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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
When pressure and temperature are variable, only of components have independent values for chemical potential and Gibbs' phase rule follows. The Gibbs−Duhem equation cannot be used for small thermodynamic systems due to the influence of surface effects and other microscopic phenomena. [2] The equation is named after Josiah Willard Gibbs and ...
The definition of the Gibbs function is = + where H is the enthalpy defined by: = +. Taking differentials of each definition to find dH and dG, then using the fundamental thermodynamic relation (always true for reversible or irreversible processes): = where S is the entropy, V is volume, (minus sign due to reversibility, in which dU = 0: work other than pressure-volume may be done and is equal ...
The theorem is Gibbs's phase rule, not Gibbs' phase rule. (In English, one leaves off the final s only when it's difficult to pronounce.) Gibb's phase rule first appeared in the Transactions of the Connecticut Academy of Sciences in the paper 'On the Equilibrium of . Heterogeneous Substances', published in parts between 1875 & 1878.
Josiah Willard Gibbs Born (1839-02-11) February 11, 1839 New Haven, Connecticut, U.S. Died April 28, 1903 (1903-04-28) (aged 64) New Haven, Connecticut, U.S. Nationality American Alma mater Yale College (BA, PhD) Known for List Statistical mechanics Chemical thermodynamics Chemical potential Cross product Dyadics Exergy Principle of maximum work Phase rule Phase space Physical optics Physics ...
= , 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
Gibbs's paper marked the beginning of chemical thermodynamics by integrating chemical, physical, electrical, and electromagnetic phenomena into a coherent system. It introduced concepts such as chemical potential, phase rule, and more, which form the basis for modern physical chemistry.
Yet also other variables may be used in that form. It is directly related to Gibbs phase rule, that is, the number of independent variables depends on the number of substances and phases in the system. An equation used to model this relationship is called an equation of state.