Bodies: black

The model of non-mteracting hannonic oscillators has a broad range of applicability. Besides vibrational motion of molecules, it is appropriate for phonons in hannonic crystals and photons in a cavity (black-body radiation). 

A2.2.4.6 APPLICATION TO IDEAL SYSTEMS BLACK BODY RADIATION... 

This is known as the Stefan-Boltzmaim law of radiation. If in this calculation of total energy U one uses the classical equipartition result = k T, one encounters the integral f da 03 which is infinite. This divergence, which is the Rayleigh-Jeans result, was one of the historical results which collectively led to the inevitability of a quantum hypothesis. This divergence is also the cause of the infinite emissivity prediction for a black body according to classical mechanics. 

This is known as the Planck radiation law. Figure A2.2.3 shows this spectral density fiinction. The surface temperature of a hot body such as a star can be estimated by approximating it by a black body and measuring the frequency at which the maximum emission of radiant energy occurs. It can be shown that the maximum of the Planck spectral density occurs at 2.82. So a measurement of yields an estimate of the... 

In this chapter, the foundations of equilibrium statistical mechanics are introduced and applied to ideal and weakly interacting systems. The coimection between statistical mechanics and thennodynamics is made by introducing ensemble methods. The role of mechanics, both quantum and classical, is described. In particular, the concept and use of the density of states is utilized. Applications are made to ideal quantum and classical gases, ideal gas of diatomic molecules, photons and the black body radiation, phonons in a hannonic solid, conduction electrons in metals and the Bose—Einstein condensation. Introductory aspects of the density... 

Boltzmaim showed that the energy density emided per second from a unit surface of a black body is a7 where T is the temperature and a is the Stefan-Boltzmaim constant, but it takes statistical mechanics to produce the fonnula... 

The explanation of the hydrogen atom spectmm and the photoelectric effect, together with other anomalous observations such as the behaviour of the molar heat capacity Q of a solid at temperatures close to 0 K and the frequency distribution of black body radiation, originated with Planck. In 1900 he proposed that the microscopic oscillators, of which a black body is made up, have an oscillation frequency v related to the energy E of the emitted radiation by... 

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. 

The spectral distribution of energy flux from a black body is expressed by Planck s law ... 

Radiated energy flux Energy flux to a black body Flow rate... 

If the target object is a black body and if the pyrometer has a detector that measures the specific wavelength signal from the object, the temperature of the object can be exactly estimated from Eq. (8-92). While it is possible to coustrucl a physical body that closely approxi-... 

Total Radiation Pyrometers In total radiation pyrometers, the thermal radiation is detec ted over a large range of wavelengths from the objec t at high temperature. The detector is normally a thermopile, which is built by connec ting several thermocouples in series to increase the temperature measurement range. The pyrometer is calibrated for black bodies, so the indicated temperature Tp should be converted for non-black body temperature. 

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... 

For higher rating systems, say 2500 A and above, sleeving is normally not used. Instead, a non-metallic, semi-glossy black paint may be provided to make the bus conductors act like a black body and dissipate more heat. This will also add to the current-carrying... 

Ratings may be improved by approximately 20% if the busbars are painted black with a non-metallic matt finish paint. This is because heat dissipation through a surface depends upon temperature, type of surface and colour. A rough surface will dissipate heat more readily than a smooth surface and a black body more quickly than a normal surface. Also refer to Section 51.4.4 and Table 51.1. 

The thermal radiation received from the fireball on a target is given by equation 9.1-31, where Q is the radiation received by a black body target (kW/m ) r is the atmospheric transmissivity (dimensionless), E = surface emitted flux in kW/m", and f is a dimensionless view factor. 

Black body A hypothetical body that has an absorptance and an emissivity of... 

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 fraction of black-body radiation actually emitted by flames is called emissivity. Emissivity is determined first by adsorption of radiation by combustion products (including soot) in flames and second by radiation wavelength. These factors make emissivity modeling complicated. By assuming that a fire radiates as a gray body, in other words, that extinction coefficients of the radiation adsorption are independent of the wavelength, a fire s emissivity can be written as... 

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 ... 

Emissivity The ratio of radiant energy emitted by a surface to that emitted by a black body of the same temperature. 

Kuhn, T. S. (1978). Black-Body Theory and the Quantum Discontinuity, 1894-1912. New York Oxford University Press. 

Celsius. The energy distribution of the radiation emitted by this surface is fairly close to that of a classical black body (i.e., a perfect emitter of radiation) at a temperature of 5,500°C, with much of the energy radiated in the visible portion of the electromagnetic spectrum. Energy is also emitted in the infrared, ultraviolet and x-ray portions of the spectrum (Figure 1). 

The heat flux radiated from a real surface is less than that from an ideal black body surface at the same temperature. The ratio of real to black body flux is the normal total emissivity. Emissivity, like thermal conductivity, is a property which must be determined experimentally. 

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. 

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