Editing Phase rule (section)

==Foundations==
{{See also|Component (thermodynamics)}}
*A phase is a form of matter that is [[Homogeneity (physics)|homogeneous]] in [[chemical composition]] and [[physical state]]. Typical phases are solid, liquid and gas. Two [[miscibility|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.<ref name="Atkins"/>
*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<ref name=Atkins/>{{rp|122–126}} 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 potential]]s 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 {{math|1=''μ''<sub>liq</sub>(''T'', ''p'') = ''μ''<sub>vap</sub>(''T'', ''p'')}}, where {{math|''μ''}}, the chemical potential, defines temperature as a function of pressure or vice versa. (Caution: do not confuse {{math|''p''}} as pressure with {{math|''P''}}, number of phases.)

To be more specific, the composition of each phase is determined by {{nowrap|''C'' − ''1''}} intensive variables (such as mole fractions) in each phase. The total number of variables is {{nowrap|(''C'' − 1)''P'' + 2}}, where the extra two are temperature ''T'' and pressure ''p''. The number of constraints is {{nowrap|''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 {{nowrap|1=''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.