Liquid-vapor coexistence line

What does it mean that (25°C, 23.8 Torr) is a point on the liquid-vapor coexistence line Consider a beaker of liquid water at 25°C, covered with a lid and allowed to come into equilibrium with its own vapor ... 

Figure 7.1 also shows the critical point (circle-x, dashed lines) of water, the terminus of the liquid-vapor coexistence line. Beyond this point (which occurs at Tc = 374°C, Pc = 217.7 atm), there is no longer a sensible distinction between liquid and vapor, so one should only speak of a supercritical fluid (or simply fluid ) beyond the dashed lines. A sample of water above Pc can never exhibit a boiling point, no matter how far the temperature is increased, nor can a sample above Tc exhibit condensation, no matter how far the pressure is increased. 

The critical state is evidently an invariant point (terminus of a line) in this case, because it lies at a dimensional boundary between states of / =2 (p = 1) and /= 1 (p = 2). The critical point is therefore a uniquely specified state for a pure substance, and it plays an important role (Section 2.5) as a type of origin or reference state for description of all thermodynamic properties. Note that a limiting critical terminus appears to be a universal feature of liquid-vapor coexistence lines, whereas (as shown in Fig. 7.1) solid-liquid and solid-vapor lines extend indefinitely or form closed networks with other coexistence lines. 

Vaporization Transition Clausius-Clapeyron Equation For the liquid-vapor coexistence line ( vapor-pressure curve ), the Clapeyron equation (7.29) becomes... 

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. 

The solid-liquid and liquid-vapor coexistence lines intersect at fi = 0.491, fip = 0.028. Further verification is obtained by examining the chemical potential fin, which is computed along the integration path as described in Section III.B.3. Free-energy values for the initial points are available for the solid-liquid line the hard-sphere value is known [76,77] (fin = 16.898), and for the liquid-vapor, it was measured during the GE simulations (fin = —3.191). Curves for both integrations are included in Figure 4, and at = 0.488 they indeed intersect very close to the triplepoint temperature just established. 

The liquid structure factor of CCI4 and its derivatives with respect to temperature at fixed pressure or fixed volume, needed by eq. (2), were evaluated by Molecular Dynamics (MD) simulations. We have used the OPLS model for tetrachloromethane [9] In this model, the CCI4 molecules are described as rigid tetrahedra (dc-ci = 1 -769 A) and the intermolecular potentials are atom centered 6-12 Lennard-Jones potentials plus the coulombic interaction with partial charges on C and Cl. We performed NVT simulations with 512 molecules for about 1 ns each. The different x-ray structure factors were obtained from the accumulated partial radial distribution functions [10], using the atomic form-factors from the DABAX database [11]. In order to estimate the partial derivatives of the structure factor, we have used finite differences we considered two different temperatures, Ti = 300 K and T2 = 328 K, and two molar volumes, Vi = 97.3 cm mol and V2 = 100.65 cm mol which are the molar volumes along the liquid-vapor coexistence line for the two temperatures Tj and Tz respectively [12]. Three simulations were then run for the temperature and molar volume conditions (TiiVi), T2,V )... 

Figure 1.19. Liquid-vapor coexistence line of SPC water and OPLS methanol (solid and dashed lines) following from the RISM/KH theory versus the simulation data (open circles and squares, respectively) and critical point estimates (closed symbols). Logarithmic and linear scales are used to resolve the density in gas and liquid state.

Figure 5.5(b) shows the phase diagram of water at intermediate pressures. From this graph we see that the liquid-vapor coexistence line does not continue indefinitely, but stops abruptly at a pressure of 220.6 bar and 647.1 K. This point is called the critical point, and represents the highest pressure (called the critical pressure, PJ and temperature (called the critical temperature, T ) at which water can exist as a liquid. Above this point, there is no fundamental distinction between a liquid and a gas—we simply have a fluid, called a supercritical fluid (SCF). 

Values derived from pqT data along the melting curve, the liquid-vapor coexistence line, and along several isobars up to 50 MPa are available [2]. 

Fig. 3.10. The pair distribution function g R) of expanded liquid cesium at various temperature-density points near the liquid-vapor coexistence line. The pair distribution functions were derived from the liquid structure factors shown in Fig. 3.11 (Winter et al., 1987, 1988).

Fig. 3.14. Dispersion curves obtained from the maxima h(o in the longitudinal current correlation function for liquid rubidium at various temperatures along the liquid-vapor coexistence line (Pilgrim et al 1991) A = 42 C V = 800 C = 1100 °C O = 1400 °C. The data for 42 "C are those of Copley and Rowe...

Fig. 3.20. DC electrical conductivity of fluid cesium as a function of temperature along the liquid-vapor coexistence line. Solid triangles, data of Borzhievskii et al. (1988) open circles with solid line, data of Hensel et al. (1991). The open circles with dotted line are the predictions of the Saha equation the crosses are the predictions of the chemical model of Reinholz and Redmer (1993).

Fig. 4.1. Optical conductivity

Fig. 4.6. NMR Knight shift as a function of density for liquid mercury close to the liquid-vapor coexistence line (El-Hanany and Warren, 1975 Warren and Hensel, 1982). Upper scale shows the corresponding values of the DC electrical conductivity.

Fig. 4.19. Effective electron mobility in fluid mercury as a function of the density along the liquid-vapor coexistence line (Gotzlaff, 1988).

Munoz, R. C. and Ascarelli, G., Hall mobility of electrons injected into fluid neopentane along the liquid-vapor coexistence line between the triple and the critical points, Phys. Rev. Lett., 51, 215,1983. 

Results of measuring x versus temperature along the liquid-vapor coexistence line are presented for 4 liquid insulators tetramethyl-silane (TMS), neopentane (NP), 2,2,4,4-tetramethylpentane (2244 TMP), and 2,2-dimethylbutane (22 DMB). 

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