Solid-vapor equilibrium line

Fig. 3.2. A stylized phase diagram for a simple pure substance. The dashed line represents 1 atm pressure and the intersection with the solid-liquid equilibrium line represents the normal boiling point and the intersection with the liquid-vapor equilibrium line represents the normal boiling point.

An exceptional case of a very different type is provided by helium [15], for which the third law is valid despite the fact that He remains a liquid at 0 K. A phase diagram for helium is shown in Figure 11.5. In this case, in contrast to other substances, the solid-liquid equilibrium line at high pressures does not continue downward at low pressures until it meets the hquid-vapor pressure curve to intersect at a triple point. Rather, the sohd-hquid equilibrium line takes an unusual turn toward the horizontal as the temperature drops to near 2 K. This change is caused by a surprising... 

Water, of course, makes transitions from solid ice to liquid water (at 0°C) to water vapor (at 100°C) as it is heated at 1.0 atm pressure. Because at the pressure of the triple-point, the transformation is directly from solid to gas, the triple point pressure must be below 1.0 atm. Because Amelt V for water is negative, by Eq. (38), the solid-liquid equilibrium line has negative slope, and the triple point must be above 0°C. Considering the steepness of the line, the difference is very small and the measured triple point of water is 0.0098°C and 611 Pa ( 4.6 torr). 

F liquid + vapor G liquid + vapor (critical point) H vapor the first dashed line (at the lower temperature) is the normal melting point, and the second dashed line is the normal boiling point. The solid phase is denser because of the positive slope of the solid/liquid equilibrium line. 

At high pressures, solid II can be converted (slowly) to solid III. Solid III has a body-centered cubic crystal structure. Line bd is the equilibrium line between solid II and solid III, while line be is the melting line for solid III.P A triple point is present between solid II, solid III, and liquid at point b. Two other triple points are present in this system, but they are at too low a pressure to show on the phase diagram. One involves solid II, liquid, and vapor while the other has solid I, solid II, and vapor in equilibrium. 

The lines separating the regions in a phase diagram are called phase boundaries. At any point on a boundary between two regions, the two neighboring phases coexist in dynamic equilibrium. If one of the phases is a vapor, the pressure corresponding to this equilibrium is just the vapor pressure of the substance. Therefore, the liquid-vapor phase boundary shows how the vapor pressure of the liquid varies with temperature. For example, the point at 80.°C and 0.47 atm in the phase diagram for water lies on the phase boundary between liquid and vapor (Fig. 8.10), and so we know that the vapor pressure of water at 80.°C is 0.47 atm. Similarly, the solid-vapor phase boundary shows how the vapor pressure of the solid varies with temperature (see Fig. 8.6). 

Univariant equilibrium for which there is one degree of freedom, represents the equilibrium between two co-existing phases. Since there is only one degree of freedom, choosing a value for one external variable, e.g. temperature, determines the remaining variable in a dependent manner, and the locus of points represented on the phase diagram for univariant behavior must lie on a line or curve. Thus the curves on the unary phase diagram represent solid-liquid, solid-vapor, solid-solid, and liquid-vapor equilibrium. 

Point T on the vapor-pressure line is called the triple point. This point represents the pressure and temperature at which solid, liquid, and gas coexist under equilibrium conditions. 

Figure 14.10 The five types of (fluid + fluid) phase diagrams according to the Scott and van Konynenburg classification. The circles represent the critical points of pure components, while the triangles represent an upper critical solution temperature (u) or a lower critical solution temperature (1). The solid lines represent the (vapor + liquid) equilibrium lines for the pure substances. The dashed lines represent different types of critical loci. (l) [Ar + CH4], (2) [C02 + N20], (3) [C3H8 + H2S],...

Figure 14.11 The critical locus for (xiQHp + x2C6F6), a system with a maximum boiling azeotrope. In (A), the circles represent the critical points (a and b) of pure components (1) and (2) the solid lines represent (vapor + liquid) equilibrium for the pure substances the dashed line is the critical locus, and the short-dashed line represents the azeotrope composition, which intersects the critical locus at point c. (B) shows the intersection of the (vapor + liquid) equilibrium lines with the critical locus.

Contact angle — The contact angle is the angle of contact between a droplet of liquid and a flat rigid solid, measured within the liquid and perpendicular to the contact line where three phases (liquid, solid, vapor) meet. The simplest theoretical model of contact angle assumes thermodynamic equilibrium between three pure phases at constant temperature and pressure [i, ii]. Also, the droplet is assumed to be so small that the force of gravity does not distort its shape. If we denote the - interfacial tension of the solid-vapor interface as ysv. the interfacial tension of the solid-liquid interface as ySL and the interfacial tension of the liquid-vapor interface as yLV, then by a horizontal balance of mechanical forces (9 < 90°)... 

The phase diagram (Figure 1-18) indicates the existence of three phases solid, liquid, and gas. The conditions under which they exist are separated by three equilibrium lines the vapor pressure line TA, the melting pressure line TC, and the sublimation pressure line BT. The three lines meet at point T,... 

The hydrate and phenol clathrate equilibrium data of the water-carbon dioxide, phenol-carbon dioxide, and water-phenol-carbon dioxide systems are presented in Table 1 and depicted in Figure 2. In order to establish the validity of the experimental apparatus and procedure the hydrate dissociation pressures of carbon dioxide measured in this work were compared with the data available in the literature (Deaton and Frost [7], Adisasmito et al. [8]) and found that both were in good agreement. For the phenol-carbon dioxide clathrate equilibrium results, as seen in Figure 2, the dramatic increase of the dissociation pressures in the vicinity of 319.0 K was observed. It was also found in the previous study (Kang et al. [9]) that the experimental phenol-rich liquid-phenol clathrate-vapor (Lp-C-V) equilibrium line of the binary phenol-carbon dioxide system could be well extended to the phenol clathrate-solid phenol-vapor (C-Sp-V) equilibrium line (Nikitin and Kovalskaya [10]). It is thus interesting to note that a quadruple point at which four individual phases of phenol-rich liquid, phenol clathrate, solid... 

The lower end of the vapor-pressure line is limited by the triple point O. This point represents the pressure and temperature at which solid, liquid, and vapor coexist under equilibrium conditions. Since the petroleum engineer seldom deals with hydrocarbons in the solid state it will not be necesaaiy to deal with this region of the diagram... 

You know that a substance s state depends on temperature and that pressure affects state changes. To get a complete picture of how temperature, pressure, and states are related for a particular substance, you can look at a phase diagram. A phase diagram has three lines. One line is a vapor pressure curve for the liquid-gas equilibrium. A second line is for the liquid-solid equilibrium, and a third line is for the solid-gas equilibrium. All three lines meet at the triple point. The triple point is the only temperature and pressure at which three states of a substance can be in equilibrium. 

Figure 2.12 is the classic pressure-temperature (FT) representation of the phase changes of a pure component. There are three primary phases of pure components solid liquid, and vapor solid-solid transitions, liquid crystal phases, and so on, are also possible but will not be considered here. The solid lines represent the sublimation curve (solid —> vapor), the vapor pressure curve (liquid —> vapor) and the melting curve (solid liquid) of the pure component. The triangle represents the triple point, at which a solid, liquid and vapor coexist in equilibrium. The circle represents the pure component critical point, where the supercritical region begins. 

Figure 4.2 Variation of the vapor pressure, Pv, of a substance with the temperature, 7, showing the phase transition between solid, liquid and vapor phases. Two phases can coexist in equilibrium only at pressures and temperatures defined by the phase boundary lines in the phase diagram, such as liquid-vapor, solid-liquid and solid-vapor lines. The liquid-vapor phase boundary terminates at the critical point, 7C. All three phases can coexist in equilibrium only at the triple point, 73, which is the intersection of the three two-phase boundaries.

Shown in figure 3.12a is the P-T-x diagram for the type of solid-SCF system described in the previous paragraph. The phase behavior depicted in figure 3.12c is observed if a P-x diagram is experimentally determined at Ti, a temperature below the critical temperature of the lighter component Tc,- At low pressure solid-vapor equilibria are observed until the three-phase SLV line is intersected. Three equilibrium phases exist at this pressure a pure solid, a liquid, and a gas. 

Shown in figure 3.18c is a solubility isotherm at a temperature, Tb, that is less than the previous temperature, Tj, but still higher than the UCEP temperature. The solubility behavior at T is similar to the behavior in figure 3.18b. But at T, the three-phase SLV line is intersected at a higher pressure, closer to the UCEP pressure. Hence, the vapor-liquid envelope has diminished in size and the solid-gas equilibrium curve is shifted toward higher solvent concentrations. As a result, the solid-gas curve is now much closer to the vapor branch of the vapor-liquid envelope. 

Figure 11.40(a) shows the phase diagram of water. The graph is divided into three regions, each of which represents a pure phase. The line separating any two regions indicates conditions under which these two phases can exist in equilibrium. For example, the curve between the liquid and vapor phases shows the variation of vapor pressure with temperature. (Compare this curve with Figure 11.35.) The other two curves similarly indicate conditions for equilibrium between ice and liquid water and between ice and water vapor. (Note that the solid-liquid boundary line has a negative slope.) The point at which all three curves meet is called the triple point, which is the only condition under which all three phases can be in equilibrium with one another. For water, this point is at 0.01°C and 0.006 atm.

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