Temperature dependence calculations

At a set temperature and concentration, the coefficient of diffusion D is constant and its temperature dependence, calculated by the Arrhenius law [36], can be ignored. However, in the presence of external forces F and F stipulating the appearance of an additional flow of the gaseous components by electrodiffusion and by thermodiffusion (Soret effect [37]), respectively, the coefficient d in Equation (2.7) describes the force of the convective diffusion as follows ... 

Fig. 74. Power-law temperature dependence of the resistivity ratio r = (pCT")- p(288)]/p(288) in amorphous Gd-Co films of different compositions. The solid lines represent temperature dependencies calculated on the basis of eq. (67) mentioned in the text (after Okuno and Sakurai, 1983).

Now we have a picture about how demanding temperature-dependent calculations are we need at each T and colO Monte Carlo points and 10 frequencies in order to cover the experimental range. Furthermore we need the three different directions jc, y and z. So we had to solve three million times the TDLDA integral equation with full inclusion of the ionic structure (via pseudopotential perturbation theory). Needless to say it seems almost impossible to perform calculations of this type for transition metals with the additional complication of the d-electrons ... 

Cadmium oxide CdO 43.639 298.15 255 (6) See Fig. 4.1-166 for temperature dependence Calculated from X-ray diffraction measurements... 

Numerical values of the effective parameters and sums of squares for the best curve fits. The first four rows correspond to temperature dependence calculations the fifth row corresponds to an... 

Fig. 29. Peak height of the pulsed neutron PDF of Tl2Ba2CaCu208 at 3.2 A as a function of temperature. The solid line is the temperature dependence calculated from the phonon density of states. The arrow indicates the superconducting transition [4]...

Since the total pressure of the vapor-liquid system is constant, the equilibrium constant, Ki, has the same temperature dependence as the vapor pressure, P9. This variation with temperature may be quite large and can significantly complicate temperature-dependent calculations. 

The boundary between condensable and noncondensable components is somewhat arbitrary, especially because it depends on the range of temperatures where calculations are made. In this monograph we consider only common volatile gases (e.g. N2,... 

Calculated with temperature-dependent UNIQUAC parameters. 

Individual contributions to the second virial coefficient are calculated from temperature-dependent correlations ... 

CALCULATE THE TEMPERATURE DEPENDENT SECOND VIRIAL COEFFICIENTS. 

TAUS CALCULATES TEMPERATURE DEPENDENT INTERACTION COEFFICIENTS TAU FOf 4 USE IN SUBROUTINE GAMMA. IF SYSTEM DATA ARE MISSING (SOME REQUIRED 4 ENTRY IN MATRIX U IN COMMON/BINARY IS ZERO) CORRESPONDING TAU IS 4 SET TO 1 AND lER IS RETURNEO AS +/- 1. FOR NONCONDENSABLES PRESENT 4 IER IS -2 OR -I (OTHERWISE 0). 

TAUS calculates temperature dependent UNIQUAC binary interaction parameters, use in subroutine GAMMA and ENTH. 

It is not necessary to limit the model to idealized sites Everett [5] has extended the treatment by incorporating surface activity coefficients as corrections to N and N2. The adsorption enthalpy can be calculated from the temperature dependence of the adsorption isotherm [6]. If the solution is taken to be ideal, then... 

Several instniments have been developed for measuring kinetics at temperatures below that of liquid nitrogen [81]. Liquid helium cooled drift tubes and ion traps have been employed, but this apparatus is of limited use since most gases freeze at temperatures below about 80 K. Molecules can be maintained in the gas phase at low temperatures in a free jet expansion. The CRESU apparatus (acronym for the French translation of reaction kinetics at supersonic conditions) uses a Laval nozzle expansion to obtain temperatures of 8-160 K. The merged ion beam and molecular beam apparatus are described above. These teclmiques have provided important infonnation on reactions pertinent to interstellar-cloud chemistry as well as the temperature dependence of reactions in a regime not otherwise accessible. In particular, infonnation on ion-molecule collision rates as a ftmction of temperature has proven valuable m refining theoretical calculations. 

Zhu L, Chen W, Hase W L and Kaiser E W 1993 Comparison of models for treating angular momentum in RRKM calculations with vibrator transition states. Pressure and temperature dependence of CI+C2H2 association J. Phys. Chem. 97 311-22... 

Grigoleit U, Lenzer T and Luther K 2000 Temperature dependence of collisional energy transfer in highly excited aromatics studied by classical trajectory calculations Z. Phys. Chem., A/F214 1065-85... 

In applying this criterion, obs. must be compared with calc, for the same temperature. In general this entails knowledge of the temperature dependence of the relevant acidity function and of the ionisation constant. The latter factor has sometimes been allowed for (as in the calculation of calc, for the nitration of 2,4,6-trimethylpyridine in 98 % sulphuric acid at 80 °C) by using the approximate relationship, -d pKf) dT = (p, -o-9)/T. 

Molality is used in thermodynamic calculations where a temperature independent unit of concentration is needed. Molarity, formality and normality are based on the volume of solution in which the solute is dissolved. Since density is a temperature dependent property a solution s volume, and thus its molar, formal and normal concentrations, will change as a function of its temperature. By using the solvent s mass in place of its volume, the resulting concentration becomes independent of temperature. 

Chlorine, a member of the halogen family, is a greenish yellow gas having a pungent odor at ambient temperatures and pressures and a density 2.5 times that of air. In Hquid form it is clear amber SoHd chlorine forms pale yellow crystals. The principal properties of chlorine are presented in Table 15 additional details are available (77—79). The temperature dependence of the density of gaseous (Fig. 31) and Hquid (Fig. 32) chlorine, and vapor pressure (Fig. 33) are illustrated. Enthalpy pressure data can be found in ref. 78. The vapor pressure P can be calculated in the temperature (T) range of 172—417 K from the Martin-Shin-Kapoor equation (80) ... 

The temperature dependence of the open circuit voltage has been accurately determined (22) from heat capacity measurements (23). The temperature coefficients are given in Table 2. The accuracy of these temperature coefficients does not depend on the accuracy of the open circuit voltages at 25°C shown in Table 1. Using the data in Tables 1 and 2, the open circuit voltage can be calculated from 0 to 60°C at concentrations of sulfuric acid from 0.1 to 13.877 m. 

Tbe enthalpy of vaporization decreases with temperature and is zero at tbe critical point. If tbe value of an enthalpy of vaporization AH is known at temperature T, this temperature dependency can be represented by tbe Watson relation to calculate another enthalpy of vaporization AH at any other temperature To ... 

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