Blackbody radiation defined

In dealing with problems of solar radiation, as opposed to blackbody radiation, the effect of the solid angle in which the radiation is confined has been examined (2-4) by considering the volume density of photons to be reduced. Landsberg(6) considers dilute radiation in the sense that the spectral distribution is retained but the radiation density is reduced. This leads to defining the temperature of a spectral component as... 

The constant h and the hypothesis that energy is quantized in integral multiples of hv had previously been introduced by M. Planck (1900) in his study of blackbody radiation.1 In terms of the angular frequency a> defined in equation (1.2), the energy E of a photon is... 

Since in reality there is no actual blackbody radiator (for which the Planck law applies, W), but a more realistic so-called greybody radiator (W7), the value e has been defined as the quotient W / W, where e can be given values between 0 and 1 (1 = genuine blackbody). For example, soot (e > 0.95) behaves almost like a blackbody radiator, whereas MgO behaves more like a greybody radiator. 

By definition, photometers do not respond to radiation in the infrared or the ultraviolet (Fig. 4-4a). They are light meters in the sense that they mimic human vision that is, they respond to photons in the visible region, similar to the light meter on a camera. A candle is a unit of luminous intensity, originally based on a standard candle or lamp. The current international unit is called a candela (sometimes still referred to as a candle ), which was previously defined as the total light intensity of 1.67 mm2 of a blackbody radiator (one that radiates maximally) at the melting temperature of pure platinum (2042 K). In 1979 the candela was redefined as the luminous intensity of a monochromatic source with a frequency of 5.40 x 1014 cycles s-1 (A, of 555 nm) emitting 0.01840 Js-1 or 0.01840 W (1.464 mW steradian-1, where W is the abbreviation for watt and steradian... 

A blackbody is defined as a perfect emitler and absorber of radiation. At a specified temperature and wavelength, no surface c.in emit more energy than a blackbody. A blackbody absorbs all incident radiation, regardless of wavelength and direction. Also, a blackbody emits radiation energy unifomily in all directions per um t area normal to direction of emission (Fig. 12-7). That is, a blackbody is a diffuse emitter. The tenti diffitse means independent of direction. The radiation energy emitted by a blackbody per unit time and per unit surface area was determined experimentally by Joseph Stefan in 1879 and expressed as... 

Therefore, we define a dimensionless quantity /x called the blackbody radiation function as... 

C Why did we define the blackbody radiation ftitic-tioii What does it represent For whal is it used ... 

The Planck theory of blackbody radiation provides a first approximation to the spectral distribution, or intensity as a function of wavelength, for the sun. The black-body theory is based upon a "perfect" radiator with a uniform composition, and states that the spectral distribution of energy is a strong function of wavelength and is proportional to the temperature (in units of absolute temperature, or Kelvin), and several fundamental constants. Spectral radiant exitance (radiant flux per unit area) is defined as ... 

A blackbody is defined as a surface or volume that absorbs all incident radiation. This includes radiation at every wavelength and from every direction. 

Emissivity. The ability of a surface to emit radiation in comparison with the ideal emission by a blackbody is defined as the emissivity of the surface. The emissivity can be defined on a spectral, directional, or total basis Directional Spectral Emissivity ... 

As described above, a blackbody is defined as a body which absorbs all radiation received by it. A strongly absorbing body is a strongly emitting body. For a blackbody, the following relation holds ... 

Thus far, we have discussed the ideal model in which the planets behave like blackbody radiators. This gives planetary astronomers a crude model from which they can estimate flux densities and search for departures. The planets would not be very interesting to study if they behaved like blackbodies since a single parameter, namely the temperature, could be used to define their radiation properties. More important, it is the departures from the simple model that allows radio astronomers to deduce the physical properties of the planets. 

Maxwell s equations describe the propagation of electromagnetic radiation as waves within the framework of classical physics however, they do not describe emission phenomena. The search for the law that defines the energy distribution of radiation from a small hole in a large isothermal cavity gave rise to quantum theory. The function that describes the frequency distribution of blackbody radiation was the first result of that new theory (Planck, 1900,1901). 

Radiation thermometry (visual, photoelectric, or photodiode) 500-50,000 Spectral intensity I at wavelength A Planck s radiation law, related to Boltzmann factor for radiation quanta Needs blackbody conditions or well-defined emittance... 

The star in the numerical model has an inside and an outside. The outside is defined as the limit beyond which it becomes transparent. This boundary is called the photosphere, or sphere of light, for it is here that the light that comes to us is finally emitted. It is thus the visible surface of the star, located at a certain distance R from the centre, which defines the radius and hence the size of the star. The photosphere has a certain temperature with which it is a simple matter to associate a colour, since to the first approximation it radiates as a blackbody, or perfect radiator. Indeed, the emissions from such a body depend only on its temperature. The correspondence between temperature and colour is simple. In fact, the relation between temperature and predominant wavelength (which itself codifies colour) is given by Wien s law, viz. 

The spectral emissivity, f.>. is defined as the ratio of the emission at wavelength /. of the object to that of an ideal blackbody at the same temperature and wavelength. When ty is unity, the foregoing equation becomes the Planck radiation equation for a black body. 

In general, the emissivity of a solid is affected by the temperature as well as the wavelength of the radiation. The concept of monochromatic emissivity is related to the radiant emission by a solid at a specific wavelength. The monochromatic emissivity e is defined as the ratio of the monochromatic-emissive power of a solid Ex to the monochromatic-emissive power of a blackbody EbX at the same temperature and wavelength, i.e.,... 

The spectral emissivity e (T) of the body for radiation at temperature T is defined as the ratio of the spectral emissive flux qx(T) of the body to the spectral blackbody emissive flux q h(T) at the same temperature. Expressed mathematically,... 

Range Above 1234.93 K. Above the freezing point of silver, an optical pyrometer is nsed to measnre the emitted radiant flux (radiant excitance per unit wavelength interval) of a blackbody at wavelength A. The defining equation is the Planck radiation law in the form... 

If all surfaces emitted radiation uniformly in all directions, the emissive power would be sufficient to quantify radiation, and we would not need to deal with intensity. The radiation emitted by a blackbody pet unit nonnal area is the same in all directions, and thus there is no directional dependence. But this is not the case for real surfaces. Before we define intensity, wc need to quantify the size of an opening in space. 

In the preceding section, we defined a blackbody as a perfect emitter and absorber of radiation and said tliat no body can emit more radiation than a blackbody at the. same temperature. Therefore, a blackbody can serve as a convenient reference in describing the emission and absorption characteristics of real surfaces. 

The emissivity of a real surface is not a constant. Rather, it varies with the temperature of the surface as well as the wavelength and tlie direction of the emitted radiation. Therefore, different emissiviiies can be defined for a surface, depending on the effects considered. The most elemental emissivity of a surface at a given lemperature is the spectral directional emissivity, which is defined as the ratio of the intensity of radiation emitted by the suiface at a specified wavelength in a speeiOed direction to the intensit) of radiation emitted by a blackbody at the same temperature at the same wavelength. That is. 

The emissivityol a surface represents the ratio of the radiation emitted by the surface at a given temperature to the radiation emilted by a blackbody at the same lemperalure. Different eitiissivilies are defined as... 

I2-3S A small surface of area A - 1 cm emits radiation as a blackbody at 1ROO K. Determine the rate at whicb radiation energy is emitted through a band defined by 0 27t and 45... 

Real surfaces emit less radiation than a blackbody surface. One may define... 

For real surfaces emissivity is defined as the ratio of the radiation emitted by the surface to the radiation emitted by a blackbody at the same temperature. So, the emissivity specifies how well a real body radiates energy as compared with a blackbody. The directional spectral emissivity ex,e X, 9, , T) of a surface at temperature T is defined as the ratio of the intensity of the radiation emitted at the wavelength A and the direction of 9 and to the intensity of the radiation emitted by a blackbody at the same values of T and... 

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