Emissive power black body

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 ... 

The emissive power of a fireball, however, will depend on the actual distribution of flame temperatures, partial pressure of combustion products, geometry of the combustion zone, and absorption of radiation in the fireball itself. The emissive power ( ) is therefore lower than the maximum emissive power (E ) of the black body radiation ... 

If the emissive power E of a radiation source-that is the energy emitted per unit area per unit time-is expressed in terms of the radiation of a single wavelength X, then this is known as the monochromatic or spectral emissive power E, defined as that rate at which radiation of a particular wavelength X is emitted per unit surface area, per unit wavelength in all directions. For a black body at temperature T, the spectral emissive power of a wavelength X is given by Planck s Distribution Law ... 

In this way, ihe emissive power of a grey body is a constant proportion of the power-emitted by the black body, resulting in the curve shown in Figure 9.35 where, for example, e = 0.6. The assumption that the surface behaves as a grey body is valid for most engineering calculations if the value of emissivity is taken as that for the dominant temperature of the radiation. 

For a grey body, the emissivity and the absorptivity are, by definition, independent of temperature and hence equation 9.115 may be applied more generally showing that, where one radiation property (a, r or e) is specified for an opaque body, the other two may be obtained from equations 9.115 and 9.124. KirchofPs Law explains why a cavity with a small aperture approximates to a black body in that radiation entering is subjected to repeated internal absorption and reflection so that only a negligible amount of the incident radiation escapes through the aperture. In this way, a - e = 1 and, at T K, the emissive power of the aperture is aT4. 

Equations similar to equation 9.158 may be obtained for each of the surfaces in an enclosure, 1 = 1,1 = 2, 1 = 3, 1 = n and the resulting set of simultaneous equations may then be solved for the unknown radiosities, qoi,qm- qun The radiation heat transfer is then obtained from equation 9.140. This approach requires data on the areas and view factors for all pairs of surfaces in the enclosure and the emissivity, reflectivity and the black body emissive power for each surface. Should any surface be well insulated, then, in this case, Qj — 0 and ... 

Shokri and Beyler correlated experimental data of flame radiation to external targets in terms of an average effective emissive power of the flame (Shokri and Beyler, 1989). The flame is assumed to be a cylindrical, black body radiator with an average emissive power, diameter (D), and height (T/f), see Figure 5-9. 

The total emission of radiant energy from a black body takes place at a rate expressed by the Stefan-Boltzmann (fourth-power) lav/ while its spectral energy distribution is described by Wien slaws, ormore accurately by Planck s equation, as well as by a n umber of oilier empirical laws and formulas, See also Thermal Radiation,... 

Equation 6.44 gives the total power emitted by a black body. However, materials and bodies whose temperatures are measured with radiation-type instruments often deviate considerably from ideal black body behaviour. This deviation is expressed generally in terms of the emissivity e of the measured body (see also Volume 1, Section 9.5.4), and the energy emitted by the body per unit area per unit time is ... 

Now that we understand the emissive power and absorptivity of bodies, we should consider Jx, the universal function of wave length and temperature describing black-body radiation. It is a little more convenient not to use this quantity, but a closely related one, u . This represents, not the energy falling on 1 sq. cm. per second, but the energy contained in a cubic centimeter of volume, or what is called the energy... 

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-... 

The emissive power of a body E is defined as the energy emitted by the body per unit area and per unit time. One may perform a thought experiment to establish a relation between the emissive power of a body and the material properties defined above. Assume that a perfectly black enclosure is available, i.e., one which absorbs all the incident radiation falling upon it, as shown schematically in Fig. 8-4. This enclosure will also emit radiation according to the T law. Let the radiant flux arriving at some area in the enclosure be q, W/m2. Now suppose that a body is placed inside the enclosure and allowed to come into temperature equilibrium with it. At equilibrium the energy absorbed by the body must be equal to the energy emitted otherwise there would... 

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. 

Thus the energy density of the radiation in a Prevost chamber and the emissivity of a perfect black body are both proportional to the fourth power of the absolute temperature. The constant (T is of universal significance, and applies to all black bodies of whatever materials they may be composed. 

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). 

Emissivity is numerically equal to absorptivity. As emissive power varies with wavelength, the ratio should be quoted at a particular wavelength for many materials. However, the emissive power is a constant fraction of the black body radiation, that is, the emissivity is constant. These materials are known as gray bodies. 

The second fundamental law of radiation, known as the Stefan-Boltzmann law, states that the rate of energy emission from a black body is proportional to the fourth power of the absolute temperature T, as shown by Eq. (38)... 

An emitter, whose emissive power, or heat flux emitted by radiation, reaches the maximum value qs in (1.58), is called a black body. This is an ideal emitter whose emissive power cannot be surpassed by any other body at the same temperature. On the other hand, a black body absorbs all incident radiation, and is, therefore, an ideal absorber. The emissive power of real radiators can be described by using a correction factor in (1.58). By putting... 

The wavelength and temperature dependency given by (5.37) correspond to a relationship found by W. Wien [5.3] in 1896 to be approximately valid for the hemispherical spectral emissive power M S(X,T ) of an ideal radiator, a black body, with a temperature T. We will come back to the properties of black bodies in section 5.1.6 and more extensively in 5.2.2. In our example a spectral irradiance E M s has been assumed, so that its indirect dependence on T appears explicitly in (5.37). 

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. 

A black body is defined as a body where all the incident radiation penetrates it and is completely absorbed within it. No radiation is reflected or allowed to pass through it. This holds for radiation of all wavelengths falling onto the body from all angles. In addition to this the black body is a diffuse radiator. Its spectral intensity LXs does not depend on direction, but is a universal function iAs(A,T) of the wavelength and the thermodynamic temperature. The hemispherical spectral emissive power MXs(X,T) is linked to Kirchhoff s function LXs(X,T) by the simple relationship... 

We refrain from deriving the equations for the spectral intensity and the hemispherical spectral emissive power of a black body, found by M. Planck [5.6], for... 

Fig. 5.23 Hemispherical spectral emissive power MXs(X,T) of a black body according to Planck s radiation law (5.50)...

The emissive power of a black body in a medium with a refractive index n will be... 

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