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)... 

By measuring the relative intensities of satellite and main lines, the population ratio is obtained, if it can be assumed that the dipole moment and line strength is not appreciably different in the two cases. From the population ratio R, the energy interval AE is obtained from the Boltzmann law i.e.,... 

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. 

When this supersaturation exists, the nucleation rate will be proportional to the probability of formation of a favorable configuration of particles of the primary product. According to the Boltzmann law, this probability is determined by the work of formation of a single nucleus ... 

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... 

Since the rate of energy absorption is proportional to An0, it is perhaps worthwhile to examine this population difference at equilibrium. According to the Boltzmann law... 

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

The first of the laws is the Stefan-Boltzmann Law relating the amount of energy emitted from a black body, F, to its temperature T ... 

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 ... 

We have discussed the transition moment (the quantum mechanical control of the strength of a transition or the rate of transition) and the selection rules but there is a further factor to consider. The transition between two levels up or down requires either the lower or the upper level to be populated. If there are no atoms or molecules present in the two states then the transition cannot occur. The population of energy levels within atoms or molecules is controlled by the Boltzmann Law when in local thermal equilibrium ... 

Local thermal equilibrium (LTE) is an assumption that allows for the molecules to be in equilibrium with at least a limited region of space and remains an assumption when using the Boltzmann law for the relative populations of energy levels. The LTE assumption notwithstanding, observation of a series of transitions in the spectrum and measurement of their relative intensities allows the local temperature to be determined. We shall see an example of this in Section 4.4 where the Balmer temperature of a star is derived from the populations of different levels in the Balmer series. 

The rotational spectrum of a molecule involves transitions between energy levels, say the R(8) transition / = 8 and J = 9, but if there are no molecules rotating in the J = 8 level then there can be no R(8) transition. The local thermal collisions will populate some of the higher J levels in a general principle called equipartition. The general expression is the Boltzmann Law, given by ... 

When the atom is in thermal equilibrium with its surroundings in the photosphere of the star, the population of the n = 2 level is given by the Boltzmann law ... 

Stefan-Boltzmann Law The relation between temperature and luminosity of a star. 

It is possible to assess the fraction of defects in a crystal that is associated using the approximate interaction energy calculated above using the Boltzmann law. This gives the information about the distribution of a population of defects between two energy states. The fraction / of the population in the upper energy state, when the energy difference between the states is AE, is... 

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 measurement of an enthalpy change is based either on the law of conservation of energy or on the Newton and Stefan-Boltzmann laws for the rate of heat transfer. In the latter case, the heat flow between a sample and a heat sink maintained at isothermal conditions is measured. Most of these isoperibol heat flux calorimeters are of the twin type with two sample chambers, each surrounded by a thermopile linking it to a constant temperature metal block or another type of heat reservoir. A reaction is initiated in one sample chamber after obtaining a stable stationary state defining the baseline from the thermopiles. The other sample chamber acts as a reference. As the reaction proceeds, the thermopile measures the temperature difference between the sample chamber and the reference cell. The rate of heat flow between the calorimeter and its surroundings is proportional to the temperature difference between the sample and the heat sink and the total heat effect is proportional to the integrated area under the calorimetric peak. A calibration is thus... 

Steeping parameters, 15 528t Steep tanks, 15 527-528 Stefan-Boltzmann law, 19 131 Stefan-Maxwell equations, 1 43-46, 598 Stefan s law, 7 327 Steinhart-Hart equation, 24 451 Stellite 1... 

Box 3.1 Relative populations of molecules in the vibrational energy levels according to the Boltzmann Law... 

The number of molecules in states 1 and 2 is N2 and N2, respectively. These numbers must satisfy the Boltzmann Law ... 

Bloch functions, 25 7, 8 Bloch state, stationary, 34 237, 246 Blow-out phenomenon, 27 82, 84 Bohr magneton, 22 267 number, 27 37 Boltzmann law, 22 280 Bonding energy, BOC-MP, 37 106-107 Bondouard disproportionation reaction, 30 196 Bond percolation, 39 6-8 Bonds activation... 

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