Poynting

These were converted from vapor pressure P to fugacity using the vapor-phase corrections (for pure components), discussed in Chapter 3 then the Poynting correction was applied to adjust to zero pressure ... 

If the data are correlated assuming an ideal vapor, the reference fugacity is just the vapor pressure, P , the Poynting correction is neglected, and fugacity coefficient is assumed to be unity. Equation (2) then becomes... 

Finally, at low pressures, the liquid fugacity can be calculated using Equation (5), i.e. we can assume that <() = 1 and that the Poynting correction = 1. 

Standard-state fugacities at zero pressure are evaluated using the Equation (A-2) for both condensable and noncondensable components. The Rackett Equation (B-2) is evaluated to determine the liquid molar volumes as a function of temperature. Standard-state fugacities at system temperature and pressure are given by the product of the standard-state fugacity at zero pressure and the Poynting correction shown in Equation (4-1). Double precision is advisable. 

POX. See Polyoxetane Poxvindae Poynting correction Poynting factor POY nylon yarn Pozzolans... 

At system pressures up to several tens of MPa, the fugacity coefficients, ( ) and and the Poynting factor, 7T, are usually near unity. A simplified version of equation 19 can therefore be used for the majority of vapor—Hquid equihbrium problems ... 

Vapor pressure is the most important of the basic thermodynamic properties affec ting liquids and vapors. The vapor pressure is the pressure exerted by a pure component at equilibrium at any temperature when both liquid and vapor phases exist and thus extends from a minimum at the triple point temperature to a maximum at the critical temperature, the critical pressure. This section briefly reviews methods for both correlating vapor pressure data and for predicting vapor pressure of pure compounds. Except at very high total pressures (above about 10 MPa), there is no effect of total pressure on vapor pressure. If such an effect is present, a correction, the Poynting correction, can be applied. The pressure exerted above a solid-vapor mixture may also be called vapor pressure but is normallv only available as experimental data for common compounds that sublime. 

The exponential is known as the Poynting factor. Equation (4-277) may now be written... 

When Eq. (4-282) is applied to XT E for which the vapor phase is an ideal gas and the liquid phase is an ideal solution, it reduces to a veiy simple expression. For ideal gases, fugacity coefficients and are unity, and the right-hand side of Eq. (4-283) reduces to the Poynting factor. For the systems of interest here this factor is always veiy close to unity, and for practical purposes <1 = 1. For ideal solutions, the activity coefficients are also unity. Equation (4-282) therefore reduces to... 

Fig. 10. The mole fraction of carbon dioxide in saturated solutions in air at — 110°C (above the lower critical end point). The full line is the experimental curve of Webster and the dashed curves are 1, an ideal gas mixture 2, an ideal gas mixture with Poynting s correction and 3, the solubility calculated from Eq. 8 and the principle of corresponding states.

Poynting (1881), from considerations based on equation (1) of 100, surmised that ice would melt, if the pressure on it is raised in such a way that any water produced flows away, under a pressure which is for a given temperature, only that on the fusion curve (i.e., when the water remains in contact with the... 

Poynting also expressed the opinion that a critical point of... 

For components near or above their critical temperatures, the liquid volume t>j was evaluated by extrapolation with respect to temperature. For supercritical components, the fugacity f° was also evaluated by extrapolation the effect of pressure was found from the Poynting relation using the previously extrapolated liquid molar volumes. 

The exponential term in equation 8.32 is known as the Poynting correction, and corrects for the effects of pressure on the liquid-phase fugacity. 

The fundamental fact on which the analysis of heterogeneous reactions is based is that when a component is present as a pure liquid or as a pure solid, its activity may be taken as unity, provided the pressure on the system does not differ very much from the chosen standard state pressure. At very high pressures, the effect of pressure on solid or liquid activity may be determined using the Poynting correction factor. 

According to the Poynting formula, the time-averaged dissipated power density Pdiss (r) at any position r within a lossy material is given by Eq. (15) ... 

There is a close similarity with planar electromagnetic cavities (H.-J. Stockmann, 1999). The basic equations take the same form and, in particular, the Poynting vector is the analog of the quantum mechanical current. It is therefore possible to experimentally observe currents, nodal points and streamlines in microwave billiards (M. Barth et.al., 2002 Y.-H. Kim et.al., 2003). The microwave measurements have confirmed many of the predictions of the random Gaussian wave fields described above. For example wave function statistics, current flow and... 

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The above reasoning has led to the fireball internal-external shocks model. This model is rather independent of the nature of the central engine. The latter one is just required to produce highly relativistic outflow, either in the form of kinetic energy or as Poynting flux. The radiation is produced in (collisionless) shocks. These can either occur due to interaction of the outflow with the cir-cumstellar material ( external shocks ) or due to interactions of different portions of the outflow with different Lorentz-factors, so-called internal shocks . 

To calculate the multicomponent vapor-liquid equilibrium, equilibrium constants for chemical reactions 1-9 are taken from literature in comparison to the original publication, in the present work different numerical values for the second dissociations of hydrogen sulfide and sulfur dioxide were chosen (cf. Appendix III). Henry s constants are evaluated from single solute solubility data without neglecting Poynting corrections ... 

Partial molar volumes at infinite dilution were adopted from the correlation of Brelvi and O Connell (20). (In the pressure range regarded here (p 100 atm) Poynting corrections are very small and can be neglected for all electrolytes as well as for water (eqs. E1, E2) ). ... 

The average energy flux in the evanescent wave is given by the real part of the Poynting vector S = (c/47t)ExH. However, the probability of absorption of energy per unit time from the evanescent wave by an electric dipole-allowed transition of moment pa in a fluorophore is proportional to lnfl - El2. Note that Re S and pa E 2 are not proportional to each other they have a different dependence on 0. 

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