Phase transitions liquid-vapor transition critical point

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. 

The mutual attraction through the slit gap affects liquid film stability, and at a certain critical vapor pressure (or film thickness) the two films form a liquid bridge (Fig. 1-1 c) followed by a spontaneous filling up of the slit (assuming the film is in contact with the bulk liquid phase). The liquid-vapor interface moves to the plate boundaries. This phase transition from dilute vapor to a dense liquid is known as capillary condensation and was observed experimentally with the surface force apparatus by Christenson (1994) and Curry and Christenson (1996). Extensive theories for this phenomenon and its critical points are provided by Derjaguin and Chu-raev (1976), Evans et al. (1986), Forcada (1993), and Iwamatsu and Horii (1996). In general, slit-shaped pores fill up at a film thickness of about HI3, or when <) l(H,h)/dh = 0, such that... 

Look back at the large phase diagram (Figure 7-1) and notice the intersection of the three lines at 0.01° and 6 X 10 atm. Only at this triple point can the solid, liquid, and vapor states of FljO all coexist. Now find the point at 374° C and 218 atm where the liquid/gas boundary terminates. This critical point is the highest temperature and highest pressure at which there is a difference between liquid and gas states. At either a temperature or a pressure over the critical point, only a single fluid state exists, and there is a smooth transition from a dense, liquid-like fluid to a tenuous, gas-like fluid. 

Helium-4 Normal-Superfluid Transition Liquid helium has some unique and interesting properties, including a transition into a phase described as a superfluid. Unlike most materials where the isotopic nature of the atoms has little influence on the phase behavior, 4He and 3He have a very different phase behavior at low temperatures, and so we will consider them separately Figure 13.11 shows the phase diagram for 4He at low temperatures. The normal liquid phase of 4He is called liquid I. Line ab is the vapor pressure line along which (gas + liquid I) equilibrium is maintained, and the (liquid + gas) phase transition is first order. Point a is the critical point of 4He at T= 5.20 K and p — 0.229 MPa. At this point, the (liquid + gas) transition has become continuous. Line be represents the transition between normal liquid (liquid I) and a superfluid phase referred to as liquid II. Along this line the transition... 

In 1958, Pitzer (141), in a remarkable contribution that appears to have been the first theoretical consideration of this phenomenon, likened the liquid-liquid phase separation in metal-ammonia solutions to the vapor-liquid condensation that accompanies the cooling of a nonideal alkali metal vapor in the gas phase. Thus, in sodium-ammonia solutions below 231 K we would have a phase separation into an insulating vapor (corresponding to matrix-bound, localized excess electrons) and a metallic (matrix-bound) liquid metal. This suggestion of a "matrix-bound analog of the critical liquid-vapor separation in pure metals preceeded almost all of the experimental investigations (41, 77, 91,92) into dense, metallic vapors formed by an expansion of the metallic liquid up to supercritical conditions. It was also in advance of the possible fundamental connection between this type of critical phenomenon and the NM-M transition, as pointed out by Mott (125) and Krumhansl (112) in the early 1960s. 

Because of the existence of the critical point, a path can be drawn from the liquid region to the gas region that does not cross a phase boundary e.g., the path from A to B in Fig. 3.1. This path represents a gradual transition from the liquid to the gas region. On the other hand, a path crossing phase boundary 2-C includes a vaporization step, where an abrupt change of properties occurs. 

This paper deals with the degradation of substances like PVC, Tetrabromobisphenol A, y-HCH and HCB in supercritical water. This process is called "Supercritical Water Oxidation", a process which gained a lot of interest in the past. The difference between subcritical and supercritical processes is easy to recognize in the phase diagram of water. The vapor pressure curve of water terminating at the critical point, i.e. at 374 °C and 221 bar. The relevant critical density is 0.32 g/cm3. This corresponds to approx. 1/3 of the density of normal liquid water. Above the critical point, a compression of water without condensation, i.e. without phase transition is possible. It is within this range that supercritical hydrolysis and oxidation are carried out. The vapor pressure curve is of special importance in subcritical hydrolysis as well as in wet oxidation. 

Simulations of the RPM predict a phase transition for the RPM at low reduced temperature and low reduced density. It was difficult to localize because of the low figures of the critical data. By corresponding states arguments this critical point corresponds to the liquid/vapor transition of molten salts and to some liquid/liquid transitions in electrolyte solutions in solvents of low dielectric constant [23, 24],... 

Let us first consider the liquid/vapor phase transition of NaCl. PVT data have been recorded up to about 2000 K, which is still far below the critical point. Extrapolations guided by simulations and theory predict Tc = 3300 K and the critical mass density dc = 0.18 g cm-3 [33], With a = 0.276 nm and e = 1, this maps onto Tc = 0.05 and p = 0.08. 

Let us clarify the nature of the fluid phases (liquid and gas) and of the critical point hy describing two different ways that a gas can he liquefied. A sample at point IVin the phase diagram of Figure 13-18b is in the vapor (gas) phase, below its critical temperature. Suppose we compress the sample at constant T from point IV to point Z. We can identify a definite pressure (the intersection of line IVZ with the vapor pressure curve AC) where the transition from gas to liquid takes place. If we go around the critical point by the path WXYZ, however, no such clear-cut transition takes place. By this second path, the density and other properties of the sample vary in a continuous manner there is no definite point at which we can say that the sample changes from gas to liquid. 

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