Perfect 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 ... 

Emissivity figures for common materials have been determined, and are expressed as the ratio to the radiation by a perfectly black body, viz. 

Surfaces will absorb radiant heat and this factor is expressed also as the ratio to the absorptivity of a perfectly black body. Within the range of temperatures in refrigeration systems, i.e. - 70°C to + 50°C (203-323 K), the effect of radiation is small compared with the conductive and convective heat transfer, and the overall heat transfer factors in use include the radiation component. Within this temperature range, the emissivity and absorptivity factors are about equal. 

The development of new low-temperature detection technology and the launch of the Cosmic Background Explorer (COBE) satellite by NASA in 1989 helped to resolve this problem. The results from these observations were amazing - an almost perfect black body curve (Figure 2.3) with a black body temperature of 2.725 0.002 K and a maximum wavelength of the radiation at kmax = 1.05 mm. 

Figure 2.3 An almost-perfect black body spectrum for the cosmic background radiation. Figure courtesy of NASA/COBE Science Team...

Strictly, a black body is defined as something that absorbs photons of all energies, and does not reflect light. Furthermore, a black body is also a perfect emitter of light. A black body is a theoretical object since, in practice, nothing behaves as a perfect black body. The best approximations are hot objects such as red- or white-hot metals. 

The physical significance of the constant K may be obtained from the following consideration. A body which absorbs all the radiation which falls on it, and which therefore neither reflects nor transmits even the smallest fraction of it, has the absorptivity A = l, and is called a perfect black body. (Charcoal is a very close approximation to a perfect black body.) -For a perfect black body, equation (1) assumes the form... 

It follows also that the intensity of the radiation inside a closed chamber in temperature equilibrium is the same as that emitted by a perfect black body at the same temperature, no matter whether the chamber contains a black body or not. (In future a chamber of this kind will be termed a Prevost chamber, after the French physicist Prevost, who first made use of it in physical reasoning.)... 

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. 

These investigators were able to realise a practically perfect black body by making use of the theorem proved above, that the radiation in a Prevost chamber at constant temperature is black. The radiation emitted from a small opening in the walls of the chamber is the same as that emitted by a black body. They found the value of the constant a to be 1-28 x 10 " cal. This is the amount of energy emitted per second from a square centimetre of a black body at the temperature 1° absolute into a space at O " abs. 

The practical application of the optical method of measuring temperature is made possible by the fact that the radiation from most solid bodies at high temperatures corresponds very closely to that from a perfect black body. In many metallurgical processes the temperature of a mass of material in a furnace has to be measured, and here the blackness of the radiation is still more perfect, as the furnace acts to a certain extent like a Prevost chamber. 

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... 

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... 

Reversible processes are but one example of a host of concepts of a similarly idealized nature in chemistry and physics— for example, ideal gases and solutions, absolute zero temperature, infinitely dilute solutions, perfect black-body radiation, isolated systems, perfect insulators, and so on. In every case, the adoption of the idealized case simplifies or makes possible the application of mathematics to physical... 

Black body radiation - The radiation emitted by a perfect black body, i.e., a body which absorbs all radiation incident on it and reflects none. The wavelength dependence of the radiated energy density p (energy per unit volume per unit wavelength range) is given by the Planck formula... 

Gray bodies are loosely defined as less than perfect black bodies. The behavior of pyrotechnic sparks fails roughly in the range between that shown beiow for black bodies and gray bodies. 

In reality, no material is a perfect black body, but rather emits and absorbs energy at some fraction of the ideal. This proportionality constant is called emissivity. A heater with higher emissivity, therefore, will deliver a larger amount of energy at a given temperature than one with a lower emissivity. 

Radiation from a body and emissivity. The basic equation for heat transfer by radiation from a perfect black body with an emissivity e = 1.0 is... 

A perfectly black body emits the maximum amount of radiation based on its temperature its emissivity is unity. According to Kirchhoff s law, its absorptivity will also be unity. In reahty, surfaces have emissivities and absorptivities for infrared radiation that are less than unity. The actual value will depend on the material, the surface roughness, the temperature, and the wavelength of the radiation. 

Emissivity is the ratio of the energy radiated by a body to that radiated by an equal area of a perfect black body. According to the Stefan-Boltzmann law, a perfect black body is an ideal material which radiates the maximum amount of energy. The emissivity of a material depends on Its structure and on its surface conditions. 

A perfect black-body that absorbs all of the radiation that is incident on it and does not reflect any light has a = 1. In general a grey-body has 0<8<1, white paint has 8 = 0.95, and polished steel has e = 0.07. The Stephen-Boltzmann constant a is given by... 

Kirchhoff, Gustav Robert (1824-87)AGermanphysicistwho founded the science of spectroscopy. He discovered the laws that govern the absorption and emission of radiation and the flow of electricity in electrical networks. In 1859 he presented the law that states that the ratio of the emission and absorption powers of all materials is the same at a given temperature and a given wavelength of radiation produced. He went on to derive the concept of a perfect black body that can absorb and emit radiation at all wavelengths. 

Kirchoff s theorem states that the ratio of a body s spectral luminance to its absorbance, L/a, is a function of the frequency and temperature of the body but not a function of the nature of the body or its geometrical dimensions. This ratio is equal to the spectral luminance of a perfect black body ... 

Luminance is the intensity of emitted radiance per unit solid angle and frequency. It is sometimes called spectral radiance, or radiant flux. Emissivity is a property of a sample measured at standard conditions. The sample must be thick enough to be both optically opaque and smooth [63]. In the case of a perfect black body, the sample cannot be reflective. This property is not composition or geometry dependent even a heated pinhole cavity will show a good black body curve. 

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