Isobaric

Predictions for the other isobaric systems (experimental data of Sinor, Steinhauser, and Nagata) show good agreement. Excellent agreement is obtained for the system carbon tetrachlor-ide-methanol-benzene, where the binary data are of superior quality. 

To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

Application of the algorithm for analysis of vapor-liquid equilibrium data can be illustrated with the isobaric data of 0th-mer (1928) for the system acetone(1)-methanol(2). For simplicity, the van Laar equations are used here to express the activity coefficients. 

The isobaric specific heat for a petroleum fraction is estimated by a correlation attributed to Watson and Nelson in 1933, which was used again by. Johnson and Grayson in 1961 as well as by Lee and Kesler in 1975. This relation is valid at low pressures i... 

Alternatively, data may be plotted as n versus T at constant pressure or as P versus T at constant n. One thus has adsorption isobars and isosteres (note Problem XVII-2). 

Read off points from Fig. XVII-1 and plot a set of corresponding isosteres and isobars. 

Thus for isobaric processes a new fimction, the enthalpy H, has been introduced and its change A// is more directly related to the heat that must have been absorbed than is the energy change At/. The same reservations about the meanmg of heat absorbed apply in this process as in the constant-volume process. 

D) CONSTANT-TEMPERATURE CONSTANT-PRESSURE (ISOTHERMAL-ISOBARIC) PROCESSES... 

Two other important quantities are the isobaric expansivity ( coefficient of themial expansion ) and the isothermal compressibility k, defined as... 

The adjectives isobaric and isothennaT and the corresponding subscripts are frequently omitted, but it is important to distinguish between the isothemial compressibility and the adiabatic compressibility. ... 

Evans D J and Morriss G P 1983 The Isothermal Isobaric molecular dynamics ensemble Phys. Lett. A 98 433-6... 

Wood W W 1968 Monte Carlo calculations for hard disks in the isothermal-isobaric ensemble J. Chem. Phys. 48 415-34... 

However, it is common practice to sample an isothermal isobaric ensemble NPT, constant pressure and constant temperature), which normally reflects standard laboratory conditions well. Similarly to temperature control, the system is coupled to an external bath with the desired target pressure Pq. By rescaling the dimensions of the periodic box and the atomic coordinates by the factor // at each integration step At according to Eq. (46), the volume of the box and the forces of the solvent molecules acting on the box walls are adjusted. 

The type of treatment described here was originally introduced by Scott and Dullien [4], who confined attention to isothermal isobaric diffusion in binary mixtures. Similar equations were independently published shortly after by Rothfeld [5], and the method was later extended to multi-component mixtures by Silveston [6], Perhaps the most complete exposition is given by Mason and Evans [7],... 

Che pore size distribution and Che pore geometry. Condition (iil). For isobaric diffusion in a binary mixture Che flux vectors of Che two species must satisfy Graham s relation... 

These are equivalent to the dusty gas model equations, but are valid only for isobaric conditions, and this fact severely limits the capability of the model to represent Che behavior of systems with chemical reaction. To see this we need only remark that (8,7) and (3.8) together imply that ... 

Though illustrated here by the Scott and Dullien flux relations, this is an example of a general principle which is often overlooked namely, an isobaric set of flux relations cannot, in general, be used to represent diffusion in the presence of chemical reactions. The reason for this is the existence of a relation between the species fluxes in isobaric systems (the Graham relation in the case of a binary mixture, or its extension (6.2) for multicomponent mixtures) which is inconsistent with the demands of stoichiometry. If the fluxes are to meet the constraints of stoichiometry, the pressure gradient must be left free to adjust itself accordingly. We shall return to this point in more detail in Chapter 11. 

Of course, these shortcomings of the Wakao-Smith flux relations induced by the use of equations (8.7) and (8.8) can be removed by replacing these with the corresponding dusty gas model equations, whose validity is not restricted to isobaric systems. However, since the influence of a strongly bidisperse pore size distribution can now be accounted for more simply within the class of smooth field models proposed by Feng and Stewart [49], it is hardly worthwhile pursuing this."... 

The parameter is better found from experiments under isobaric... 

It must be emphasized that equation (10.14) is based on the assumption of strictly isobaric diffusion. In practice, we may ask, how closely must the pressures on the two sides of the diffusion cell be balanced if undue error is not to be associated with the use of (10.14) The answer, of course, is that pressure gradients must be small enough that the term in grad p on the right hand side of equation (10.4) is negligible coranared with the term in grad Since the viscous term dominates the coeffi-... 

Remick and Geankoplis made flux measurements for both species in the isobaric diffusion of nitrogen and helium through their tube bundle. Pressures spanned the interval from 0.444 nim, Hg to 300,2 ram Hg, which should cover the whole range between the limits of Knudsen streaming and bulk diffusion control. Then, since K and K, are known in this case, the form of the proposed flux relations could be tested immediately by plotting the left hand side of equation (10.15) against... 

They then compared measured and predicted fluxes for diffusion experiments in the mixture He-N. The tests covered a range of pressures and a variety of compositions at the pellet faces but, like the model itself, they were confined to binary mixtures and isobaric conditions. Feng and Stewart [49] compared their models with isobaric flux measurements in binary mixtures and with some non-isobaric measurements in mixtures of helium and nitrogen, using data from a variety of sources. Unfortunately the information on experimental conditions provided in their paper is very sparse, so it is difficult to assess how broadly based are the conclusions they reached about the relative merits oi their different models. 

As In the case of the isobaric experiment, it would also be possible to interpret these flux measurements in terms of a Fick equation with an effective... 

Equations (10.32) and (10.37) show that same, so an "effective diffusivity" determined from an isobaric... 

Wicke-Kallenbach experiment would incorrectly predict the flux in the second experiment if used in a simple Fick equation of the form (10.31). However, if the isobaric flux measurements had been interpreted in terms of... 

It appears that a loose interpretation of this type may be the origin of a discrenancy found by Otanl and Smith [59] in attempting to apply effective diffusivities from Wakao and Smith s [32] isobaric diffusion data to measurements on a chemically reacting system. This was pointed out by Steisel and Butt [60], and further pursued to the point of detailed computer modeling of a particular pore network by Wakao and Nardse [61]. 

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