Weber equation

The data available in the literature up to 1973 have been reviewed by Jamieson el al. (1975). The Weber equation (Weber, 1880) can be used to make a rough estimate of the thermal conductivity of organic liquids, for use in heat-transfer calculations. 

The nucleation rate constant (Eq. (5.8.5)) k depends on the size of the critical crystallization nucleus according to the Volmer-Weber equation... 

The synthesis of diarsirane by exposing diarsene to an ethereal solution of diazomethane at room temperature was reported by Weber (Equation (16)) <89CB1809>. 

From an experimental point of view, however, it seems that little progress has been made since the evaluation of the Volmer-Weber equation in 1926. The experimentalist is bound to use Eq. (62), disregarding the small noninfor-mative dependence of ki from rjc derived from the Zeldovich factor or the attachment frequency Wa,c ... 

Keywords Counter-current gas diffusion. Permeation, Transport parameters. Mean Transport-Pore Model, Maxwell-Stefrn equation, Weber equation... 

As a model we have used the Mean Transport-Pore Model (MTPM) [6] which assumes that the decisive part of the gas transport takes place in transport-pores that are visualized as cylindrical capillaries. The transport-pore radii are distributed around the mean value (first model parameter). The width of this distribution is characterized hy the mean value of the squared transport-pore radii, (second model parameter). The third model parameter is the ratio of porosity, y/i, and tortuosity of transport-pores, qt, q/= Pore diffusion is described by the Maxwell-Stefan diffusion equation extended to account for Knudsen transport [6]. For gas permeation the simplified form of Weber equation [8-10] is used. 

The first term is essentially the reciprocal of the Weber number and the second term is a function of the Ohnesorge number. Equation 13 may be invaHd for airblast atomizers operating at high pressures, >1 MPa (>10 atm), or with high viscosity Hquids. 

Tbe 1993 ASHRAE Handbook—Fundamentals (SI ed.) gives saturation data to 150 C and a diagram to 20 bar, 150 C. For equation of state including decomposition, see Weber, L. A., paper 69, Proc, 18th Int. Congt Reftig., Montreal, 1991. 

Equations (6-236) to (6-239) are based on experiments on cube-oc tahedrons, octahedrons, cubes, and tetrahedrons for which the sphericity f ranges from 0.906 to 0.670, respectively. See also Chft, Grace, and Weber. A graph of drag coefficient vs. Reynolds number with y as a parameter may be found in Brown, et al. (Unit Operations, Whey, New York, 1950) and in Govier and Aziz. 

For example, in the case of dilute solutions, the van t Hoff s equation may be used to piedict the osmotic pressure (jr = CRT) where n is the osmotic pressure of the solution, C is the molar concentration of the solute, ft is the universal gas constant and T is the absolute temperature, Fm dissociating solutes, the concentration is that of the total ions. For example, NaCI dissociates in water into two ions Na" " and Cl . Therefore, the total molar concentration of ions is hvice the molar concentration of NaCI. A useful rule of thumb for predicting osmotic pressure of aqueous solutions is 0,01 psi/ppm of solute (Weber, 1972). 

Equation (14.101) was first derived by Weber, although it is formally represented in a different way. 

In their analysis, however, they neglected the surface tension and the diffusivity. As has already been pointed out, the volumetric mass-transfer coefficient is a function of the interfacial area, which will be strongly affected by the surface tension. The mass-transfer coefficient per unit area will be a function of the diffusivity. The omission of these two important factors, surface tension and diffusivity, even though they were held constant in Pavlu-shenko s work, can result in changes in the values of the exponents in Eq. (48). For example, the omission of the surface tension would eliminate the Weber number, and the omission of the diffusivity eliminates the Schmidt number. Since these numbers include variables that already appear in Eq. (48), the groups in this equation that also contain these same variables could end up with different values for the exponents. 

Thermodynamic and mechanical equilibrium on a curved vapor-liquid interface requires a certain degree of superheat in order to maintain a given curvature. Characteristics of homogeneous and heterogeneous nucleation can be estimated in the frame of classical theory of kinetics of nucleation (Volmer and Weber 1926 Earkas 1927 Becker and Doring 1935 Zel dovich 1943). The vapor temperature in the bubble Ts.b can be computed from equations (Bankoff and Flaute 1957 Cole 1974 Blander and Katz 1975 Li and Cheng 2004) for homogeneous nucleation in superheated liquids... 

Busch and Weber (ref. 1) first reported the Pd catalyzed coupling of halogenated aromatic compounds. Their reaction conditions and some examples of their work are shown in equations (4) to (7). 

Measurements of tan A as a function of temperature for the six humic fractions are plotted in Figures 2a-f. These measurements were made at pH 6.5. These plots show a maximum between 6 °C emd 25 °C. Equation 15 offers another method for the calcuation of the molar volume based on the emisotropy of the molecule and the temperature and viscosity at the experimental maximum of the tan A plots. The consequences of obtaining the volume in this manner are discussed by Mantulin and Weber U8J. 

Silva and Weber (1993) reported vapor pressure measurements for the 1-ch oro-l,l-Difluoroethane (RI42b) and 1,1 -Difluoroethane (R152a) refrigerants. The data are given in Tables 3.5 and 3.6 respectively. Use Antoine s equation to correlate the data for R142b and the following equation for R152a (Silva and Weber, 1993)... 

Weber (8) states that the intermediate thiophosphoryl chloride can be obtained from phosphorus pentachloride, as shown in Equation 10. 

According to equation 7.15, at higher temperatures and low pH values (around pH 2). As already stated, Weber (1984) was able to carry out a thioester synthesis starting from glycerinealdehyde and A-acetylcysteine. 

Wesolowski, T. A. and J. Weber. 1996. Kohn-Sham equations with constrained electron density an iterative evaluation of the ground-state electron density of interacting molecules. Chem. Phys. Lett. 248,71. 

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