In thermodynamics, ergal, symbol J, is defined by the following expression:


which quantifies the system as a summation function of Cartesian coordinates, x,y, and z, for the work W done by the component forces, X, Y, and Z, acting on the particles of the system, where J0 is the ergal of the system at some initial state. The generalized expression for the ergal of a single particle acted on by a force is:

Ergal a

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In 1875, German physicist Rudolf Clausius, in his second edition "Mathematical Introduction" section, explicitly introduced the term "ergal", as the negative value of Irish mathematician William Hamilton's “force function”, deemed to represent a quantity the subtraction of which gives the work performed, a quantity which had been also given the name “potential energy” by Scottish physicist William Rankine. [1]

Clausius’ use of the term ergal seems, although he does not say this explicitly, to have its roots in the classical Greek term “ergon”, such as used by Aristotle, e.g. in Nicomachean Ethics, as "function, task, or work". [2] Heraclitus, likewise, prior to Aristotle, used the term "en-ergon" as representative of fire, the primary source of activity, or the father of everything, according to his three element theory, which is the modern root of the term "energy". [3] Clausius, e.g., defines internal energy or its magnitude U as the sum of the "thermal and ergonal content" of a body.

Internal energy
The ergal, as explained in Clausius' 1875 "Mathematical Introduction", along with the vis viva T, is one of the components of the internal energy U of the body:

Internal energy

which quantifies the law of conservation of energy in nature.

Internal work
In reference to internal work, according to Clausius, the “internal forces”, i.e. those forces which the atoms and molecules of a body exert among themselves when undergoing a change, “have an ergal”. [1]

1. Clausius, Rudolf. (1875). The Mechanical Theory of Heat (§: Mathematical Introduction, pgs. 11-20; §§6: On the Ergal, pgs. 11-13; pg. 28). London: Macmillan & Co, 1879.
2. Ergon (disambiguation) – Wikipedia.
3. (a) Feekes, Gerrit B. (1986). The Hierarchy of Energy Systems: from Atom to Society (pg. 1). Pergamon Press.
(b) Lancaster, Justin. (1989). “The Theory of Radially Evolving Energy” (abs), Int. J. General Systems, 16: 43-73.
(c) Arnopoulos, Paris. (1993). Sociophysics: Cosmos and Chaos in Nature and Culture (pg. 21). Nova Publishers, 2005.
4. Clausius, Rudolf. (1865). The Mechanical Theory of Heat: with its Applications to the Steam Engine and to Physical Properties of Bodies (Ѻ) (translator: Thomas Hirst) (pg. 357). John van Voorst, 1867.

Further reading
● Clausius, Rudolf. (1874). “On the Theorem of the Mean Ergal, and its Application to the Molecular Motions of Gases”, Translated from a separate impression, communicated by the Author, read at the Meeting of the Niederrheinische Gesellschaft fur Natur-und Heilkunde, Nov 09; in: Philosophical Magazine, Vol. L., 4th Series, Jul-Dec, 1875.

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