Isobar cut

Isobaric cuts from the threedimensional diagram at. C equilibrium mole fraction of C>2 in the sorbed... 

FIG. 3.S. Isobar cut across the valley of stability showing schetnalically the position of difTerent kinds of nuclei. 

As there exists a phase equilibrium both phases must have reached in the internal thermodynamic equilibrium with respect to the arrangement and distribution of the molecules the measuring time. Therefore, no time effects or path dependencies of the thermodynamic properties in the liquid crystalline phase should be expected. To check this point for the l.c. polymer, a cut through the measured V(P) curves at 2000 bar has been made (Fig. 6) and the volume values are inserted at different temperatures in Fig. 7, which represents the measured isobaric volume-temperature curve at 2000 bar 38). It can be seen from Fig. 7 that all specific volumes obtained by the cut through the isotherms in Fig. 6 he on the directly measured isobar. No path dependence can be detected in the l.c. phase. From these observations we can conclude that the volume as well as other properties of the polymers depend only on temperature and pressure. The liquid crystalline phase of the polymer is a homogeneous phase, which is in its internal thermodynamic equilibrium within the normal measuring time. 

The threedimensional diagram for N2 and O2, for various mixtures, is shown on Figure 3. Cuts at constant total pressure give isobars, an example of which is given in Figure 4, and represents ability of adsorption of each sorbate at different equilibrium con-... 

Froment et al. [5,6] proposed a short-cut method for the first estimate of E, which turned out to be extremely efficient. Consider two experiments carried out in an isobaric flow reactor, one at a reference temperature T the other at the reference temperature, T2 and let the conditions be such that the temperature difference AT = T, — Tj is the same over the whole length of the reactor. The reaction taking place is homogeneous and of the type A B. If the feed rates are adjusted so that equal conversions are obtained then the conversion x or the pjt versus V... 

This equation, related to Poisson s equation of Section 13.6.1, states that the mean curvature of the pressure surface is zero. Figure 5.26 shows the predicted isobars for a flow into a mould with a cut-out (computed using the steady-state heat flow analogue). The velocity vectors are perpendicular to the isobars the circular arc isobars near the gate show there is radial flow, but in sections with parallel side walls, the velocity is parallel to the walls. 

In all Figures in this Report the p(x) isotherms, the T(x) isobars, and the p(T) isopleths [= p(T) cuts for x = const.] are represented by solid lines, all kinds of critical curves by thick solid lines, the p(T) phase diagrams of the pure components by dashed lines, and the three-phase curves (e.g, LLG) by ———. Two-phase regions are indicated by hatching. 

Gas-Liquid Critical Curves of Binary Systems. In Figure la the pressure-temperature-composition surface is represented schematically for the gas-liquid equilibria of a binary system in a simple case. The dashed lines are the vapour pressure curves of the pure components they end at the critical points CP I and CP II of the pure components I and II. Some pressure-composition cuts for constant temperature are given. The critical point of the binary system is situated at the extreme value of each p x) isotherm or (not shown in Figure la) at the extreme value of each T x) isobar. The line that connects the critical points of all binary mixtures is the critical curve in a pressure-temperature projection the critical curve is the envelope of all p T) curves for constant composition (so-called isopleths). At temperatures and pressures beyond the critical curve the constituents are miscible in all proportions. 

The polymer injection project consists of 18 producing wells and 4 injectors, distributed among 3 contiguous zones, representing a pore volume of 640 000 m. Four producers were turned into injectors for this purpose, but no additional well was drilled. The choice of the injectors was based on the results of interference tests and the isobar and isopach maps (fig. 2 and 3). Before injection, the cumulative production of the Courtenay field was 332 000 m3 oil, with an average oil cut of about 11 %. 

Figure4.6 shows the van der Waals chemical potential along three isobars close to the critical point (top) and over an expanded temperature range (bottom), i.e. we compute p along three horizontal lines in the lower panel of Fig. 4.4 just below, at, and just above the critical pressure. For p = 0.96 we cut across the gas-liquid phase transition. Notice that the dashed lines indicate the continuation of the liquid (low t) and gas (high t) chemical potentials into their respective metastable region, i.e. the region between spinodal and binodal line. This justifies our sketches of the chemical potential in Fig.(3.20) and in principle also in Fig.(3.21). At p = 1 the chemical potential still exhibits a kink, whereas above its slope changes smoothly.

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