Boundary curves

Liquid gas boundary curves, 87 Lithium atom, ground state of, 313 Lithium hydride, electronic correlation, 324... 

Solid gas boundary curves, 87 Solid liquid boundary curves, 87 Solubility, in a compressed gas, 92 of a solid in a liquid, 86 of quartz, 99... 

FIGURE 8.10 The liquid-vapor boundary curve is a plot of the vapor pressure of the liquid (in this case, water) as a function of temperature. The liquid and its vapor are in equilibrium at each point on the curve. At each point on the solid liquid boundary curve (for which the slope is slightly exaggerated), the solid and liquid are in equilibrium. 

The study of the peak temperature sensitivity to the reactor operating parameters and the construction of sensitivity boundary curves for stable reactor operation were previously reported ( l). This paper presents a computer study on conceptual relationships between the conversion-product properties and the reactor operating parameters in a plug flow tubular reactor of free radical polymerization. In particular, a contour map of conversion-molecular weight relationships in a reactor of fixed size is presented and the sensitivity of its relationship to the choice of initiator system, solvent system and heat transfer system are discussed. 

The normal melting, boiling, and triple points give three points on the phase boundary curves. To construct the curves from knowledge of these three points, use the common features of phase diagrams the vapor-liquid and vapor-solid boundaries of phase diagrams slope upward, the liquid-solid line is nearly vertical, and the vapor-solid line begins at P = 0 and P = 0 atm. 

If there are included among the diluents mixed with the crystalline polymer some which are sufficiently poor solvents, the phase diagram may then exhibit liquid-liquid phase separation, in addition to the liquid-crystal boundary curve. Examples are shown in Figs. 133... 

A phase diagram describes how a system reacts to changing conditions of pressure and temperature and consists of a field in which only one phase is stable, separated by boundary curves along which a combination of phases coexist in equilibrium. 

Within the PV region delimited by the two saturation boundary curves, liquid and vapor phases coexist stably at equilibrium. To the right of the vapor saturation curve, only vapor is present to the left of the liquid saturation curve, vapor is absent. Let us imagine inducing isothermal compression in a system composed of pure H2O at T = 350 °C, starting from an initial pressure of 140 bar. The H2O will initially be in the gaseous state up to P < 166 bar. At P = 166 bar, we reach the vapor saturation curve and the liquid phase begins to form. Any further... 

The liquid region, limited by the vaporization boundary (i.e., the liquid saturation and vapor saturation boundary curves) and the critical isobar. 

The main usefulness of Eh-pH diagrams consists in the immediacy of qualitative information about the effects of redox and acid-base properties of the system on elemental solubility. Concerning, for instance, cerium, figure 8.20 immediately shows that, within the stability field of water, delimited upward by oxidation boundary curve o and downward by reduction boundary curve r, the element (in the absence of other anionic ligands besides OH groups) is present in solution mainly as trivalent cerium Ce and as soluble tetravalent hydroxide Ce(OH)2. It is also evident that, with increasing pH, cerium precipitates as trivalent hydroxide Ce(OH)3. 

Figure 6. Phase diagram of a three-component system consisting of one binary and one ternary compound. Boundary curves are solid and composition lines are dashed. The arrows indicate the direction of falling temperature.

Figure 8.24. Simpler circuits of compression refrigeration (see also Example 8.17). (a) Basic circuit consisting of a compressor, condenser, expansion valve and evaporator (load), (b) Conditions of the basic circuit as they appear on a pressure-enthalpy diagram the primed points are on the vapor-liquid boundary curve, (c) Circuit with circulation of refrigerated brine to process loads, (d) Circuit with two-stage compression and intercooling.

As the temperature is further decreased, the compositions of a and a are changed along the gap boundary curve. At the temperature T,... 

These lines are called liquidus isotherms. The intersections of adjoining liquidus surfaces like ae, be and ce are called the boundary curves. When a liquid whose composition lies in the region surrounded by Aceh is cooled, the first crystalline phase that appears is A, and hence A is called the primary phase and the region Aceh is the primary field of A. In this field, solid A is the last solid to disappear when any composition within this field is heated. Similarly,B and C are primary phases in their respective primary fields, Baec and Caeb. 

In this case, the Alkemade line C-AB does not cross die boundary curve ef) between these primary phases. Now, we state the Alkemade theorem in a more general form ... 

The direction of falling temperature on the boundary curve of two intersecting primary phase areas is always away from die Alkemade line. 

If die Alkemade line intersects the boundary curve, the point of intersection represents a temperature maximum on the boundary curve. 

If the Alkemade line does not intersect die boundary curve, then temperature maximum on the curve is represented by that end which if prolonged would intersect the Alkemade line. 

The ternary invariant points (e.g., e and /in the above diagrams) that appear in a system without solid solution are either ternary eutectics or ternary peritectics. Whether it is eutectic or peritectic is determined by the directions of falling temperatures along the boundary curves. 

If an invariant point is the minimum point in temperature along all three boundary curves, it is a ternary eutectic. 

At point w which is an arbitrary point on the boundary curve ue, the mean composition of the solid is represented by the point x. Proportions of solid A and solid B are determined by the lever rule (solid A)/(solid B) = x-B/A-x. The ratio of liquid to solid is also given by the lever rule q-x/w-q. 

Because the primary fields of A and BC are not in contact with each other, and hence these two fields do not form a boundary curve. 

Phase 8 continues to crystallise out until the liquid composition contacts the boundary curve between 8 and J3 at point k. 

Both extensions of the boundary curves of the single phase areas must project either into the triangle (y comer), or outside triangle (P comer), but not in mix. Hie a comer is wrong. 

The thermodynamic analysis predicted that the minimum steam ratio should decrease with increasing temperature above 650°C and gradually level off at round 900°C. Similarly, the experimentally established coke boundary curve exhibits very much the same behavior, however, the experimental values of the minimum ratio are considerably higher than the theoretical ones at all temperatures. 

It is well known that the polymer systems undergo various mechanical treatments during their exploitation. This leads to the change of component compatibility and to the shift of boundary curves. The theory of this phenomenon has been worked out. The present article is dealing with the study of influence of the shear rates (j) and stresses (d) on phase transitions in the systems PDMS (1 =2.7 105) -MEK and CA-I (Mn=6.1 lC)4 > degree of substitution (DS)2.4)-dioxane-water,... 

Fig.2 shows the boundary curves for PDMS-MEK system under static and dinamic conditions. One can see that, shear deformation causes the shift of the boundary curves at the low shear rat.e( ) and stress (6) (6=, where 1 -the viscosity of the system) the component compatibility increases that manifests itself in the decrease of Tph, at the high(j) or (3) the shear field causes the increase of Tph testifying to the decrease of the mutual compatibility. So an inversion of the effect that the shear- field has on phase transitions was discovered for this system. 

The boundary curves for the systems CA-I-acetone-water and CA-11-dioxane-water are shown in Fig.3.(a,b). 

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