Liquid-vapor boundary, equilibrium phase

A feature of the phase diagram in Fig. 8.12 is that the liquid-vapor boundary comes to an end at point C. To see what happens at that point, suppose that a vessel like the one shown in Fig. 8.13 contains liquid water and water vapor at 25°C and 24 Torr (the vapor pressure of water at 25°C). The two phases are in equilibrium, and the system lies at point A on the liquid-vapor curve in Fig. 8.12. Now let s raise the temperature, which moves the system from left to right along the phase boundary. At 100.°C, the vapor pressure is 760. Torr and, at 200.°C, it has reached 11.7 kTorr (15.4 atm, point B). The liquid and vapor are still in dynamic equilibrium, but now the vapor is very dense because it is at such a high pressure. 

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). 

SOLUTION Although the phase diagram in Fig. 8.6 is not to scale, we can find the approximate locations of the points. Point A is at 5 Torr and 70°C so it lies in the vapor region. Increasing the pressure takes the vapor to the liquid-vapor phase boundary, at which point liquid begins to form. At this pressure, liquid and vapor are in equilibrium and the pressure remains constant until all the vapor has condensed. The pressure is increased further to 800 Torr, which takes it to point B, in the liquid region. 

The phase equilibrium for pure components is illustrated in Figure 4.1. At low temperatures, the component forms a solid phase. At high temperatures and low pressures, the component forms a vapor phase. At high pressures and high temperatures, the component forms a liquid phase. The phase equilibrium boundaries between each of the phases are illustrated in Figure 4.1. The point where the three phase equilibrium boundaries meet is the triple point, where solid, liquid and vapor coexist. The phase equilibrium boundary between liquid and vapor terminates at the critical point. Above the critical temperature, no liquid forms, no matter how high the pressure. The phase equilibrium boundary between liquid and vapor connects the triple point and the... 

Figure 7.5 Phase diagram of elemental sulfur, showing the stable solid phases a-sulfur (orthorhombic red sulfur ) and /3-sulfur (monoclinic yellow sulfur ) and equilibrium phase boundaries (solid lines) as well as the metastable phase boundary (dashed line) that connects a-sulfur to liquid and vapor phases.

In the phase diagram, panel (a). solid C02 (Dry Ice) is in equilibrium with gaseous C02 at a temperature of —78.7°C and a pressure of 1.00 bar." The solid sublimes without turning into liquid. At any temperature above the triple point at —56.6°C, there is a pressure at which liquid and vapor coexist as separate phases. For example, at 0°C, liquid is in equilibrium with gas at 34.9 bar. Moving up the liquid-gas boundary, we see that two phases always exist until the critical point is reached at 31.3 C... 

A triple point is a point where three phase boundaries meet. For water, it occurs at 4.6 Torr and 0.01°C (see Fig. 8.5). At the triple point, all three phases (ice, liquid, and vapor) coexist in dynamic equilibrium. Under these conditions, water molecules leave ice to become liquid and return to form ice at the same rate liquid vaporizes and vapor condenses at the same rate and ice sublimes and vapor condenses directly to ice again at the same rate. The location of the 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. The normal freezing point of water is found to lie 0.01 K below the triple point, so 0°C corresponds to 273.15 K. 

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.

In this equation Av// is the molar change in enthalpy for the conversion of substance from the equilibrium liquid to the equilibrium vapor phase. AVF is the molar change in volume when the substance changes from the liquid to the gas. This equation allows calculation of the enthalpy of vaporization from vapor pressure, and it is the second law method. Measurement of enthalpy of vaporization with a calorimeter is the first law method. The quantities AWH and AVF are functions of temperature along the phase boundary. Equation (1.1) can also be written as,... 

This report is concerned with contact angle hysteresis and with a closely related quantity referred to as "critical line force (CLF)." More particularly, it is concerned with the relationship between contact angle hysteresis and the magnitude of the contact angle itself. Two sets of liquid-solid-vapor systems have been investigated to provide the experimental data. One set consists of Teflon [poly(tetrafluoroethylene), Du Pont] and a series of liquids forming various contact angles at the Teflon-air interface. The second set consists of polyethylene and a similar series of liquids. In neither case was the ratio of air to test liquid vapor at the boundary line controlled, but it can be assumed that the ambient vapor phase operative in all the systems was close to an equilibrium mixture. 

This allows us to actively influence the location of the pseudoproduct point of the intermediate section in order to maintain sharp separation (i.e., separation at which the intermediate section trajectory ends at some boundary element of the concentration simplex). This is feasible in the case when inside concentration simplex there is one trajectory of reversible distillation for pseudoproduct point x ) that ends at mentioned boundary element, and there is the second trajectory inside this boundary element. To maintain these conditions, pseudoproduct point x j) of the intermediate section should be located at the continuation of the mentioned boundary element, because only in this case can liquid-vapor tie-hues in points of reversible distillation trajectory located in this boundary element he at the lines passing through the pseudoproduct point x jy. We discuss these conditions in Chapter 4. It was shown that in reversible distillation trajectory tear-off point x[ev e from the boundary element the component absent in it should be intermediate at the value of the phase equUibrium coefficient between the components of the top product and of the entrainer rev,D > Kevj > Kev.s)- This condition is the structural condition of reversible distillation trajectory tear-off for the intermediate section. Mode condition of tear-off as for other kinds of sections consists of the fact that in tear-off point the value of the parameter (LfV) should be equal to the value of phase equilibrium coefficient of the component absent at the boundary element in tear-off point of reversible distillation trajectory ((L/V)m =... 

Before approaching the problem of dynamics of contact line, we shall briefly review the equilibrium properties of gas-liquid interfaces and their dependence on the proximity to solid surfaces. We shall consider the simplest one-component system a liquid in equilibrium with its vapor. Thermodynamic equilibrium in a two-phase system implies equilibrium of the interphase boundary, which tends to minimize its area. The thermodynamic quantity that expresses additional energy carried by the interface is surface tension, defined as the derivative of the Helmholtz or Gibbs free energy with respect to interfacial area E ... 

Figure 3.1.9 shows the general location of the phase boundaries between the solid, the liquid, and the gas phase and the respective diagram for water. Note the small decrease of the melting temperature with increasing pressure, which is the result of the anomaly of water by which the liquid phase has a higher density than ice. All three phases are in equilibrium at the triple point. If the temperature and pressure exceed the so-called critical values, 374 °C and 218bar for water, the phase boundary between liquid and vapor vanishes. For this supercritical state, a... 

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