In science, a phase refers to a given composition and thermodynamic state of a given body without regard to its quantity or form.

The first to discuss the fact that matter can exist in three states: solid, liquid, and gas, being but a factor of the temperature of the matter or of the degree of heat penetrated or released, into or out of the body, respectively, was French chemist Antoine Lavoisier, who in his1787 Elements of Chemistry, discussed Boerhaave’s law, the Papin digester, the possibility of absolute zero, the terms homogenous and heterogeneous substances, and then following a bit of argument, stated what he called the first corollary:

“Solidity, liquidity, and aeriform elasticity [gas], are only three different states of existence of the same matter, or three particular modifications which almost all substances are susceptible of assuming successively, and which solely depend on the degree of temperature to which they are exposed; or, in other words, upon the quantity of caloric [entropy] which they are penetrated.”

In 1876, American engineer Willard Gibbs, in his section “On the Coexistent Phases of Matter” of his On the Equilibrium of Heterogeneous Substances, coined the term phase as follows: [2]

“In considering the different homogeneous bodies which can be formed out of any set of component substances, it will be convenient to have a term which shall refer solely to the composition and thermodynamic state of any such body without regard to its quantity or form. We may call such bodies as differ in composition or state different phases of the matter considered, regarding all bodies which differ only in quantity and form as different examples of the same phase. Phases which can exist together, the dividing surfaces being plane, in an equilibrium which does not depend upon passive resistances to change, we shall call coexistent.

If a homogeneous body has n independently variable components, the phase of the body is evidently capable of n+1 independent variations. A system of r coexistent phases, each of which has the same n independently variable components is capable of n+2–r variations of phase. For the temperature, the pressure, and the potentials for the actual components have the same values in the different phases, and the variations of these quantities are by (97) subject to as many conditions as there are different phases. Therefore, the number of independent variations in the values of these quantities, i.e., the number of independent variations of phase of the system, will be n+2–r.

This "n+2–r" number of "variations of phase" is what is know known as the phase rule. Gibbs continues:

Or, when the r bodies considered have not the same independently variable components, if we still denote by n the number of independently variable components of the r bodies taken as a whole, the number of independent variations of phase of which the system is capable will still he n + 2 – r. In this case, it will be necessary to consider the potentials for more than n component substances. Let the number of these potentials be n + h. We shall have by (97), as before, r relations between the variations of the temperature, of the pressure, and of these n + h potentials, and we shall also have by (43) and (51) h relations between these potentials, of the same form as the relations which subsist between the units of the different component substances.

Hence, if r = n + 2, no variation in the phases (remaining coexistent) is possible. It does not seem probable that r can ever exceed n+2. An example of 7i = l and r = 3 is seen in the coexistent solid, liquid, and gaseous forms of any substance of invariable composition. It seems not improbable that in the case of sulphur and some other simple substances there is more than one triad of coexistent phases; but it is entirely improbable that there are four coexistent phases of any simple substance. An example of n = 2 and r = 4 is seen in a solution of a salt in water in contact with vapor of water and two different kinds of crystals of the salt.”

Polish-born American mechanical engineer Joseph Kestin, in his 1966 section “Phase”, credits Gibbs, above, with the coining of the term phase. [3]

1. Lavoisier, Antoine. (1787). Elements of Chemistry (pg. 29). Dover, 1965.
2. Gibbs, Willard. (1876). "On the Equilibrium of Heterogeneous Substances" (§: On the Coexistent Phases of Matter, pg. 96), Transactions of the Connecticut Academy, III. pp. 108-248, Oct., 1875-May, 1876, and pp. 343-524, may, 1877-July, 1878.
3. Kestin, Joseph. (1966). A Course in Thermodynamics (§7.4.1: Phase, pg. 276). London: Blaisdell Publishing Co.

See also
Human phase
Phase rule
Phase thermodynamics
Phase transition
Social phase

Further reading
● Perrot, Pierre. (1998). A to Z of Thermodynamics (Phase, pg. 235). Oxford University Press.

External links
Phase – Wikipedia.

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