Pressure volume diagram, liquid-vapor

Phe smooth curve passing through the critical point and bounding the two-phase liquid-vapor region in a pressure-volume diagram is familiar to every student of thermodynamics. The mathematical description p(P) of this coexistence curve or saturation boundary is the subject of this chapter. 

The PVT behavior of a pure substance may also be described on a pressure-volume diagram, as shown in Figure 1.2. The variation of volume with pressure at various fixed temperatures is represented by the isotherms. If temperature of the isotherm is above the critical, the pressure decreases continuously as the volume increases and no phase change takes place. The critical temperature isotherm is also continuous but has an inflection point at the critical pressure. On subcritical isotherms, the pressure of a liquid drops steeply with small increases in the volume until the liquid starts to vaporize. At this point the pressure remains constant as the total volume increases. 

Water exists in three basic forms vapor, liquid, and solid. The relationship among the three forms of water is described by the pressure-volume-temperature phase diagram (Figure 1.1). 

The thermodynamic properties of a number of compounds are shown in Appendix D as pressure-enthalpy diagrams with lines of constant temperature, entropy, and specific volume. The vapor, liquid, and two-phase regions are clearly evident on these plots. The conditions under which each compound may exhibit ideal gas properties are identified by the region on the plot where the enthalpy is independent of pressure at a given temperature (i.e., the lower the pressure and the higher the temperature relative to the critical conditions, the more nearly the properties can be described by the ideal gas law). 

The pressure-temperature phase diagrams also serve to highlight the fact that the polymorphic transition temperature varies with pressure, which is an important consideration in the supercritical fluid processing of materials in which crystallization occurs invariably at elevated pressures. Qualitative prediction of various phase changes (liquid/vapor, solid/vapor, solid/liquid, solid/liquid/vapor) at equilibrium under supercritical fluid conditions can be made by reference to the well-known Le Chatelier s principle. Accordingly, an increase in pressure will result in a decrease in the volume of the system. For most materials (with water being the most notable exception), the specific volume of the liquid and gas phase is less than that of the solid phase, so that... 

From the temperature-entropy diagram, the parameters associated with isentropic expansion of saturated liquid hydrogen from several initial pressures were evaluated. These parameters include the isentropic spouting velocity, sonic velocity, Mach number, specific flow area, and the volume ratio of vapor to mixture Fr. The results are shown graphically in Figs. 1 through 4. 

As an example, let the system contain a fixed amount n of a pure substance divided into liquid and gas phases, at a temperature and pressure at which these phases can coexist in equilibrium. When heat is transferred into the system at this T and p, some of the liquid vaporizes by a liquid-gas phase transition and V increases withdrawal of heat at this T and p causes gas to condense and V to decrease. The molar volumes and other intensive properties of the individual liquid and gas phases remain constant during these changes at constant T and p. On the pressure-volume phase diagram of Fig. 8.9 on page 208, the volume changes correspond to movement of the system point to the right or left along the tie line AB. 

Some selected basic properties of water are given in Table 15.1. The unique characteristics of water, although not obvious, will become apparent as we learn more about it. The three-dimensional phase diagram for water, up to the pressure of 10,000 atm and for the temperature range of —50°C to - - 50°C, is shown in Fig. 15.1. The density of ice (ice I) is less than that of water up to about 2,200 atm. Above this pressure, ice exists in various different crystalline modifications. The two-dimensional phase diagram for water is shown in Fig. 15.2, where the triple point, 0.0100°C, consists of solid ice, water, and water vapor at 4.579 torr in equilibrium. Also shown is the critical point above which liquid water cannot exist in the liquid state. The negative slope of the P-T line is due to the difference in molar volumes of liquid and solid, that is, (V, — VJ < 0, and because... 

A more complete phase diagram is provided by Figure 7.8, in which the pressure is plotted as a function of volume and temperature. Here we see that depending on the temperature, we may either pass through the two-phase region or, if the fluid is above its critical temperature, we avoid a phase separation. The point at the top of the liquid-vapor region is the critical point of the fluid. The region marked LIQUID-VAPOR depicts the two-phase envelope—below this curve two phases exist in equilibrium. 

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. 

This method was later improved by van Lierop and co-workers (6). In this improved version of the method, vaporization of the solvent is completely suppressed by pressurizing the autoclave with an inert gas prior to heating while the subsequent heating is carried out batch at constant volume. Thus, the entire procedure is carried above the vapor-liquid interface of a Pressure-Temperature (P-T) diagram, shown as route A -B (2) in Figure 1. 

---