Orthobaric curve

This statement is, of course, in a contradiction with the conventional mean-field assumption that the orthobaric curve forms a line along which e,s,v all increase monotonically on passing from liquid, through the critical point, to the gas. 

Fig. 13.2 Vapor pressures (PV,T) and liquid molar volumes (Vm,T) along the orthobaric LV equilibrium line for reference isotopomer pairs, showing their distinctly different behaviors (schematic). The thicker lines label the heavier isotopomers. The curves begin at the triple points and end at the critical points (except for He which has no triple point under orthobaric conditions). Not to scale, isotopic differences are exaggerated (Reprinted from Van Hook, W. A., Rebelo, L. P. N. and Wolfsberg, M., Fluid Phase Equilib. 257, 35 (2007), copyright 2007, with permission from Elsevier)...

These observations are in agreement with the idea that the critical point is a single temperature and not a range of temperatures. It does appear, however, that the coexistence curve for gas and liquid has a very flat top. This is responsible for the rather large differences in critical densities which have been reported. Orthobaric densities for liquid and vapor (Table III) have been determined by Miller et al. (212) from 9° to 43°. In this work liquid sulfur hexafluoride was found to be a good solvent for nitrogen. 

Iteration for Coexisting Densities. Orthobaric densities near the critical point generally cannot be obtained accurately from isochoric PpT data by extrapolation to the vapor-pressure curve because the isochore curvatures become extremely large near the critical point. The present, nonanalytic equation of state, however, can be used to estimate these densities by a simple, iterative procedure. Assume that nonlinear parameters in the equation of state have been estimated in preliminary work. For data along a given experimental isochore (density), it is necessary merely to find the coexistence temperature, Ta(p), by trial (iteration) for a best, least-squares fit of these data. 

The curves for Pr < 1 terminate at a curve representing orthobaric densities. The latter curve can itself be predicted using the Principle of Corresponding States equations for this purpose have been proposed by Guggenheim. ... 

Finally we want to note that using the orthobaric densities from PVT data and the D values from eq. (3.6),we find that the following relationship holds for thermodynamic states along the coexistence curve... 

On figure 2, from reference (6), a shift towards low frequencies is observed as the temperature of the liquid methyl fluoride is increased gradually along the liquid-gas coexistence curve (i.e. under orthobaric conditions). Here the density effect is essentially responsible for the frequency shift following the loosening of local structures. 

Fia. 5.7. Sketch of the phase diagram of the penetrable-sphere model. The fiill curve is the orthobaric line and the dashed curve is the line of symmetry. 

Fig. 6.1. The orthobaric liquid density of a Lennard-Jones fluid as found fiom computer simulations of the liquid-gas surface. Own circles, Chapela et closed circles. Liu trian es, Rao and Levesque inverted triangle, Ophz squares, Lee et aL The curve is the best estimate of p from simubtions of homogeneous systems. ...

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