Black-body conditions

The last point is worth considering in more detail. Most hydrocarbon diffusion flames are luminous, and this luminosity is due to carbon particulates that radiate strongly at the high combustion gas temperatures. As discussed in Chapter 6, most flames appear yellow when there is particulate formation. The solid-phase particulate cloud has a very high emissivity compared to a pure gaseous system thus, soot-laden flames appreciably increase the radiant heat transfer. In fact, some systems can approach black-body conditions. Thus, when the rate of heat transfer from the combustion gases to some surface, such as a melt, is important—as is the case in certain industrial furnaces—it is beneficial to operate the system in a particular diffusion flame mode to ensure formation of carbon particles. Such particles can later be burned off with additional air to meet emission standards. But some flames are not as luminous as others. Under certain conditions the very small particles that form are oxidized in the flame front and do not create a particulate cloud. 

Black-body and Non-black-body Conditions.—Optical pyrometers are usually calibrated to read correctly when sighted on a black body. Many furnaces approximate black-body conditions very satisfactorily. In a perfect black body the details of the inside of the furnace vanish and a piece of steel, for example, which is being heated cannot be distinguished from the back ground. If the... 

In many processes where smoke cannot be eliminated or where black-body conditions are not satisfactory, a porcelain or other refractory tube with a closed end is inserted into the furnace. The pyrometer is sighted into this tube which if fairly uniformly heated over a sufficient area affords an excellent black body. This method has been employed also for obtaining the true temperature of molten metals but suitable refractory tubes for many molten metals have yet to be developed. 

All alloys in the system were single phase and had hep structure at room temperature. The solidus temperature for each alloy was determined in vacuum using a calibrated optical pyrometer focused on a 1 mm hole drilled to a depth of 3-4 mm in an attempt to achieve black body conditions (normally a 10 1 ratio of depth to diameter is required for black body conditions). 

The emissivity of a material is defined as the ratio of the radiation per unit area emitted from a real or from a grey surface (one for which the emissitivity is independent of wavelength) to that emitted by a black body at the same temperature. Emissivities of real materials are always less than unity and they depend on the type, condition and roughness of the material, and possibly on the wavelength and direction of the emitted radiation as well. For diffuse surfaces where emissivities are independent of direction, the emissivity, which represents an average over all directions, is known as the hemispherical emissivity. For a particular wavelength X this is given by ... 

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). 

Specific solar radiation conditions are defined by the air mass (AM) value. The spectral distribution and total flux of radiation outside the Earth s atmosphere, similar to the radiation of a black body of 5,900 K, has been defined as AM-0. The AM-1 and AM-1.5 are defined as the path length of the solar light relative to a vertical position of the Sun above the terrestrial absorber, which is at the equator when the incidence of sunlight is vertical (90°) and 41.8°, respectively. The AM-1.5 conditions are achieved when the solar flux is 982 Wm2. However, for convenience purpose the flux of the standardized AM-1.5 spectrum has been corrected to 1,000 Wm2. 

Several silver salts—in particular, AgNO —are deadly when ingested, even in small amounts. When ingested, the silver compounds are slowly absorbed by the body, and the skin turns bluish or black, a condition referred to as argyria. In the past, the eyes of newborn babies were swabbed with dilute silver nitrate to prevent blindness from STDs (sexually transmitted diseases, in particular gonorrhea). This procedure is no longer performed. 

In complete equilibrium, the ratio of the population of an atomic or molecular species in an excited electronic state to the population in the groun d state is given by Boltzmann factor e — and the statistical weight term. Under these equilibrium conditions the process of electronic excitation by absorption of radiation will be in balance with electronic deactivation by emission of radiation, and collision activation will be balanced by collision deactivation excitation by chemical reaction will be balanced by the reverse reaction in which the electronically excited species supplies the excitation energy. However, this perfect equilibrium is attained only in a constant-temperature inclosure such as the ideal black-body furnace, and the radiation must then give -a continuous spectrum with unit emissivity. In practice we are more familiar with hot gases emitting dis-... 

Atoms and molecules absorb only specific frequencies of radiation dictated by their electronic configurations. Under suitable conditions they also emit some of these frequencies. A perfect absorber is defined as one which absorbs all the radiation falling on it and, under steady state conditions, emits all frequencies with unit efficiency. Such an absorber is called a black body. When a system is in thermal equilibrium with its environment rates of absorption and emission are equal (Kirchhoff s law). This equilibrium is disturbed if energy from another source flows in. Molecules electronically excited by light are not in thermal equilibrium with their neighbours. 

From the preceding discussions it is evident that at least four different temperatures have to be considered which under laboratory conditions are all equal the excitation temperature Tex of the molecule, defined by the relative populations of the levels, the kinetic temperature Tk, corresponding to the Maxwellian velocity distribution of the gas particles, the radiation temperature Traa, assuming a (in some cases diluted) black body radiation distribution, and the grain temperature 7, . With no thermodynamic equilibrium established, as is common in interstellar space, none of these temperatures are equal. These non-equilibium conditions are likely to be caused in part by the delicate balance between the various mechanisms of excitation and de-excitation of molecular energy levels by particle collisions and radiative transitions, and in part by the molecule formation process itself. Table 7 summarizes some of the known distribution anomalies. The non-equilibrium between para- and ortho-ammonia, the very low temperature of formaldehyde, and the interstellar OH and H20 masers are some of the more spectacular examples. 

The Sun delivers a spectral irradiance at the Earth s surface at AM 1.0 (air mass), without concentrator, of 1.16 W m nm at 2 = 700 nm [2]. The solid angle represented by the Sun seen from the Earth is Q = 6.8 x 10 steradian. From Eq. (10), one calculates in this case Tr = 5500 K, and from Eq. (12) with T = 298 K one obtains rj = 0.946. If the solar spectrum were that of a black body, all wavelengths would lead to the same values of Jr and Figure 1 shows that this condition is fulfilled only if the receiver is outside the atmosphere. At the Earth s surface, absorption by atmospheric oxygen, ozone, water, and carbon dioxide makes the structured solar irradiance spectrum deviate significantly from the ideal black-body spectrum and requires rR(A) to be calculated for each wavelength. 

The law of Stefan and Boltzmann is exactly valid for an absolutely black body in vacuo, as it is based on the two laws of thermodynamics and on Maxwell s equations of the electromagnetic field, which are exact under these conditions. The law of Stefan and Boltzmaun may therefore be used not only... 

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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