Stefan Law

The theorem of the equipartition of energy when extended to the thermal equilibrium between matter and ether was very well confirmed as far as the infrared part of black-body radiation was concerned. Its extension to the ultraviolet domain, however, leads to absurd results, so that, at least for the time being, one is unable to derive the Boltzmann-Stefan law and Wien s displacement law without reference to thermodynamical results. At the present time one cannot see how these difficulties can be solved.217... 

Stefans law is an indication that the surface molecules are oriented differently than in the bulk phase. This observation is useful in order to understand the surface phenomena. 

In such measurements great care must be taken to avoid viscous effects, especially at small separations. For a liquid bridge between parallel plates, for example, the Stefan law as modified by Healey(3i) tells that the time to separate them from Zj to Z2 is... 

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. 

Stefan s law states that the total energy / radiated by a blackbody per unit time and area (power per unit area) varies as the fourth power of the absolute temperature ... 

Thermal Emission Laws. AH 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 equiUbrium, 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-Boltzmaim law,... 

The total energy radiating from a blackbody of unit area is given by the Stefan-Boltzman law ... 

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)... 

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 use of Stefan-Boltzmann s law to calculate radiation requires the knowledge of the fire s temperature and emissivity. Turbulent mixing causes fire temperature to vary. Therefore, it can be more useful to calculate radiation from data on the... 

The radiation from a black body is proportional to the fourth power of the adiabatic flame temperature, according to the Stefan-Boltzmann s law ... 

Equation 10.30 is known as Stefan s Law(3). Thus the bulk flow enhances the mass transfer rate by a factor Cj/Cjj, known as the drift factor. The fluxes of the components are given in Table 10.1. 

It may be noted that equation 10.86 is identical to equation 10.30. (Stefan s Law) and. Stefan s law can therefore also be derived from Maxwell s Law of Diffusion. 

By comparing equation 10.89 with Stefan s Law (equation 10.30) the effective diffu-sivity of A in the mixture (/> ) is given by ... 

Stefan-Boltzmann law and is usually written The name Stefan-Boltzmann law... 

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... 

A qualitative interference that can be drawn from Stefan s law pertains to the effect of high absolute temperatures on the quantities of heat radiated. This aspect is of great practical importance. As the temperature of a body is raised above that of its surroundings, the amount of heat it can radiate to them increases at a phenomenal rate. 

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... 

The theory on the level of the electrode and on the electrochemical cell is sufficiently advanced [4-7]. In this connection, it is necessary to mention the works of J.Newman and R.White s group [8-12], In the majority of publications, the macroscopical approach is used. The authors take into account the transport process and material balance within the system in a proper way. The analysis of the flows in the porous matrix or in the cell takes generally into consideration the diffusion, migration and convection processes. While computing transport processes in the concentrated electrolytes the Stefan-Maxwell equations are used. To calculate electron transfer in a solid phase the Ohm s law in its differential form is used. The electrochemical transformations within the electrodes are described by the Batler-Volmer equation. The internal surface of the electrode, where electrochemical process runs, is frequently presented as a certain function of the porosity or as a certain state of the reagents transformation. To describe this function, various modeling or empirical equations are offered, and they... 

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