Emissive of a black body

E), and Ay are functions of the chemical properties of the body and of the wave length, but their ratio at constant temperature is solely a function of the wave length, and is equal to the emissivity of a black body for the same wave length. The black body has therefore the greatest emissivity of all bodies for all wave lengths. 

The emissivity of a black body is therefore given by the equa-... 

The final problem of the theory of radiation is the determination of the emissivity of a black body for any wave length as a function of the wave length and the temperature in other words,... 

The emissivity of a black body is proportional to the radiation density and hence the amount of energy radiated is proportional to the fourth power of the absolute temperature, which is Stefan s law for total radiation... 

Electromagnetic radiation in thermal equilibrium within a cavity is often approximately referred to as the black-body radiation. A classical black hole is an ideal black body. Our own star, the Sun, is pretty black A perfect black body absorbs all radiation that falls onto it. By Kirchhoff s law, which states that a body must emit at the same rate as it absorbs radiation if equilibrium is to be maintained , the emissivity of a black body is highest. As shown below, the use of classical statistical mechanics leads to an infinite emissivity from a black body. Planck quantized the standing wave modes of the electromagnetic radiation within a black-body cavity and solved this anomaly. He considered the distribution of energy U among A oscillators of frequency... 

Within this system of classification by substance name, there exists a class of pertinent information for which no specific substance name would be appropriate, e.g., Theory of the Thermal Conductivity of Gases or New Technique for the Viscosity Measurement of Liquids or Emissivity of a Black-Body Cavity. Literature covering this class of publications is not reported in this volume but is available at TPRC and a special computer search and retrieval can be made upon request. 

The color of a star is a measure for its temperature, blue stars are hotter than red stars. This is a consequence of Wien s law that states that the peak of emission of a black body shifts toward shorter wavelengths when the temperature is higher ... 

Both emission and absorption processes rely on the background radiation, which is present throughout the universe and which has a wavelength distribution characteristic of a black body and a temperature of about 2.7 K. This radiation is a consequence of the big bang with which the universe supposedly started its life. 

Nonblack or nongrey bodies are characterized by wavelength dependence of their spectral emissivity. Let be defined as the temperature of the body corresponding to the temperature of a black body. If the ratio of its radiant intensities at the wavelengths Xi, and Xo equals... 

Emissive power is the total radiative power leaving the surface of the fire per unit area and per unit time. Emissive power can be calculated by use of Stefan s law, which gives the radiation of a black body in relation to its temperature. Because the fire is not a perfect black body, the emissive power is a fraction (e) of the black body radiation ... 

Emissivity Table 15.5 shows the total heat emissivity of various aluminium surfaces, as a percentage of that of a black body. The figures have been recalculated from the data of Hase. The emissivity of anodised aluminium rises rapidly with film thickness up to 3 fim after which the rate of increase diminishes. 

The plot of CE = Pout/Ps (from Eqs (5.10.33) and (5.10.37)) versus Ag for AM 1.2 is shown in Fig. 5.65 (curve 1). It has a maximum of 47 per cent at 1100 nm. Thermodynamic considerations, however, show that there are additional energy losses following from the fact that the system is in a thermal equilibrium with the surroundings and also with the radiation of a black body at the same temperature. This causes partial re-emission of the absorbed radiation (principle of detailed balance). If we take into account the equilibrium conditions and also the unavoidable entropy production, the maximum CE drops to 33 per cent at 840 nm (curve 2, Fig. 5.65). 

Turning now to the wavelength distribution of the starlight. The emission from a black body must, by definition, produce radiation at all wavelengths, i.e. a wavelength distribution. It turns out for a black body that the wavelength at which the maximum radiation flux occurs is characteristic of the temperature and is given by Wien s Law ... 

In contrast to line and band emissions, the emissivity of a hot body can be a function of temperature only. Hence, after absorbing incident radiation, the hot body re-emits a spectrum dependent on its surface temperature, which is known as black body radiation. 

Figure 3.4-3 a Infrared absorption spectrum of butadiene at a pressure of 107 mbar at room temperature, thickness 10 cm b infrared emission spectrum of the same sample at T = 800 K compared to the emission spectrum of a black body of 800 K, recorded with Lcitz prism spectrometer (Gutberlet, 1978). 

Fig. 3.4-3 shows the infrared emission spectrum (the spectral radiance) of a sample of butadiene gas alp = 107 mbar in a cuvette v, th a thickness of 10 cm at 800 K, compared to the emi.ssion spectrum of a black body at the same temperature. It is interesting to note that - as theory predicts - the percentage emission of butadiene compared to that of a black body almost equals the percentage absorption of the same gas at room temperature as recorded with an ordinary spectrometer. 

A very interesting alternative to using hot sources or samples and cold detectors is to record IR spectra with a cooled sample and a detector at room temperature. The same equations are valid, but the features of the sample can be measured with a higher resolution (Mink and Keresztury, 1988). If the thickness of a sample for emission spectroscopy is too large, then its spectrum approaches that of a black body. In this case, a steep thermal gradient is imposed upon the sample heating the front and cooling the back, or vice versa can help resolve the spectral features of thin layers (Jones and McClelland, 1989). 

Figure 3.5-14 Thermal emission Relative signal, recorded by a Germanium detector of a sample, thickness 1 cm, with the absorption properties of water (broken lines) and of a black body (full lines) in the range of the Raman spectrum excited with the Nd YAG laser at 1064 nm.

These laws apply, however, only to bodies in vacuo or in the same homogeneous medium. The emissivity of two black bodies in two different media A and B of refractive index and %... 

For a black body, <2 = 1. The emissive power is therefore E. The black body is a perfect radiator and is used as the comparative standard for other surfaces. The emissivity e of a surface is defined as the ratio of the emissive power E of the surface to the emissive power of a black body at the same temperature Eh, as shown by Eq. (37). 

For metallic surfaces (emissivity close to 0.1), heat transfer can be as low as 5% compared to that of black bodies (e=l). We also see that for materials such as silicon and WSix (e is about 0.6), heat transfer can be quite efficient and the radiation is about 50% of that of a black body (emissivity 1.0). 

Hollow enclosure radiation and radiation of a black body (a x = 1) have identical properties. The black body radiates diffusely from (5.18) it holds for its hemispherical spectral emissive power that... 

This is the law from G.R. Kirchhoff [5.5] Any body at a given temperature T emits, in every solid angle element and in every wavelength interval, the same radiative power as it absorbs there from the radiation of a black body (= hollow enclosure radiation) having the same temperature. Therefore, a close relationship exists between the emission and absorption capabilities. This can be more simply expressed using this sentence A good absorber of thermal radiation is also a good emitter. 

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