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In thermodynamics, heterogeneous refers to a system composed of more than one phase, e.g. a liquid-solid system, as compared to a one-phase homogeneous system. [1]

Etymology
The word was used by French chemist Antoine Lavoiser in his 1787 treatise The Elements of Chemistry, who in discussing the possible experiments that might be carried out on French physicist Denis Papin’s digester, where by excessive red heat could be used to make sensible substances (stones, salts, and the greater parts that compose the mass of the earth), could be softened and changed into fluids or liquids, and likewise in the reverse sense. He states:

“If the earth were suddenly transported to a very cold region, the fluids [of the earth] would be converted into solid mountains and hard rocks, at first diaphanous and homogeneous, like rock crystal, but which, in time, becoming mixed with foreign heterogeneous substances, would become opaque stones of various colors.”

He goes on to explain his theory that the amount of caloric, or the power of repulsion inside of bodies, is what keeps substances in different states of equilibrium, or specifically: [2]

“That solidity, liquidity, and aeriform elasticity, are the only three states of existence of the same matter, or three particular modification 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 with which they are penetrated.”

In 1875, German physicist Rudolf Clausius, in his chapter “On Homogeneous Bodies”, defined a homogeneous body as one of the same condition of aggregation. [3]

This logic was taken up further in engineer Willard Gibbs 1876 treatise On the Equilibrium of Heterogeneous Substances, where he utilized both the quantities of heat and entropy, instead of caloric, to explain graphically the thermodynamic nature of heterogeneous systems composed of various phases. [4]

References
1. Anderson, Greg and Crerar, David A. (1993). Thermodynamics in Geochemistry: the Equilibrium Model (pg. 323). Oxford University Press.
2. Lavoisier, Antoine. (1789). Elements of Chemistry (pgs. 28-29). London: G.G. and J.J. Robinsons.
3. Clausius, Rudolf. (1875). The Mechanical Theory of Heat (ch. 8: “On Homogeneous Bodies”, pgs. 175-194). London: Macmillan & Co.
4. Gibbs, Willard. (1876). "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy, III. pp. 108-248, Oct., 1875-May, 1876, and pp. 343-524, may, 1877-July, 1878.

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