Radiation Boltzmann laws

Blackbody Radiation Engineering calculations of thermal radiation from surfaces are best keyed to the radiation characteristics of the blackbody, or ideal radiator. The characteristic properties of a blackbody are that it absorbs all the radiation incident on its surface and that the quality and intensity of the radiation it emits are completely determined by its temperature. The total radiative fliix throughout a hemisphere from a black surface of area A and absolute temperature T is given by the Stefan-Boltzmann law ... 

I By Radiation (Wr) This heat loss is related to the difference of the fourth power of the absolute temperatures and the emissivity of the enclosure, and is represented by the Stefan-Boltzmann law expressed by (see Dwight ci al.. 1940)... 

The most common states of a pure substance are solid, liquid, or gas (vapor), state property See state function. state symbol A symbol (abbreviation) denoting the state of a species. Examples s (solid) I (liquid) g (gas) aq (aqueous solution), statistical entropy The entropy calculated from statistical thermodynamics S = k In W. statistical thermodynamics The interpretation of the laws of thermodynamics in terms of the behavior of large numbers of atoms and molecules, steady-state approximation The assumption that the net rate of formation of reaction intermediates is 0. Stefan-Boltzmann law The total intensity of radiation emitted by a heated black body is proportional to the fourth power of the absolute temperature, stereoisomers Isomers in which atoms have the same partners arranged differently in space, stereoregular polymer A polymer in which each unit or pair of repeating units has the same relative orientation, steric factor (P) An empirical factor that takes into account the steric requirement of a reaction, steric requirement A constraint on an elementary reaction in which the successful collision of two molecules depends on their relative orientation. 

The total quantity of radiation emitted by a black body can be calculated by integrating the curves of Figure 3.19. This has been supplemented by experimental data. The result is the Stefan-Boltzmann law, which is given by... 

The Net OLR, Aq (W m-2), from the ground surface to the atmosphere is given by the Stefan-Boltzmann law. The linear temperature change between the surface temperature of the Earth (Ts) and the effective temperature of the atmosphere (Te) indicates that the radiation occurs layer-by-layer through the atmosphere (Figure 9). Since the net OLR is constant through the atmosphere the net OLR through layer n is... 

Also known as the Stefan-Boltzmann law. The total radiation from a black body is proportional to the fourth power of its absolute temperature. 

This quantity is the total amount of radiation at all wavelengths radiating through the surface of the sphere and is simply the Stefan-Boltzmann Law multiplied by the surface area of the photosphere. 

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 ... 

Lasers are devices for producing coherent light by way of stimulated emission. (Laser is an acronym for light amplification by stimulated emission of radiation.) In order to impose stimulated emission upon the system, it is necessary to bypass the equilibrium state, characterized by the Boltzmann law (Section 9.6.2), and arrange for more atoms to be in the excited-state E than there are in the ground-state E0. This state of affairs is called a population inversion and it is a necessary precursor to laser action. In addition, it must be possible to overcome the limitation upon the relative rate of spontaneous emission to stimulated emission, given above. Ways in which this can be achieved are described below, using the ruby laser and the neodymium laser as examples. 

The remaining mechanism by which heat is transferred is radiation, that is electromagnetic radiation in the range 0.1—lOOjum. The Stefan— Boltzmann Law for a black body states... 

The total energy E, of all wavelengths radiated per m2 per second by a black body at temperature TK is given by the Stefan-Boltzmann law... 

Boltzmann s Law. The law of the equipartition of energy to a molecular system. Stef an-Boltzmann Law states that the total energy radiated from a black body is proportional to its absolute temp raised to the fourth power. It is expressed by E= a (T4 - T ) where E - total energy in ergs,... 

Thermal Emission Laws. All bodies emit infrared radiation by virtue of their temperature. The total amount of radiation is governed by Kirchhoff s law, which states that a body at thermal equilibrium, ie, at the same temperature as its surroundings, must emit as much radiation as it absorbs at each wavelength. An absolutely blackbody, one that absorbs all radiation striking it, must therefore emit the most radiation possible for a body at a given temperature. The emission of this so-called blackbody is used as the standard against which all emission measurements are compared. The total radiant emittance, M, for a blackbody at temperature Tis given by the Stefan-Boltzmann law,... 

Prove that the Stefan-Boltzmann law for thermal radiation given in Eq. (1.59) can be derived by using Planck s formula given in Eq. (1.62). Also show that... 

Thermal radiation can take place without a medium. Thermal radiation may be understood as being emitted by matter that is a consequence of the changes in the electronic configurations of its atoms or molecules. Solid surfaces, gases, and liquids all emit, absorb, and transmit thermal radiation to different extents. The radiation heat transfer phenomenon is described macroscopically by a modified form of the Stefan-Boltzmann law, which is... 

Black-body Radiation and the Stefan-Boltzmann Law.—Light is simply electromagnetic radiation, a wave motion in space, in which the... 

From Eq. (1.3) we can easily piove a law called the Stefan-Boltzmann law relating the density of radiation to the temperature. 

Equation (8-3) is called the Stefan-Boltzmann law, Eh is the energy radiated per unit time and per unit area by the ideal radiator, and a is the Stefan-Boltzmann constant, which has the value... 

We will express the IR emitted by a leaf at a temperature 74eaf using the Stefan-Boltzmann law (Eq. 6.18a), which describes the maximum rate of radiation emitted per unit area. For the general emission case we incorporate a coefficient known as the emissivity, or emittance (e)y which takes on its maximum value of 1 for a perfect, or blackbody, radiator. The actual radiant energy flux density equals (Tact )4 (Eq. 6-18b), which is the same as actual temperatures to describe... 

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