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In thermodynamics, the phase rule is a general principle governing multi-component, multi-phase systems in thermodynamic equilibrium.For a system without chemical reactions, it relates the number of freely varying intensive properties (F) to the number of components (C), the number of phases (P), and number of ways of performing work on the system (N): [1] [2] [3]: 123–125
He wrote the phase rule n + 2 - r, where r is the number of phases. Because n is now used otherwise, I call C, the components, the number of independent constituents (Gibbs's 'n'). The phase rule is thus C + 2 - P, where C is your 'number of "chemically independent" components'.
If multiple phases of matter are present, the chemical potentials across a phase boundary are equal. [8] Combining expressions for the Gibbs–Duhem equation in each phase and assuming systematic equilibrium (i.e. that the temperature and pressure is constant throughout the system), we recover the Gibbs' phase rule .
In chemistry, the lever rule is a formula used to determine the mole fraction (x i) or the mass fraction (w i) of each phase of a binary equilibrium phase diagram. It can be used to determine the fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line. [1]
A plot of typical polymer solution phase behavior including two critical points: a LCST and an UCST. The liquid–liquid critical point of a solution, which occurs at the critical solution temperature, occurs at the limit of the two-phase region of the phase diagram. In other words, it is the point at which an infinitesimal change in some ...
Phase reduction is a method used to reduce a multi-dimensional dynamical equation describing a nonlinear limit cycle oscillator into a one-dimensional phase equation. [1] [2] Many phenomena in our world such as chemical reactions, electric circuits, mechanical vibrations, cardiac cells, and spiking neurons are examples of rhythmic phenomena, and can be considered as nonlinear limit cycle ...
[2] These phases may consist of one chemical component (e.g. flow of water and water vapour), or several different chemical components (e.g. flow of oil and water). [3] A phase is classified as continuous if it occupies a continually connected region of space (as opposed to disperse if the phase occupies disconnected regions of space). The ...
The discontinuity in , and other properties, e.g. internal energy, , and entropy,, of the substance, is called a first order phase transition. [12] [13] In order to specify the unique experimentally observed pressure, (), at which it occurs another thermodynamic condition is required, for from Fig.1 it could clearly occur for any pressure in the range .