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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
The phase diagram shows, in pressure–temperature space, the lines of equilibrium or phase boundaries between the three phases of solid, liquid, and gas. The curves on the phase diagram show the points where the free energy (and other derived properties) becomes non-analytic: their derivatives with respect to the coordinates (temperature and ...
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.
A generic phase diagram with unspecified axes; the invariant point is marked in red, metastable extensions labeled in blue, relevant reactions noted on stable ends of univariant lines. This rule is geometrically sound in the construction of phase diagrams since for every metastable reaction, there must be a phase that is relatively stable. This ...
Gibbs' phase rule suggests that different phases are completely determined by these variables. Consider a test apparatus consisting of a closed and well-insulated cylinder equipped with a piston. By controlling the temperature and the pressure, the system can be brought to any point on the phase diagram.
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 .
These lines generally divide the diagram into subtriangles since, in accordance with Gibb's phase rule, a system of three components will contain three phases except at the degenerate compositions represented by the points and lines. The composition within each subtriangle will be a mixture of the pure phases found at the corners of the ...
This could ease the theoretical phase diagram generation of multicomponent systems. For alloys containing transition metal elements there is a difficulty in interpretation of the Hume-Rothery electron concentration rule, as the values of e/a values (number of itinerant electrons per atom) for transition metals have been quite controversial for ...