Triple-point line

Figure 8.1 Phase diagram for CCF. Point (a) is the critical point and point (b) is the triple point. Line ab gives the vapor pressure of the liquid, line be gives the vapor pressure of the solid, and line bd gives the melting temperature as a function of pressure.

On the P — T diagram, at right, each of the mixed-phase regions is represented by a single co-existence line. The value of the chemical potential must be the same for the two phases at any point on a co-existence line. The lines meet at the triple point where all three phases are in equilibrium. The triple-point line on the P — V diagram is marked TP. 

Figure 2.2. The van der Waals-type phase diagram for one mole of argon. C = 150 K is the critical point, TP is the triple point line of the coexistence between solid, liquid and vapor. The upper shaded area represents the liquid-vapor coexistence, while the lower that of solid-vapor. Vapor exists on the right hand side of the shaded areas, while liquid and solids on their left. The supercritical region is that above the critical point, where (at high pressures) the vapor density is comparable to that of liquid. Supercooled vapor is also indicated by a series of solid points. After [Flowers and Mendoza, 1970].

Our steering results are demonstrated using an experimentally validated numerical model [20] of droplet motion inside the UCLA electrowetting system [21, 22], This model of EWOD fluid dynamics includes surface tensimi and electrowetting interface forces, viscous low Reynolds two-phase fluid flow, and the essential loss mechanisms due to contact angle saturatimi, triple point line pinning, and the related mechanism of contact angle hysteresis. 

Fig. 19. Binodals (solid lines) and spinodals (dashed lines) in the temperature-composition plane at pa /kgT = 0.16. The critical point is marked by a filled circle, diamonds, and a horizontal dashed line mark the triple point. The unstable liquid-liquid critical point is indicated by a square. Above the triple point, lines of constant nucleation barriers are shown. An open circle on the line of nucleation barriers ISk T marks the condensation of solvent-vapor into a solvent-rich liquid inside the critical nucleus. The dotted vertical line atx = 0.68 (ending in crosses) marks the path at which the nucleation barrier is examined in Fig. 18. From [164]...

The normal melting point of a substance is the temperature at which solid and hquid are in equilibrium at atmospheric pressure. At the triple point, the pressure is the equilibrium vapour pressure of the system (solid liquid - vapour) and the temperature differs from the melting point. The difference is, however, quite small—usually only a fraction of a degree—since the line TV departs only slightly from the vertical within reasonable ranges of pressure. 

Helium Purification and Liquefaction. HeHum, which is the lowest-boiling gas, has only 1 degree K difference between its normal boiling point (4.2 K) and its critical temperature (5.2 K), and has no classical triple point (26,27). It exhibits a phase transition at its lambda line (miming from 2.18 K at 5.03 kPa (0.73 psia) to 1.76 K at 3.01 MPa (437 psia)) below which it exhibits superfluid properties (27). 

Values recalculated into SI units from those of Din. Theimodynamic Functions of Gases, vol. 2, Butterworth, London, 1956. Above the solid line the condensed phase is solid below the line it is liquid, t = triple point c = critical point. 

Values extracted and in some cases rounded off from ttose cited in RaLinovict (ed.), Theimophysical Propeities of Neon, Ai gon, Kiypton and Xenon, Standards Press, Moscow, 1976. Ttis source contains values for tte compressed state for pressures up to 1000 bar, etc. t = triple point. Above tbe sobd line tbe condensed phase is solid below it, it is liquid. Tbe notation 5.646. signifies 5.646 X 10 . At 83.8 K, tbe viscosity of tbe saturated liquid is 2.93 X 10 Pa-s = 0.000293 Ns/ui . Tbis book was published in English translation by Hemisphere, New York, 1988 (604 pp.). 

Liquid helium-4 can exist in two different liquid phases liquid helium I, the normal liquid, and liquid helium II, the superfluid, since under certain conditions the latter fluid ac4s as if it had no viscosity. The phase transition between the two hquid phases is identified as the lambda line and where this transition intersects the vapor-pressure curve is designated as the lambda point. Thus, there is no triple point for this fluia as for other fluids. In fact, sohd helium can only exist under a pressure of 2.5 MPa or more. 

Because a phase change is usually accompanied by a change in volume the two-phase systems of a pure substaiice appear on a P- V (or a T- V) diagram as regions with distinct boundaries. On a P- V plot, the triple point appears as a horizontal line, and the critical point becomes a point of inflection of the critical isotherm, T = T (see Figure 2-78 and Figure 2-80). 

Assumed data of for the purpose of illustrating the calculation of the position of the boundary lines and triple points and B see Fig. 7.67... 

Therefore, the calculated coordinates of the triple point for the coexistence of MO, MS and A/SO4 are logPso2 = +2 and logpo = - 12 and the slope of the MO/MSO4 boundary is - y. The straight line from point B having slope — y gives the boundary line (i) between the stability areas of MO and A/SO4. This completes the construction of the phase stability diagram forM-S-O at 1000 K. 

The boiling point is limited by the critical temperature at the upper end, beyond which it cannot exist as a liquid, and by the triple point at the lower end, which is at the freezing temperature. Between these two limits, if the liquid is at a pressure higher than its boiling pressure, it will remain a liquid and will be subcooled below the saturation condition, while if the temperature is higher than saturation, it will be a gas and superheated. If both liquid and vapour are at rest in the same enclosure, and no other volatile substance is present, the condition must lie on the saturation line. 

Phase diagram of water (not to scale). The curves and line represent the temperatures and pressures at which phases are in equilibrium. The triple point is at 0.0rC, 4.56 mm Hg the critical point is at 374°C. 

In the P-T projection the difference in slopes of the three-phase lines -clathrate-gas and liquid-clathrate-gas at the quadruple point R is determined by the heat of fusion of the number of moles of hydroquinone associated with one mole of argon in the clathrate under the conditions prevailing at R. If we extrapolate the three-phase line liquid-clathrate-gas to lower pressures (where it is no longer stable), the value of yA decreases until it becomes zero when we are dealing with pure / -hydroquinone. Hence, the metastable part of this three-phase line ends in the triple point B of /1-hydro-... 

Figure 8.4 Graph of temperature against molar volume (a), and density (b). for CO (gas) and C02 (liquid) in the temperature range from the triple point to the critical point. The dashed line in (b) is the average density. The area enclosed within the curves is a two-phase region, with the molar volume or the density of the gas and liquid at a particular temperature given by the horizontal (dotted) tie-lines connecting the gas and liquid sides of the curve.

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. 

FIGURE 8.6 The phase diagram for water (not to scale). The solid blue lines define the boundaries of the regions of pressure and temperature at which each phase is the most stable. Note that the freezing point decreases slightlv with increasing pressure. The triple point is the point at which three phase boundaries meet. The letters A and B are referred to in Example 8.3. 

Three boundary lines meet in a single point (shown by a red dot), called a triple point. All three phases are stable simultaneously at this unique combination of temperature and pressure. Notice that, although two phases are stable under any of the conditions specified by the boundary lines, three phases can be simultaneously stable only at a triple point. 

The normal melting, boiling, and triple points give three points on the phase boundary curves. To construct the curves from knowledge of these three points, use the common features of phase diagrams the vapor-liquid and vapor-solid boundaries of phase diagrams slope upward, the liquid-solid line is nearly vertical, and the vapor-solid line begins at P = 0 and P = 0 atm. 

Fig. 1.15. Diagram showing the homogenization temperature of fluid inclusions vs. the iron content of the host sphalerite growth zone for sample locality NJP-X on the OH vein. The line shows the predicted iron content of the sphalerite if the sulfur fugacity of the system had been buffered by the triple point — Fe-chlorite (daphnite), pyrite, hematite (Hayba et al., 1985).

Not shown region of gaseous H20 at pressures below 22 MPa. The line delimiting the liquid and ice VII continues up to at a triple point at 43 GPa and 1370 °C at this triple point it probably meets the line delimiting ice VII and ice X. The melting point continues to move upward until approximately 2150 °C at 90 GPa... 

The point where the three lines join is called the triple point, because three phases coexist at this single value of p and T. The triple point for water occurs at T = 273.16 K (i.e. at 0.01 °C) and p = 610 Pa (0.006/ °). We will discuss the critical point later. 

All stable pure compounds have a triple point and a critical point. The critical point is the endpoint of the liquid-gas line in the phase diagram and the point where the liquid and gas phases become indistinguishable. Any gaseous compound becomes supercritical when compressed to a pressure higher than the critical pressure (Pc) above the critical temperature Cf ). Figure 2 shows photographs... 

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