Boltzmanns constant

Boltzmann Constant. A molecular constant arising in thermodynamic calculation of the energy of a single molecule or oscillator. 

Boltzmann Equation of State and Its Modification by Hirschfelder Rosevere. See under Detonation (and Explosion), Equations of State 

Break of Detonation. See under Detonation Attenuation, Break, Cutoff, Decay, Dying-out, Extinction, Fadeout, Fading and Failure of 

Breaking Force in Detonation. See under Breaking Theory of Detonation in Vol 2 of Encycl, p B362 and in this section under (. Detonation (and Explosion), Breaking Theory of Carlf  

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Another important accomplislnnent of the free electron model concerns tire heat capacity of a metal. At low temperatures, the heat capacity of a metal goes linearly with the temperature and vanishes at absolute zero. This behaviour is in contrast with classical statistical mechanics. According to classical theories, the equipartition theory predicts that a free particle should have a heat capacity of where is the Boltzmann constant. An ideal gas has a heat capacity consistent with tliis value. The electrical conductivity of a metal suggests that the conduction electrons behave like free particles and might also have a heat capacity of 3/fg,... 

If we knew the variation m A as a fiinction of coverage 0, this would be the equation for the isothenn. Typically the energy for physical adsorption in the first layer, -A E, when adsorption is predominantly tlnongh van der Waals interactions, is of the order of lO/rJ where T is the temperature and /rthe Boltzmann constant, so that, according to equation (B1.26.6), the first layer condenses at a pressure given by PIPq. 10... 

In tliennal equilibrium at tire temperature T, tire distribution of electrons in tire band is given by tire Fenni-Dirac distribution function f E) = [I where k is tire Boltzmann constant. The function/ E) describes... 

The Boltzmann constant is ks and T the absolute temperature. — is the Dirac delta function. Below we assume for convenience (equation (5)) that the delta function is narrow, but not infinitely narrow. The random force has a zero mean and no correlation in time. For simplicity we further set the friction to be a scalar which is independent of time or coordinates. 

The temperature T of a system is related to the mean kinetic energy of all atoms N via Eq. (36), where kg is the Boltzmann constant and the average of the squared velocities of atom i. 

HyperChern immediately scales (adjusts) the velocities of each atom so that the total kinetic energy is equal lo V.,kT, where k is the Boltzmann constant and f is the specified starting ternpera-... 

Calculate the % difference between L found by this method and the modem value of 6.022 X 10. Does this support the idea that the Boltzmann constant is the gas constant per particle ... 

Kelvin, or a point in /c-space a constant Boltzmann constant kilograms... 

Spectral bandwidth of excita- Stefan-Boltzmann constant a... 

Another useful version is /zv = 5kT, where k is the Boltzmann constant. 

In Equation 7.1, n+/n is the ratio of the number of positive ions to the number of neutrals evaporated at the same time from a hot surface at temperature T (K), where k is the Boltzmann constant and A is another constant (often taken to be 0.5 see below). By inserting a value for k and adjusting Equation 7.1 to common units (electronvolts) and putting A = 0.5, the simpler Equation 7.2 is obtained. 

The Boltzmann equation (Equation 18.2) shows that, under equilibrium conditions, the ratio of the number (n) of ground-state molecules (A ) to those in an excited state (A ) depends on the energy gap E between the states, the Boltzmann constant k (1.38 x 10" J-K" ), and the absolute temperature T(K). 

Fig. 2. (a) Energy, E, versus wave vector, k, for free particle-like conduction band and valence band electrons (b) the corresponding density of available electron states, DOS, where Ep is Fermi energy (c) the Fermi-Dirac distribution, ie, the probabiUty P(E) that a state is occupied, where Kis the Boltzmann constant and Tis absolute temperature ia Kelvin. The tails of this distribution are exponential. The product of P(E) and DOS yields the energy distribution... 

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