Liquid and vapor phases coexistence

The shaded region is that part of the phase diagram where liquid and vapor phases coexist in equilibrium, somewhat in analogy to the boiling line for a pure fluid. The ordinary liquid state exists on the high-pressure, low-temperature side of the two-phase region, and the ordinary gas state exists on the other side at low pressure and high temperature. As with our earlier example, we can transform any Type I mixture... 

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 regions below ABC in Fig. 3.6 and above ABC in Fig. 3.7 represent subcooled liquid no vapor is present. The regions above ADC in Fig. 3.6 and below ADC in Fig. 3.7 represent superheated vapor no liquid is present. The area between the curves is the region where both liquid and vapor phases coexist. 

VP indicates vapor pressure point CVGT indicates constant volume gas thermometer point TP indicates triple point (equilibrium temperature at which the solid, liquid, and vapor phases coexist) FP indicates freezing point, and MP indicates melting point (the equihbrium temperatures at which the solid and liquid phases coexist under a pressure of 101 325 Pa, one standard atmosphere). The isotopic composition is that naturally occurring. 

The curve AD that divides the soUd region from the gaseous region gives the vapor pressures of the sohd at various temp atures. This curve intersects the other curves at point A, the triple point, which is the point on a phase diagram representing the temperature and pressure at which three phases of a substance coexist in equilibrium. For water, the triple point occurs at 0.01°C, 0.00603 atm (4.58 mmHg), and the solid, liquid, and vapor phases coexist. ... 

Triple point The temperature and pressure at which the solid, liquid, and vapor phase of a substance can coexist in equilibrium, 233 Tryptophan, 622t Tyrosine, 622t... 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

The NPT + test particle method [8, 9] aims to determine phase coexistence points based on calculations of the chemical potentials for a number of state points. A phase coexistence point is determined at the intersection of the vapor and liquid branches of the chemical potential versus pressure diagram. The Widom test particle method [7] of the previous paragraph or any other suitable method [10] can be used to obtain the chemical potentials. Corrections to the chemical potential of the liquid and vapor phases can be made, using standard thermodynamic relationships, for deviations... 

The principal features of elemental sulfur in the displayed T, P range are the usual liquid and vapor phases and two solid forms, a-sulfur ( red sulfur, of orthorhombic crystalline form) and /3-sulfur ( yellow sulfur, monoclinic needle-like crystals), both of which are available as common stockroom species. The stable phase ranges for each elemental form are shown by the solid lines in Fig. 7.5. The liquid-vapor coexistence line terminates in a critical point at 1041°C, and will not be discussed further. 

At such a maximum (dotted line) the compositions of coexisting liquid and vapor phases necessarily coincide, and the two-phase hole closes as liquid and vapor curves meet at this point. Examples of such maxima occur frequently, for example, in alcohol-water mixtures, as in the C2H50H/H20 system at vh2o = 0.20. 

The order of a transition can be illustrated for a fixed-stoichiometry system with the familiar P-T diagram for solid, liquid, and vapor phases in Fig. 17.2. The curves in Fig. 17.2 are sets of P and T at which the molar volume, V, has two distinct equilibrium values—the discontinuous change in molar volume as the system s equilibrium environment crosses a curve indicates that the phase transition is first order. Critical points where the change in the order parameter goes to zero (e.g., at the end of the vapor-liquid coexistence curve) are second-order transitions. 

Gibbs Ensemble Monte Carlo (GEMC) is an ingenious method introduced by Panagiotopoulos [72], which allows one to simulate the coexistence of liquid and vapor phases without having to deal with a physical interface between them. 

The region lying above the upper surface of Fig. 12.1 is the subcooled-liquid region that below the under surface is the superheated-vapor region. The interior space between the two surfaces is the region of coexistence of both liquid and vapor phases. If one starts with a liquid at F and reduces the pressure at constant temperature and composition along vertical line FG, the first bubble of vapor appears at point L, which lies on the upper surface. Thus, L is a bubble point, and the upper surface is the bubble-point surface. The state of the vapor bubble in equilibrium with the liquid at L must be represented by a point on the under surface at the temperature and pressure of L. This point is indicated by the letter V. Line VL is an example of a tie line, which connects points representing phases in equilibrium. 

The experiment began by charging the equilibrium cell with about 30 cm3 of either phenoPp-cresol or phenol-water solution mixture. The cell was then pressurized with either methane or carbon dioxide until the phenol clathrate formed under sufficient pressure. The systems were cooled to about 5 K below the anticipated clathrate-forming temperature. Clathrate nucleation was then induced by agitating the magnetic spin bar. After the clathrates formed, the cell temperature was slowly increased until the clathrate phase coexisted with the liquid and vapor phases. The nucleation and dissociation steps were repeated at least twice in order to diminish hysteresis phenomenon. The clathrates, however, exhibited minimal hysteresis and the excellent reproducibility of dissociation pressures was attained for all the temperatures and found to be within 0.1 K and 1.0 bar at each time. When a minute amount of phenol or p-cresol clathrate crystals remains and the system temperature was kept constant for at least 8 hours after attaining pressure stabilization, the pressure was considered as an equilibrium dissociation pressure at that specified temperature. 

The Density-Temperature Diagram. Consider the densities of the liquid and vapor that coexist in the two-phase region. If these densities are plotted as a function of temperature the curves AC and BO in Figure 22 are obtained. Points 4 and B represent the densities... 

Example. Ten pounds of a hydrocarbon are placed in a one cubic foot vessel at 60° F. The densities of the coexisting liquid and vapor are known to be 25 Ib/cu ft and 0.06 Ib/cu ft, respectively, at this temperature. Calculate the wei ts and volumes of the liquid and vapor phases. 

There will be an isotherm similar to ABCD for each temperature. The complete P-V diagram for the i-pentane, w-heptane S3retem containing 52.4 weight per cent w-heptane is shown in Figure 24. The critical point is the point where the bubble-point line and dew-point line meet. This is equivalent to the statement that the intensive properties of the coexisting liquid and vapor phases are identical at the critical point. Consequently, the liquid and tiie vapor are indistinguishable at the critical pressure and temperature, The critical... 

The point (T, p) at which solid, liquid, and vapor phases can all coexist is called the triple point of the substance. 

We may discard the last two terms. The reduced coexistence volumes i>/(P) and Vg P) for the liquid and vapor phase are in equilibrium at T < Tc equivalently, so are the corresponding quantities (pi and vapor phases with reference to Fig. 7.1.2 (where, however, the pressure vs. volume is plotted in a highly schematic manner for purely illustrative purposes) we apply Maxwell s equal area rule to require that, for a fixed value of t < 0, V dP = 0 = Vc — l)dP. The last integral follows since... 

Vapor/liquid equilibrium (VLE) is the state of coexistence of liquid and vapor phases. In this qualitative discussion, we limit consideration to systems comprised of two chemical species, because systems of greater complexity cannot be adequately represented graphically. 

For a pure species coexisting liquid and vapor phases are in equilibrium when they have the same temperature, pressure, and fugacityJ... 

For the hydrocarbon--CO2 systems studied here, at pressures above the critical pressure (7.383 MPa) and above the critical temperature (304.21 K) of C02 the isobaric x,T coexistence plots of liquid and vapor phases form simple closed loops. The minimum occurs at the lower consolute point or the Lower Critical Solution Temperature (LCST). Since pressure is usually uniform in the vicinity of a heat transfer surface, such diagrams serve to display the equilibrium states possible in a heat transfer experiment. 

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