Free energy - bound energy (diagram)
A depiction of the location of bound energy for the isothermal-isochoric potential, aka Helmholtz free energy (or Helmholtz energy).
In thermodynamics, bound energy or gebundene energie (German), TS, is the amount of energy of a system that unavailable to do external work. [1] The product is defined, according to Hermann Helmholtz, the 1882 coiner of the term, as “expressing the mechanical equivalent of that quantity of heat Q which must be conveyed into a body at temperature T in order to raise its entropy to the value S.”

The remaining portion of energy, namely that which can be converted into external useful work, is called "free energy". [4]

The etymology of the term derives from various difficulties in the development of the theory of chemical affinity, during the years 1750 to 1850, approximately. [2] Helmholtz’s derivation rested primarily on the work of Clausius. In 1854, Clausius had stated, in a phrasing similar to French chemist Antoine Lavoisier’s ‘combined heat’, that during a complete cycle there is a Verwandlungsinhalt or ‘bound transformation content’, which he denoted by the integral of dQ/T between T1 and T2, and which he later termed entropy [3]. On this terminology, Helmholtz conceptually divided the portion of the total energy U available for conversion to other forms as ‘free energy’, G or F, and the residual ‘bound energy’, TS. [5]

The term bound energy was latter used, via extrapolation, to distinguish conceptions of energies in human systems by those as Nicholas Georgescu-Roegen and Xenophon Zolotas.

In general, Helmholtz pointed out, any external work takes place at the expense of free energy, while heat production results in a loss of bound energy only (a result which is not valid for adiabatic processes). If the temperature of a chemical system increases, free energy is converted into bound energy. [2]

1. Thims, Libb. (2007). Human Chemistry (Volume Two), (preview), (index: "bound energy", pgs. 422, 429, 437, 483, 458, 659, 661). Morrisville, NC: LuLu.
2. Cahan, David (1993). Hermann von Helmholtz and the Foundations of Nineteenth-Century Science (Ch. 10: "Between Physics and Chemistry - Helmholtz's Route to a Theory of Chemical Thermodynamics" by Helge Kragh). University of California Press.
3. Fruton, Joseph. S. (1999). Proteins, Enzymes, Genes: the Interplay of Chemistry and Biology, (pgs. 249-50). Yale University Press.
4. (a) Helmholtz, Hermann. (1882). “Die Thermodynamik Chemischer Vorgänge (The Thermodynamics of Chemical Operations”, SB: 22-39, in Wissenschaftliche Abhandlungen von Hermann von Helmholtz. 3 vols. Leipzig: J.A. barth, 1882-95. 2:958-78.
(b) Young, Paul T. (1936). Motivation of Behavior – the Fundamental Determinants of Human and Animal Activity, (ch. 2: “The Energetics of Activity”, pg. 68) New York: Wiley.
5. Kubo, Ryogo. (1976). Thermodynamics (Divertissement 8: On the Names of Thermodynamic Functions). North Holland.

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