Triple point liquid density

Figure 5 Vibrational influence spectra for a diatomic solute in Ar under two different thermodynamic conditions a high-density supercritical state (upper curves) and a near-triple-point liquid (lower curves) (50). For each thermodynamic state, the total influence spectrum (solid) is contrasted with the portion stemming from binary modes (dashed).

The range of validity of the present equation of state is for all fluid states at densities to the triple-point liquid density, temperatures from the triple-point to infinity, and pressures to at least 700 bar. Vapor pressures of the solid at temperatures below the triple point are replaced by an extrapolation of the vapor-pressure curve to absolute zero temperature, and a completely new type of formulation is presented for densities of saturated vapor from absolute zero to the critical-point temperature. 

Specific volume Density as a liquid Boiling point Melting point Critical temperature Critical pressure Critical density Triple point... 

Fig. 1(a). The density dependence of various electronic transitions in solid xenon, extrapolated to the triple-point liquid. - solid, Steinberger and Asaf, 1973 O- liquid, ditto - Steinberger et al., 1970 A - Baldini, 1962. 

Molecular dynamics and density functional theory studies (see Section IX-2) of the Lennard-Jones 6-12 system determine the interfacial tension for the solid-liquid and solid-vapor interfaces [47-49]. The dimensionless interfacial tension ya /kT, where a is the Lennard-Jones molecular size, increases from about 0.83 for the solid-liquid interface to 2.38 for the solid-vapor at the triple point [49], reflecting the large energy associated with a solid-vapor interface. 

The regression constants A, B, and D are determined from the nonlinear regression of available data, while C is usually taken as the critical temperature. The hquid density decreases approximately linearly from the triple point to the normal boiling point and then nonhnearly to the critical density (the reciprocal of the critical volume). A few compounds such as water cannot be fit with this equation over the entire range of temperature. Liquid density data to be regressed should be at atmospheric pressure up to the normal boihng point, above which saturated liquid data should be used. Constants for 1500 compounds are given in the DIPPR compilation. 

Integral equation approaches with improved self-consistency were reviewed recently by Caccamo [55]. Unfortunately, in the case of almost all approaches, their accuracy begins to decrease as one leaves the liquid state region located shghtly above the triple point in temperature and follows the liquid-gas coexistence curve in the density-temperature plane up to the critical region. In particular, the shape of the coexistence curve and location... 

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.

In contrast to the Gibbs ensemble discussed later in this chapter, a number of simulations are required per coexistence point, but the number can be quite small, especially for vapor-liquid equilibrium calculations away from the critical point. For example, for a one-component system near the triple point, the density of the dense liquid can be obtained from a single NPT simulation at zero pressure. The chemical potential of the liquid, in turn, determines the density of the (near-ideal) vapor phase so that only one simulation is required. The method has been extended to mixtures [12, 13]. Significantly lower statistical uncertainties were obtained in [13] compared to earlier Gibbs ensemble calculations of the same Lennard-Jones binary mixtures, but the NPT + test particle method calculations were based on longer simulations. 

Table 2.2 clearly shows the strong differences between the two quantum liquids . It is worth noting that both isotopes have very low boiling and critical temperatures and a low density (the molar volume is more than the double than that corresponding to a classic liquid). Figure 2.4 shows the p-T phase diagrams besides the presence of a superfluid phases it is to be noted for both isotopes the missing of a triple point. 

II, 12,321) jjjg density of liquid phosphine in the temperature range between the triple-point and the boiling point can be obtained from the equation... 

Colorless, odorless gas density 6.41 g/L about five times heavier than air liquefies at -50.7°C (triple point) density of liquid 1.88 g/mL at -50.7°C sublimes at -63.8°C critical temperature 45.54°C critical pressure 37.13 atm critical volume 199 cm /mol slightly soluble in water soluble in ethanol. 

White monoclinic crystals density 5.09 g/cm melts at 64°C (triple point) sublimes at 56.6°C critical temperature 232.65°C critical pressure 46 atm critical volume 250 cm /mol reacts with water forming UO2F2 and HF soluble in chloroform, carbon tetrachloride and fluorocarbon solvents soluble in liquid chlorine and bromine dissolves in nitrobenzene to form a dark red solution that fumes in air. 

Recently, the effective mass of the electron has been calculated [148] within a Wigner-Seitz framework [175] for Ar, Kr, and Xe. In all three liquids, m decreases with increasing density. At the triple point densities, m = in argon and m =... 

Polanyi s theory is adequate in a large domain near the normal boiling temperature of the adsorbate, with p taken equal to the density of pz of the liquid. Thus the adjustable parameters were adjusted to give a common tangent for the two curves p vs. T and pi vs. T, at a reference temperature T0, which is the normal boiling temperature, or the triple point temperature for C02. The following equation was obtained (17) ... 

The results of the calculations of the spectra are illustrated by Figs. 18 and 19. The first figure refers to the temperature T = 133 K, which is near the triple point (131 K for CH3F). In this case the density p of a liquid, the maximum dielectric loss t j( in the Debye region, and the Debye relaxation time xD are substantially larger than those for T = 293 K (the latter is rather close to the critical temperature 318 K) to which Fig. 19 refers. The fitted parameters are such that the Kirkwood correlation factor is about 1 at T = 293 K. 

As a second example, we consider liquid fluoromethane CH3F, which is a typical strongly absorbing nonassociated liquid. For our study we choose the temperature T 133 K near the triple point, which is equal to 131 K. The relevant experimental data [43] were summarized in Table IV. As we see in Table VIII, which presents the fitted parameters of the model, the angle p is rather small. At this temperature the density p of the liquid, the maximum dielectric loss and the Debye relaxation time rD are substantially larger than they would be, for example, near the critical temperature (at 293 K). At such small (5 the theory given here for the hat-curved model holds. For calculation of the complex permittivity s (v) and absorption a(v), we use the same formulas as for water. 

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