Pressure-temperature projection

Figu re I. I. The pressure-temperature projection of a typical binary solvent-solute system. See text for discussion. SLV, solid/liquid/vapor LCEP, lower critical end point UCEP, upper critical end point. 

Figure 1. Pressure -Temperature Projection of Vapor Pressure Curve for Pentane and Solid-Liquid-Gas Equilibrium Curve for Pentane-TPP Mixtures.

With reference to the pressure-temperature projection in Fig. 2, we see that in order to construct a P-x diagram at Ti, a line parallel to the pressure axis passing from low pressure to high pressure is drawn and the points of intersection with features in the projection are noted. For the P-x at Ti example, the construction line intersects the vapor pressure curve for pure A, the dew and bubble pressure curves for the mixture with... 

In the Type IV pressure temperature projection illustrated in Fig. 3, the binary mixture exhibits partial miscibility at low temperature and near the critical... 

Fig. 4 Possible pressure-temperature projections for Type I binaries including solids.

Fig. 5 Possible pressure-temperature projections for Type IV binaries including solids where the melting point of component A increases from A to D.

A simple pressure-temperature projection of the pressure-temperature-composition diagram for a mixture is given in Figure 2. It is necessary to define the terms bubble point, dew point, maxcondentherm, and maxcondenbar. A bubble point is a state of liquid mixture at which, if the pressure is decreased slightly, a second phase, a vapour, appears. Similarly, a dew point is a state of a vapour at which, if the pressure is increased slightly, a liquid phase appears. The dew point locus and the bubble point locus are continuous curves meeting at the critical point. The maxcondentherm and maxcondenbar are the maximum temperature and maximum pressure respectively on the bubble point-dew point... 

Figure 2 is the simplest pressure-temperature projection. More complicated projections have been discussed elsewhere, and are reviewed in Chapter 4. 

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 phase equilibria and the critical phenomena are most easily understood with the aid of the pressure-temperature projections of the critical lines. The most important types are schematically represented in Figure lb. The critical... 

Fig. 27. Pressure—temperature projection of the phase diagram of a binary mixture of pentamer + monomer with = 1 (a) and = 0.9 (b). The filled symbols are simulation results for the critical line, while the empty symbols are simulation results for the vapor—liquid coexistence of the pure components. The short-dashed line is the critical line from TPTl, while the long-dashed line is the critical line from TPTl when parameters are rescaled to the critical point of the pure components. Full lines are TPTl predictions for the vapor pressure of the pure components (results from [244])...

Fig. 30. Panel (a) shows the pressure-temperature projection of mixtures of n-alkanes and CO2 for several chain lengths. At high pressnres, all such lines become almost vertical, a featnre characteristic of hquid-hquid immiscibihty. In panel (b) the critical temperatures at 1600 bar are used to plot a Flory—Schulz plot in order to show the occurrence of a high pressure 0 point...

Glassification of Phase Boundaries for Binary Systems. Six classes of binary diagrams have been identified. These are shown schematically in Figure 6. Classifications are typically based on pressure—temperature (P T) projections of mixture critical curves and three-phase equiHbria lines (1,5,22,23). Experimental data are usually obtained by a simple synthetic method in which the pressure and temperature of a homogeneous solution of known concentration are manipulated to precipitate a visually observed phase. 

The pressure-temperature-composition diagram presented by Morey is shown in Fig. 8. The vapor pressure of pure water (on the P-T projection) terminates at the critical point (647 K, 220 bar). The continuous curve represents saturated solutions of NaCl in water, i.e., there is a three-phase equilibrium of gas-solution-solid NaCl. The gas-phase pressure maximizes over 400 bar at around 950 K. Olander and Liander s data for a 25 wt. % NaCl solution are shown, and T-X and P X projections given. At the pressure maximum, the solution phase contains almost 80% NaCl. 

The engineering challenges include heat exchanger design, performance and accommodation of high pressures, temperatures and thermal stresses. If successfully developed the technology could be applied in the liquefaction of natural gas to provide a low-cost alternative to diesel fuel. So far one unit is reported built having a liquefaction capacity of about 35 kg/h. In this unit, 30% of the input natural gas stream was consumed as heat input, with a 70% yield of LNG. A future system with a capacity of about 700 kg/h LNG and with a projected liquefaction rate of 85 % of the input gas stream is under development. 

The projection of the three-dimensional surface on the pressure-temperature plane gives the familiar pressure-temperature diagram of a one component system. The projection for only the solid, liquid, and vapor phases... 

Figure 5.11. Projection of the Gibbs energy surface on the pressure-temperature plane.

Figure 7.7 Phase relationships in the system Al2Si05-Mn2Si05 in pressure-temperature-composition space projected onto the P,Tplane (from Abs-Wurmbach et al., 1983 Langer, 1988). Note the large increase of the andalusite stability field (And) with increasing Mn3+ contents plotted as mole per cent theoretical MnjSiO end-member. Insets (a) and (b) show how the triple point at 500 °C and 3.8 kb for pure Al2Si05 increases with rising Mn3 content of andalusite. [Legend to Mn-Al solid-solutions (ss) Ky = kyanite Sill = sillimanite Bm=braunite Cor=corundum Vir=viridine Qu=quartz.]...

Activation by increased pressure, temperature or kinetic energy (collision), or some catalytic process, happens with conservation of angular momentum, (but not during photochemical activation). As the activated atom moves into an anisotropic molecular environment angular momentum vectors in projection along the Z-axis therefore reappear as for the free atom. Optimal alignment of all such vectors fixes the final molecular geometry. 

A new, versatile apparatus for the determination of reliable SLV and LLE phase-equilibrium data has been designed and tested. In a first project this equipment will be used for the separation of polymers by molecular weight with the SAS process. We will test the concept of using pressure, temperature and gas content to fine-tune the selectivity of that process. 

To determine the final temperature, enter the superheated-steam table at 14.7 psia (101.4 kPa), the final pressure, and project across to an enthalpy value equal to or less than the known enthalpy, 1231.3 Btu/lb (2864.0 kJ/kg). [The superheated steam table is used because the T-S diagram (Fig. 19.8) shows that the steam is superheated in the final state.] At 14.7 psia (101.4 kPa) there is no tabulated enthalpy value that exactly equals 1231.3 Btu/lb (2864.0 kJ/kg). The next lower value is 1230 Btu/lb (2861.0 kJ/kg) at T = 380°F (193.3°C). The next higher value at 14.7 psia (101.4kPa) is 1239.9 Btu/lb (2884.0 kJ/kg) at T = 400°F (204.4°C). Interpolate between these enthalpy values to find the final... 

In P-T projections, the composition axis is collapsed into the pressure-temperature plane. The vapor pressure curve for component A is labeled LV(A) and that for component B is labeled LV(B). These curves terminate at the component critical points (L = V) designated as hollow circles. In Fig. 2, dew pressure and bubble pressure curves for an intermediate composition x intersect at a point on the (L = V) critical locus where the liquid and vapor phases become critically identical. Normally, dew and bubble pressure curves are not shown in projections. They are shown here so that the construction of the related P-x at fixed T, and T-x at fixed P, phase diagrams is clearly illustrated. Each critical point on the critical locus corresponds to a fixed composition. Points close to the critical point of component A are critical points for mixtures with high concentrations of A, whereas points closer to the critical point of... 

Fig. 2 Pressure-temperature phase projection and examples of pressure-composition and temperature-composition phase diagrams for a Type I binary mixture.

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