Temperature dependent part

To expedite the evaluation of transport properties, one could fit the temperature dependent parts of the pure species viscosities, thermal conductivities, and pairs of binary diffusion coefficients. Then, rather than using the complex expressions for the properties, only comparatively simpler polynomials would be evaluated. The fitting procedure must be carried out for the particular system of gases that is present in a given problem. Therefore the fitting cannot be done once and for all but must be done once at the beginning of each new problem. 

Let us separate the T = 0 part and the temperature-dependent part of y and 8. The first part equals... 

The temperature-dependent part GT of the conductivity through the metallic cluster is calculated as the sum of conductances of open constrictions. The distribution f(eL) of constrictions over the activation energies can be evaluated from the relevant part of the conductance GT [85] ... 

For a packed catalyst bed, the temperature-dependence part of the mass transfer coefficient for a gas-phase reaction can be written as... 

In the Orbach process the transfer rate is composed of a temperature-dependent part associated with the phonon-occupation number nq and a temperature independent part corresponding to energy transfer accompanied by spontaneous phonon emission. 

Setting the temperature-dependent parts equal yields... 

It seems useful to summarize all optical relaxation data that have been obtained so far. In the preceding sections it was shown that for the temperature dependent part of 7 the following phenomenological expression fitted all presently available data T (7 )= 7 (oo)exp(AE/kT ). For... 

In Equ. 2.53, the very general model equation r = /(x, fc) is shown separated into concentration- and temperature-dependent parts. The reaction rate constants are therefore regarded as temperature dependent, as illustrated with type 3 in Fig. 4.12. 

The temperature dependence of the threshold power is determined by the temperature dependence of the Frank constant and of the permittivity. Bearing in mind the fact that the Frank constant K varies with temperature as the square of the order parameter while the anisotropy of the permittivity (Ref. 12), we can separate the temperature-dependent part in expression (12)forPFr intheformPpr° As the temperature... 

The temperature in the canonical BOMD simulation was controlled by a Nos6-Hoover chain thermostat (Hoover 1985 Martyna et al. 1992 Nos6 1984). In order to study the temperature dependency of the sodium cluster polarizabilities the polarizability tensor a was calculated along the recorded trajectories. For this purpose the first 20 ps of each trajectory were discarded and a was then calculated in 100 fs time steps along the remaining 200 ps. Due to the computational demand of the analytical polarizability calculation along the BOMD trajectories we employed the LDA kernel. Thus, the computational level for the calculation of the temperature dependent part of the cluster polarizabilities was VWN/TZVP-FIP/GEN-A2. The temperature dependent mean sodium cluster polarizability was then calculated as ... 

The standard chemical potential is then the molar free energy of the gas atunit pressure. The above equation subdivides the chemical potential of a gas into a temperature-dependent part, p,°i, and a concentration-dependent part, In(ai) -pressure is equivalent to concentration for a gas. 

The temperature-dependent part of the thermal rate-coefficient expression is then... 

In Equation (1.45), all the quantities which do not contain the temperature explicitly are independent of temperature (to within corrections of the type of difference in heat capacities, AC T). Writing the temperature-dependent part of Equation (1.45) in the form exp [-E(n)/RT], we find that the quantity E(n) is the apparent real activation energy at the overpotential and the coefficient in... 

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