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Gibbs' phase rule〔Gibbs, J.W., Scientific Papers (Dover, New York, 1961)〕〔 Chapter 6〕 was proposed by Josiah Willard Gibbs in his landmark paper titled ''On the Equilibrium of Heterogeneous Substances'', published from 1875 to 1878. The rule applies to non-reactive multi-component heterogeneous systems in thermodynamic equilibrium and is given by the equality : where ''F'' (alternatively Γ) is the number of degrees of freedom, ''C'' (alternatively N) is the number of components and ''P'' (alternatively π or Φ) is the number of phases in thermodynamic equilibrium with each other. The number of degrees of freedom is the number of independent intensive variables, i. e. the largest number of properties such as temperature or pressure that can be varied simultaneously and arbitrarily without affecting one another. An example of one-component system is a system involving one pure chemical, while two-component systems, such as mixtures of water and ethanol, have two chemically independent components, and so on. Typical phases are solids, liquids and gases. ==Foundations== *A phase is a form of matter that is homogeneous in chemical composition and physical state. Typical phases are solid, liquid and gas. Two immiscible liquids (or liquid mixtures with different compositions) separated by a distinct boundary are counted as two different phases, as are two immiscible solids. *The number of components (C) is the number of chemically independent constituents of the system, i.e. the minimum number of independent species necessary to define the composition of all phases of the system.〔 For examples see component (thermodynamics). *The number of degrees of freedom (F) in this context is the number of intensive variables which are independent of each other. The basis for the rule (Atkins and de Paula,〔 justification 6.1) is that equilibrium between phases places a constraint on the intensive variables. More rigorously, since the phases are in thermodynamic equilibrium with each other, the chemical potentials of the phases must be equal. The number of equality relationships determines the number of degrees of freedom. For example, if the chemical potentials of a liquid and of its vapour depend on temperature (T) and pressure (p), the equality of chemical potentials will mean that each of those variables will be dependent on the other. Mathematically, the equation μliq(T, p) = μvap(T, p), where μ = chemical potential, defines temperature as a function of pressure or vice versa. (Caution: do not confuse p = pressure with ''P'' = number of phases.) To be more specific, the composition of each phase is determined by ''C – 1'' intensive variables (such as mole fractions) in each phase. The total number of variables is ''(C–1)P + 2'', where the extra two are temperature T and pressure p. The number of constraints are ''C(P–1)'', since the chemical potential of each component must be equal in all phases. Subtract the number of constraints from the number of variables to obtain the number of degrees of freedom as ''F = (C–1)P + 2 – C(P–1) = C – P + 2''. The rule is valid provided the equilibrium between phases is not influenced by gravitational, electrical or magnetic forces, or by surface area, and only by temperature, pressure, and concentration. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「phase rule」の詳細全文を読む スポンサード リンク
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