Temperature-versus-pressure phase diagram

Figure 8. Temperature versus pressure phase diagram of a micellar solution of sodium oleate, 13 wt % in water. (Adapted from ref. 19).

Fig. 4.37 (a) The NMR centrai-line spectra of in the 3-phase and S-phase of RbAg4l5 at 169.5 K and pressures of 640 and 650 MPa, respectively and (b) the temperature-versus-pressure phase diagram of RbAg4l5. ... 

F is at most two because the minimum value for p is one. Thus, the temperature and pressure can be varied independently for a one-component, one-phase system and the system can be represented as an area on a temperature versus pressure diagram. 

At a given pressure and temperature, the total Gibbs free energy of mixing of a one-phase polymer-solvent system of composition 2 should be necessarily minimum, otherwise the system will separate into two phases of different composition, as it is represented in a typical AG versus cp phase diagram of a binary solution (Fig. 25.3). The volume fractions at the minima (dAGIdcp = 0), cp, and (p will vary with temperature (binodal) up to critical conditions (T and (p ) where cp = tp" (Fig. 25.3b). 

Fig. 8.2 Illustration of basic phase diagrams of gas, liquid and solid of the single component system separately according to temperature versus pressure (/ ) and temperature versus density (right)...

Figure 6.6 Room-temperature pressure versus composition phase diagram of Bai Sr,fRu03 [34].

For a pure substance, the phase diagram is simply a graph of temperature versus pressure. For mixtures, the phase diagram also includes variables that describe the composition of the substance. To illustrate the information contained in a phase diagram, we will examine the phase diagrams of two pure substances water and carbon dioxide. 

FIG. 4.4 The surface conditions of different places in the solar system plotted on a phase diagram of temperature versus pressure. Note how the Earth sits in the liquid water region and Titan sits in the liquid methane region, but other places fall outside these regions and do not maintain surface oceans. 

Fig. 45. Specific heat divided by temperature versus Fig. 46. Zero-field temperature versus pressure temperature for a polycrystalline sample of UPtj at various phase diagram for UPt3 based on the data...

Figure A2.5.1. Schematic phase diagram (pressure p versus temperature 7) for a typical one-component substance. The full lines mark the transitions from one phase to another (g, gas liquid s, solid). The liquid-gas line (the vapour pressure curve) ends at a critical point (c). The dotted line is a constant pressure line. The dashed lines represent metastable extensions of the stable phases.

Figure A2.5.3. Typical liquid-gas phase diagram (temperature T versus mole fraction v at constant pressure) for a two-component system in which both the liquid and the gas are ideal mixtures. Note the extent of the two-phase liquid-gas region. The dashed vertical line is the direction x = 1/2) along which the fiinctions in figure A2.5.5 are detemiined.

Figure A2.5.5. Phase diagrams for two-eomponent systems with deviations from ideal behaviour (temperature T versus mole fraetion v at eonstant pressure). Liquid-gas phase diagrams with maximum (a) and minimum (b) boiling mixtures (azeotropes), (e) Liquid-liquid phase separation, with a eoexistenee eurve and a eritieal point.

Solid-Fluid Equilibria The phase diagrams of binai y mixtures in which the heavier component (tne solute) is normally a solid at the critical temperature of the light component (the solvent) include solid-liquid-vapor (SLV) cui ves which may or may not intersect the LV critical cui ve. The solubility of the solid is vei y sensitive to pressure and temperature in compressible regions where the solvent s density and solubility parameter are highly variable. In contrast, plots of the log of the solubility versus density at constant temperature exhibit fairly simple linear behavior. 

Hydrogen phase diagram (pressure versus temperature). 

At a given temperature and pressure eqs. (4.7) and (4.8) must be solved simultaneously to determine the compositions of the two phases a and P that correspond to coexistence. At isobaric conditions, a plot of the composition of the two phases in equilibrium versus temperature yields a part of the equilibrium T, x-phase diagram. 

Figure 5.12 is the pressure versus temperature phase diagram for the methane+ water system. Note that excess water is present so that, as hydrates form, all gas is incorporated into the hydrate phase. The phase equilibria of methane hydrates is well predicted as can be seen by a comparison of the prediction and data in Figure 5.12 note that the predicted hydrate formation pressure for methane hydrates at 277.6 K is 40.6 bar. 

Figure 5.13 is the equivalent ethane + water pressure versus temperature phase diagram. Note that the Aq-sI-V line intersects the Aq-V-Lhc line at 287.8 K and 35 bar. Due to differences in the volume and enthalpy of the vapor and liquid hydrocarbon, the three-phase hydrate formation line changes slope at high temperature and pressure from Aq-sI-V to Aq-sI-Lhc, due to the intersectiion of Aq-sI-V line with the Aq-V-Lhc line (slightly higher than the ethane vapor pressure). Note that the hydrate formation pressure for ethane hydrates at 277.6 K is predicted to be 8.2 bar. 

Figure 5.14 is the propane + water pressure versus temperature phase diagram. Note that the data are scattered along the Aq-sII-Lhc line due to difficulty... 

To evaluate the phase equilibria of binary gas mixtures in contact with water, consider phase diagrams showing pressure versus pseudo-binary hydrocarbon composition. Water is present in excess throughout the phase diagrams and so the compositions of each phase is relative only to the hydrocarbon content. This type of analysis is particularly useful for hydrate phase equilibria since the distribution of the guests is of most importance. This section will discuss one diagram of each binary hydrate mixture of methane, ethane, and propane at a temperature of 277.6 K. 

To test the predictions, experiments were carried out at the Delft University of Technology (TUD) (Ballard et al., 2001). In CSMGem, the pressure versus temperature phase diagram was generated using the model and then confirmed by experimental data. Figure 5.19 is the pressure versus temperature diagram for a 30/70 mixture of ethane and propane in contact with excess water. 

On the phase diagram (Figure 23.3) the lines AD, BC and EF when extrapolated meet at a point labelled as the triple point, corresponding to one single specific temperature and one single specific pressure at which all three phases (solid, liquid and gas) will coexist and be equally stable (see Frame 50, section 50.4). This corresponds to the situation (at a specific pressure which we have labelled P ) where the curves of Gg, G and Gs versus temperature mutually intersect with one another. 

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