If we equate the chemical potential of the solute in the condensed phase with the chemical potential of the solute in the gas phase at equilibrium, we obtain [Pg.377]

It is convenient, therefore, to choose the pure condensed phase at the temperature of the solution at the equilibrium vapor pressure of the pure condensed phase as the standard state for the component in the solution (see Ref. 1). Thus, Equation (14.6) can also be written [Pg.321]

For transitions from a condensed phase into the vapor phase (the vapor phase is assumed to be perfect Vy — V nd Vy = R T/p) the solution of the CC equation results in [Pg.7]

Figure 6. Solutions of the gap equations and the charge neutrality condition (solid black line) in the /// vs //, plane. Two branches are shown states with diquark condensation on the upper right (A > 0) and normal quark matter states (A = 0) on the lower left. The plateau in between corresponds to a mixed phase. The lines for the /3-equilibium condition are also shown (solid and dashed straight lines) for different values of the (anti-)neutrino chemical potential. Matter under stellar conditions should fulfill both conditions and therefore for //,( = 0 a 2SC-normal quark matter mixed phase is preferable. |

Therefore we seek ways for computing conceptuals of condensed phases while avoiding the need for volumetric equations of state. One way to proceed is to choose as a basis, not the ideal gas, but some other ideality that is, in some sense, "doser" to condensed phases. By "closer" we mean that changes in composition more strongly affect properties than changes in pressure or density. The basis exploited in this chapter is the ideal solution. We still use difference measures and ratio measures, but they will now refer to deviations from an ideal solution, rather than deviations from an ideal gas. [Pg.184]

However, for reasons which are obvious today, no quantitative treatment of the thermod3mamic properties of condensed phases can be based on the largely empirical Van der Waals equation of state. Increasing experimental evidence also showed that the liquid state has many features (large number of first neighbours, local order, etc.) in common with crystals. For this reason several attempts were made around 1925-1930 to base the theory of liquid solutions on a lattice [Pg.460]

The quasi-steady-state theory has been applied particularly where a condensed phase exists whose volume changes slowly with time. This is true, for example, in the sublimation of ice or the condensation of water vapor from air on liquid droplets (M3, M4). In the condensation of water vapor onto a spherical drop of radius R(t), the concentration of water vapor in the surrounding atmosphere may be approximated by the well-known spherically symmetric solution of the Laplace equation [Pg.105]

Fickett in "Detonation Properties of Condensed Explosives Calculated with an Equation of State Based on Intermolecular Potentials , Los Alamos Scientific Lab Rept LA-2712 (1962), pp 34-38, discusses perturbation theories as applied to a system of deton products consisting of two phases one, solid carbon in some form, and the other, a fluid mixt of the remaining product species. He divides these theories into two classes conformal solution theory, and what he chooses to call n-fluid theory. Both theories stem from a common approach, namely, perturbation from a pure fluid whose props are assumed known. They differ mainly in the choice of expansion variables. The conformal solution method begins with the assumption that all of the intermolecular interaction potentials have the same functional form. To obtain the equation of state of the mixt, some reference fluid obeying a common reduced equation of state is chosen, and the mixt partition function is expanded about that of the reference fluid [Pg.470]

The simulation of condensed phase systems by statistical mechanical methods has become a major research area in recent years. Of course, much of this work has been directed toward biologically relevant systems. The contributions in this section of ECC tend toward theory as much as computation and include the articles by Rob Coal son Poisson-Boltzmann Type Equations Numerical Methods), Peter Cummings Classical Dynamics of Nonequilibrium Processes in Fluids), a second article by Cummings Supercritical Water and Aqueous Solutions Molecular Simulation), Brian Laird Interfaces Liquid-Solid), Chi Mak Condensed- [Pg.3446]

Equation (11.4) provides a convenient value for that constant. Planck s statement asserts that 5qk is zero only for pure solids and pure liquids, whereas Nernst assumed that his theorem was applicable to all condensed phases, including solutions. According to Planck, solutions at 0 K have a positive entropy equal to the entropy of mixing. (The entropy of mixing is discussed in Chapters 10 and 14). [Pg.262]

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