It has been suggested that this article or section be merged with Gibbs' phase rule. (Discuss)

It has been suggested that this article or section be merged with phase equilibrium. (Discuss)

Gibbs' phase rule (formulated by the American physicist Josiah Willard Gibbs) specifies the number of degrees of freedom for a given system at equilibrium. In thermodynamics the number of degrees of freedom is the smallest number of intensive variables (i.e. pressure, temperature, and concentrations of components in each phase) that must be specified to completely describe the state of the system. Wikipedia does not have an article with this exact name. ... It has been suggested that this article or section be merged with Gibbs phase rule. ... Wikipedia does not have an article with this exact name. ... A phase boundary describes the interface two substances that can remain in contact indefinitely (that is to say, at equilibrium) without mixing, as when oil meets water or air meets stone. ... A physicist is a scientist trained in physics. ... Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American mathematical physicist who developed much of the theoretical foundation that led to the development of chemical thermodynamics and was one of the founders of vector analysis. ... The phrase degrees of freedom is used in three different branches of science: in physics and physical chemistry, in mechanical and aerospace engineering, and in statistics. ... This article needs to be cleaned up to conform to a higher standard of quality. ...

Gibbs' phase rule can be expressed as:

F = c − p + 2

where F is the number of degrees of freedom, c is the number of components in the system, and p is the number of phases in the system. In thermodynamics, a component is a chemically distinct constituent of a system. ... In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i. ...

Gibbs' phase rule implies that the number of degrees of freedom increases as the number of components in the system increases and decreases as the number of phases increases. For example the phase rule indicates that a single component system with only one phase, such as liquid water, has 2 degrees of freedom. For this case the degrees of freedom correspond to temperature and pressure, indicating that the system can exist in equilibrium for any arbitrary combination of temperature and pressure. However, if we allow the formation of a gas phase, there is only 1 degree of freedom. This means that at a given temperature, water in the gas phase will evaporate or condense until the corresponding equilibrium water vapor pressure is reached. It is no longer possible to arbitrarily fix both the temperature and the pressure, since the system will tend to move toward the equilibrium vapor pressure. For a single component with three phases (gas, liquid, and solid) there are no degrees of freedom. Such a system is only possible at the temperature and pressure corresponding to the triple point. At other conditions one of phases will evaporate, condense, melt or freeze. The vapor pressure is the pressure (if the vapor is mixed with other gases, the partial pressure) of a vapor. ... In physics, the triple point of a substance is the temperature and pressure at which three phases (gas, liquid, and solid) of that substance may coexist in thermodynamic equilibrium. ...

The rule is especially powerful in sytems with more than one component (eg the iron-carbon phase diagram). Thermodynamically, the relation comes about because for phases to be in equilibrium, the chemical potential of each component must be the same in every phase. The chemical potential of a thermodynamic system is the amount by which the energy of the system would change if an additional particle were introduced, with the entropy and volume held fixed. ...

Reference

Moore W J (1964) Physical Chemistry, (4th edition), Prentice-Hall, NJ