Black-body radiators

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... 

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... 

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... 

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 ... 

Historical Background.—Relativistic quantum mechanics had its beginning in 1900 with Planck s formulation of the law of black body radiation. Perhaps its inception should be attributed more accurately to Einstein (1905) who ascribed to electromagnetic radiation a corpuscular character the photons. He endowed the photons with an energy and momentum hv and hv/c, respectively, if the frequency of the radiation is v. These assignments of energy and momentum for these zero rest mass particles were consistent with the postulates of relativity. It is to be noted that zero rest mass particles can only be understood within the framework of relativistic dynamics. 

To integrate equation (10.149) we must know how dn is related to v. Debye assumed that a crystal is a continuous medium that supports standing (stationary) waves with frequencies varying continuously from v = 0 to v = t/m. The situation is similar to that for a black-body radiator, for which it can be shown that... 

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. 

Studies of black-body radiation led to Planck s hypothesis of the quantization of electromagnetic radiation. The photoelectric effect provides evidence of the particulate nature of electromagnetic radiation. 

Example -CH2CH2CH2-. black body An object that absorbs and emirs all frequencies of radiation without favor, black-body radiation The electromagnetic radiation emitted by a black body. 

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 difficulty in setting up the initial system for color comparisons cannot be underestimated. The problem was enormous. Questions as to the suitability of various lamp sources, the nature of the filters to be used, and the exact nature of the primary colors to be defined occupied many years before the first attempts to specify color in terms of the standard observer were started. As we said previously, the Sun is a black-body radiator having a spectral temperature of about 10,000 °K (as viewed directly from space). Scattering and reflection... 

Egglescliffe School. Black Body Radiation. Available online. URL http //www.egglescliffe.org.uk/physics/astronomy/black-body/bbody.html. 

Figure 3.19 Influence of temperature on amount and distribution of black-body radiation.

The function /(x) = (5-x)e — 5 arises in the theory of black-body radiation. Obviously, it has a zero at x = 0. A plot of this function (Fig. 8) shows that it has a second zoo near x = 5. As this function appears to be well behaved in this region, Newton s method might be expected to yield a value for the second root... 

Simple stellar models - black body radiation... 

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 ... 

The black body radiation model for the continuum radiation from stars works well but it is not quite right. Careful consideration of the radiation profile shows deviations from the curves shown in Figure 2.1 due to the structure of the star itself. These deviations form the basis of a more detailed analysis including the effects of circulation within the star and will be left to others to explain we shall use black body radiation as our model for stars. 

The ability of a body at a characteristic temperature to absorb and emit radiation at all wavelengths with equal and unit efficiency. The general application of all of the laws of black body radiation to the description of stars... 

---