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Extended phase rule for non-reactive, multiphase, multicomponent chemical systems

Fluid Phase Equilibria
Publication Date
DOI: 10.1016/0378-3812(90)87009-e
  • Chemistry
  • Design
  • Engineering
  • Mathematics
  • Physics


Abstract A comprehensive phase rule has been developed for non-reacting, multicomponent, multiphase systems, which considers, in addition to phase-intensive variables such as temperature, pressure and phase compositions, system-intensive variables such as overall or total density, overall composition and phase volume fractions. This extended phase rule, incorporating as it does overall density and composition, may be of use to engineers who design chemical processing equipment and to theoreticians concerned with the nature of thermodynamic equilibrium. It describes thermodynamic paths often followed by experimentalists. The number of degrees of freedom is given as ( C + 1), where ( C) is the number of components. This phase rule is for a relative thermodynamic system; that is, one in which relative phase sizes are relevant. It is in contrast to Gibb's phase rule and Duhem's theorem for open and closed systems, respectively. The Gibbs phase rule is incorporated into the present formulation. For a single phase, the system-intensive variables are the same as phase-intensive variables, and the rule given here and that of Gibbs are coincident. When the maximum possible number of phases is present (for example, for a pure substance at its triple point), only system-intensive variables such as total density or phase volume fractions can be specified. For cases other than those involving a single phase or the maximum possible number of phases, no phase-intensive variables need be specified to determine the state of thermodynamic equilibrium. However, in the case of vapor-liquid equilibrium, it is useful to fix the phase-intensive variable, temperature, along with the system-intensive variables, total density and composition. Along such thermodynamic paths mixtures behave similarly to pure fluids, in that the mixture can be represented by pure-fluid-like vapor pressure and coexistence density curves.

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