In thermodynamics, the phase rule or "Gibbs phase rule" states that the number of distinct phases for any system at equilibrium is determined by the following expression:

Gibbs phase rule

where P is the number of phases, C the number of components, and F the number of degree of freedom. [1]

The phase rule was derived by American chemical engineer Willard Gibbs who first formulated it in his 1876 treatise On the Equilibrium of Heterogeneous Substances.

The first proof of the phase rule was said to have been made by French physicist Pierre Duhem as found in what is called the Gibbs-Duhem equation, argued to be the basis of the phase rule. [2]

Human thermodynamics
See main: Social phase
American historian Henry Adams wrote his 1909 article “The Rule of Phase Applied to History” based on a crude interpretation of Gibbs phase rule. [3] In it Adams attempted to use Maxwell’s demon, as an historical metaphor, though he seems to have misunderstood and misapplied the principle. Adams interpreted history as a process moving towards "equilibrium", but he saw militaristic nations (he felt German pre-eminent in this class) as tending to reverse this process, a "Maxwell's demon of history". Adams made many attempts to respond to the criticism of his formulation from his scientific colleagues, but the work remained incomplete at Adams' death in 1918. It was only published posthumously.

1. Daintith, John. (2005). Oxford Dictionary of Science. Oxford University Press.
2. (a) Duhem-Margules Equation – McGraw-Hill’s Digital Engineering Library.
(b) Alberty, Robert A. (2003). Thermodynamics of Biochemical Reactions (2.4: Gibbs-Duhem equation and the Phase Rule, pgs. 25-26). John Wiley and Sons.
3. Adams, Henry. (1909). “The Rule of Phase Applied to History”. Washington.

Further reading
● Berry, R. Stephen and Smirnov, Boris M. (2011). “The Phase Rule: Beyond Myopia to Understanding” (abs), Structure and Bonding, 1-9.

External links
Gibbs’ phase rule – Wikipedia.

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