted radiation decreases. The area under the curve indicates the intensity of the energy emitted by the black body, and is proportional to 7 4...

Black body radiators are used as sources of infrared radiation in the range 2-15 yum, e.g. the Nemst glower, which consists of a hollow rod made of the fused oxides of zirconium, yttrium and thorium. For use it is preheated and, when a voltage is applied, it emits intense continuous infrared radiation with very little visible radiation. 

Black-body radiation is the radiation emitted by a black-colored solid material, a so-called black body, that absorbs and also emits radiation of all wavelengths. A black body emits a continuous spectrum of radiation, the intensity of which is dependent on its wavelength and on the temperature of the black body. Though a black body is an idealized system, a real solid body that absorbs and emits radiation of aU wavelengths is similar to a black body. The radiation intensity of a black body, at... 

Fig. 2.2 The intensity of black-body radiation as a function of angular frequency, to, for two different temperatures, and Tz, where T2> . The dashed curve gives the classical Rayleigh-Jeans law at temperature, T2.

Black-body radiation Figure 22 shows the frequency dependence of the intensity of the radiation that is emitted from a black body at two different temperatures, Tx and T2, where T2 > Tv We see that at high frequencies the emitted intensity, /, is much less than that predicted by the Rayleigh-Jeans law, namely... 

LI The Planck Distribution of Black-body Radiation. The Planck relationship between the energy of the photon and the frequency of monochromatic light leads to the equation of distribution of the intensity of light as a function of frequency (or wavelength)... 

Figure 2.10 Examples of the intensity versus wavelength or frequency distribution of black-body radiation according to the Planck equation. Each distribution corresponds to a temperature T of the radiating body...

We have described the effects of black body radiation in free space. In a closed cavity the radiation is confined to the allowed modes of the cavity. In essence all the thermal radiation is forced into the cavity modes, raising the intensity at the... 

The experimental value of the constant is 5.67 X 10 8 W-m 2k 4. A few years later, in 1893, Wilhelm Wien examined the shift in color of black-body radiation as the temperature increases and discovered that the wavelength corresponding to the maximum in the intensity, max, is inversely proportional to the temperature, Xmax °c I IT, and therefore that max X T is a constant (Fig. 1.6). This quantitative result is now called Wien s law and is normally written... 

Einstein s derivation of the black-body radiation law is particularly important, for it gives us an insight into the kinetics of radiation processes. Being a kinetic method, it can be used even when we do not have thermal equilibrium. Thus if we know that radiation of a certain intensity is falling on atoms, we can find how many will be raised to the excited state per second, in terms of the coefficient Bn. But this means that we can find the absorptivity of matter made of these atoms, at this particular wave length. Conversely, from measurements of absorptivity, we can deduce experimental values of Bn. And from Eq. (2.8) we can find the rate of emission, or the emissive power, if we know the absorptiv-... 

If the vibrational temperature is determined by using the intensities of different bands, a distinct value is obtained for each band. These values do not represent the arithmetic mean of all temperatures. Due to the nonlinear increase of the spectral radiance by the black body radiator, the hot zones appear more pronounced than the cold ones. On the other hand, the influence of the more distant zones with respect to the observer is reduced by stronger self-absorption. The vibrational temperatures deduced from bands with high absorption coefficient are therefore lower than those derived from bands with smaller absorption coefficient. Nevertheless, all thus obtained temperature values are between the lowest and the highest temperature of the sample. The method of fitting calculated spectral profiles to the observed ones has been successfully applied in these cases, too. 

Black-body sources have the attraction of being primary standards but are rather cumbersome. A quite hot furnace is required to produce sufficient intensity, particularly at visible wavelengths. In addition, the source is usually too large to be positioned near the sample region (assuming the spectrometer could tolerate the heat ), so coupling optics are required. These optics should attempt to position the source image at the normal laser and collection focus and may not introduce their own response function. At least for routine use, a black-body radiator is unlikely to be practical. 

The equality of the three pairs of absorptivities and emissivities, namely ax(X,T) = ex(X,T), a (/3,ip,T) = j3,ip,T) and a(T) = e(T), is only given if the absorbing and emitting surfaces have particular properties, or if the incident spectral intensity Kx of the radiation satisfies certain conditions in terms of its directional and wavelength dependency. These conditions are satisfied by incident black body radiation, when the black body is at the same temperature as the absorbing body, which does not apply for heat transfer. In practice, the more important cases are those in which the directional spectral emissivity e x of the absorbing body at least approximately satisfies special conditions. We will once again summarise these conditions ... 

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