Phase rule - Soritsu (English spelling)

Japanese: 相律 - そうりつ（英語表記）phase rule

This is the law that determines the degrees of freedom when there is multiphase equilibrium, that is, equilibrium between two or more phases. It was published by American J. W. Gibbs between 1876 and 1878, and is also known as the Gibbs phase rule. The number of independent state variables (pressure, temperature, and concentrations of component substances) required to determine the state of a system in equilibrium is called the degrees of freedom. If the degrees of freedom are f , then when a system consists of n components and is in equilibrium as p phases, then:
f = n + 2 - p
For example, in a one-component system ( n = 1), if the system is in one phase (any one of gas, liquid, or solid, i.e., p = 1), then f = 2, and the two variables temperature and pressure can be freely changed (for example, when only water vapor is present). In a one-component system in which two phases coexist (for example, liquid and gas), f = 1, and once either the temperature or pressure is determined, all the others are determined (for example, when water and water vapor are present). Furthermore, when three phases coexist, both the temperature and pressure become constant values specific to that substance. The triple point of water is an example of this, and in a system consisting of a single component, water ( n = 1), and in which three phases coexist ( p = 3), water vapor (gas phase), water (liquid phase), and ice (solid phase), then:
f = 1 + 2 - 3 = 0
For systems with two or more components, the equation becomes more complicated, with variables such as temperature and pressure, as well as the concentration of the components (usually expressed as mole fractions).

[Toda Genjiro and Nakahara Katsunori]

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

多相平衡、すなわち二つ以上の相の間で平衡が成立しているとき、その自由度を決める法則をいう。1876年から1878年にかけてアメリカのJ・W・ギブスによって発表され、ギブスの相律ともいう。平衡にある系の状態を決めるのに必要な独立の状態変数（圧力、温度および成分物質の濃度）の数を自由度というが、その自由度をfとするとき、n個の成分からなり、p個の相として平衡にある場合、
　　f＝n＋2－p
で示される。たとえば、一成分系（n＝1）では、その系が一つの相（気相、液相、固相のうちどれか一つ、すなわちp＝1）であればf＝2となり、温度と圧力の2変数を自由に変えることができる（たとえば水蒸気のみが存在する場合）。一成分系で二つの相（たとえば液相と気相）が共存する系では、f＝1となり、温度または圧力のどちらか一つを決めるとほかはすべて決まる（たとえば水と水蒸気が存在する場合）。また三つの相が共存すれば、温度も圧力もその物質に特有な一定値となってしまう。水の三重点はこの例で、水という一つの成分からなって（n＝1）、水蒸気（気相）、水（液相）、氷（固相）の三相共存（p＝3）では、
　　f＝1＋2－3＝0
となる。二成分系以上では、変数として温度と圧力のほかに成分の濃度（普通モル分率で表す）が入り複雑になる。