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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 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 .
Phase transitions and critical exponents appear in many physical systems such as water at the critical point, in magnetic systems, in superconductivity, in percolation and in turbulent fluids. The critical dimension above which mean field exponents are valid varies with the systems and can even be infinite.
= , where k B is the Boltzmann constant, and Ω denotes the volume of macrostate in the phase space or otherwise called thermodynamic probability. d S = δ Q T {\displaystyle dS={\frac {\delta Q}{T}}} , for reversible processes only
The number of components represents the minimum number of independent chemical species necessary to define the composition of all phases of the system. [2] Calculating the number of components in a system is necessary when applying Gibbs' phase rule in determination of the number of degrees of freedom of a system.
If multiple phases of matter are present, the chemical potentials across a phase boundary are equal. [6] 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.
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 ...
where α is an exponent specific to the system (e.g. in the absence of a potential field, α = 3/2), z is exp(μ/k B T) where μ is the chemical potential, Li is the polylogarithm, ζ is the Riemann zeta function, and T c is the critical temperature at which a Bose–Einstein condensate begins to form.