Editing Thermodynamic free energy (section)

== Meaning of "free" ==
The basic definition of "energy" is a measure of a body's (in thermodynamics, the system's) ability to cause change. For example, when a person pushes a heavy box a few metres forward, that person exerts mechanical energy, also known as work, on the box over a distance of a few meters forward. The mathematical definition of this form of energy is the product of the force exerted on the object and the distance by which the box moved ({{nowrap|1=Work = Force × Distance}}). Because the person changed the stationary position of the box, that person exerted energy on that box. The work exerted can also be called "useful energy", because energy was converted from one form into the intended purpose, i.e. mechanical use. For the case of the person pushing the box, the energy in the form of internal (or potential) energy obtained through metabolism was converted into work to push the box. This energy conversion, however, was not straightforward: while some internal energy went into pushing the box, some was diverted away (lost) in the form of heat (transferred thermal energy). 

For a reversible process, heat is the product of the absolute temperature <math>T</math> and the change in entropy <math>S</math> of a body (entropy is a measure of disorder in a system). The difference between the change in internal energy, which is <math>\Delta U</math>, and the energy lost in the form of heat is what is called the "useful energy" of the body, or the work of the body performed on an object. In thermodynamics, this is what is known as "free energy". In other words, free energy is a measure of work (useful energy) a system can perform at constant temperature. 

Mathematically, free energy is expressed as

<math display="block">A=U-TS</math>

This expression has commonly been interpreted to mean that work is extracted from the internal energy <math>U</math> while <math>TS</math> represents energy not available to perform work. However, this is incorrect. For instance, in an isothermal expansion of an ideal gas, the internal energy change is <math>\Delta U=0</math> and the expansion work <math>w=-T\Delta S</math> is derived exclusively from the <math>TS</math> term supposedly not available to perform work. But it is noteworthy that the derivative form of the free energy: <math>dA=-SdT-PdV</math> (for Helmholtz free energy) does indeed indicate that a spontaneous change in a non-reactive system's free energy (NOT the internal energy) comprises the available energy to do work (compression in this case) <math>-PdV</math> and the unavailable energy <math>-SdT</math>.<ref>{{Cite journal|last1=Osara|first1=Jude A.|last2=Bryant|first2=Michael D.|date=September 2019|title=Thermodynamics of grease degradation|url=http://dx.doi.org/10.1016/j.triboint.2019.05.020|journal=Tribology International|volume=137|pages=433–445|doi=10.1016/j.triboint.2019.05.020|s2cid=182266032|issn=0301-679X}}</ref><ref name=":0">{{Cite book|last=Callen|first=Herbert B.|url=http://worldcat.org/oclc/651933140|title=Thermodynamics|date=October 1966|publisher=Wiley|isbn=0-471-13035-4|oclc=651933140}}</ref><ref name=":1">{{Cite book|last=Kondepudi, Dilip, 1952-|url=http://worldcat.org/oclc/1167078377|title=Modern thermodynamics : from heat engines to dissipative structures|date=1998|publisher=John Wiley|isbn=0-471-97393-9|oclc=1167078377}}</ref> Similar expression can be written for the Gibbs free energy change.<ref>{{Cite journal|last1=Osara|first1=Jude|last2=Bryant|first2=Michael|date=3 April 2019|title=A Thermodynamic Model for Lithium-Ion Battery Degradation: Application of the Degradation-Entropy Generation Theorem|journal=Inventions|volume=4|issue=2|pages=23|doi=10.3390/inventions4020023|issn=2411-5134|doi-access=free}}</ref><ref name=":0" /><ref name=":1" />

In the 18th and 19th centuries, the [[theory of heat]], i.e., that heat is a form of energy having relation to vibratory motion, was beginning to supplant both the [[caloric theory]], i.e., that heat is a fluid, and the [[four element theory]], in which heat was the lightest of the four elements.  In a similar manner, during these years, heat was beginning to be distinguished into different classification categories, such as "free heat", "combined heat", "radiant heat", [[specific heat]], [[heat capacity]], "absolute heat", "latent caloric", "free" or "perceptible" caloric (''calorique sensible''), among others.

In 1780, for example, [[Laplace]] and [[Lavoisier]] stated: “In general, one can change the first hypothesis into the second by changing the words ‘free heat, combined heat, and heat released’ into ‘[[vis viva]], loss of vis viva, and increase of vis viva.’"  In this manner, the total mass of caloric in a body, called ''absolute heat'', was regarded as a mixture of two components; the free or perceptible caloric could affect a thermometer, whereas the other component, the latent caloric, could not.<ref>{{cite book | last = Mendoza | first = E. | title = Reflections on the Motive Power of Fire – and other Papers on the Second Law of Thermodynamics | editor1-first = E. | editor1-last = Clapeyron | editor2-first = R. | editor2-last = Carnot | publisher = Dover Publications, Inc. | year = 1988 | isbn = 0-486-44641-7}}</ref> The use of the words "latent heat" implied a similarity to latent heat in the more usual sense; it was regarded as chemically ''bound'' to the molecules of the body.  In the [[Adiabatic process|adiabatic]] [[Gas compression|compression]] of a gas, the absolute heat remained constant but the observed rise in temperature implied that some latent caloric had become "free" or perceptible.

During the early 19th century, the concept of perceptible or free caloric began to be referred to as "free heat" or "heat set free".  In 1824, for example, the French physicist [[Nicolas Léonard Sadi Carnot|Sadi Carnot]], in his famous "[[Reflections on the Motive Power of Fire]]", speaks of quantities of heat ‘absorbed or set free’ in different transformations. In 1882, the German physicist and physiologist [[Hermann von Helmholtz]] coined the phrase ‘free energy’ for the expression <math>A=U-TS</math>, in which the change in ''A'' (or ''G'') determines the amount of energy ‘free’ for [[work (thermodynamics)|work]] under the given conditions, specifically constant temperature.<ref>{{cite book | last = Baierlein | first = Ralph | title = Thermal Physics | publisher = [[Cambridge University Press]] | year = 2003 | isbn = 0-521-65838-1 | url-access = registration | url = https://archive.org/details/thermalphysics00ralp }}</ref>{{rp|235}}

Thus, in traditional use, the term "free" was attached to Gibbs free energy for systems at constant pressure and temperature, or to Helmholtz free energy for systems at constant temperature, to mean ‘available in the form of useful work.’<ref name="Perrot" >{{cite book | last = Perrot | first = Pierre | title = A to Z of Thermodynamics | publisher = [[Oxford University Press]] | year = 1998 | isbn = 0-19-856552-6}}</ref> With reference to the Gibbs free energy, we need to add the qualification that it is the energy ''free'' for non-volume work and compositional changes.<ref>{{cite book | last = Reiss | first = Howard | title = Methods of Thermodynamics | publisher = Dover Publications | year = 1965 | isbn = 0-486-69445-3}}</ref>{{rp|77–79}}

An increasing number of books and journal articles do not include the attachment "free", referring to ''G'' as simply Gibbs energy (and likewise for the [[Helmholtz free energy|Helmholtz energy]]). This is the result of a 1988 [[International Union of Pure and Applied Chemistry|IUPAC]] meeting to set unified terminologies for the international scientific community, in which the adjective ‘free’ was supposedly banished.<ref>{{cite journal|title=Glossary of Atmospheric Chemistry Terms (Recommendations 1990) |url=http://www.iupac.org/publications/pac/1990/pdf/6211x2167.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.iupac.org/publications/pac/1990/pdf/6211x2167.pdf |archive-date=9 October 2022 |url-status=live|journal=[[Pure and Applied Chemistry|Pure Appl. Chem.]]|volume=62|pages=2167&ndash;2219|year=1990|last1=[[International Union of Pure and Applied Chemistry]] Commission on Atmospheric Chemistry|access-date=28 December 2006|doi=10.1351/pac199062112167|first1=J. G.|issue=11|s2cid=53117465}}</ref><ref>{{cite book|last=[[International Union of Pure and Applied Chemistry]] Commission on Physicochemical Symbols Terminology and Units|title=Quantities, Units and Symbols in Physical Chemistry|publisher=Blackwell Scientific Publications|location=Oxford|year=1993|url=https://archive.org/details/quantitiesunitss0000unse/page/48|isbn=0-632-03583-8|access-date=28 December 2006|pages=[https://archive.org/details/quantitiesunitss0000unse/page/48 48]|edition=2nd}}</ref><ref>{{cite journal |title=Glossary of Terms in Quantities and Units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996) |url=http://www.iupac.org/publications/pac/1996/pdf/6804x0957.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.iupac.org/publications/pac/1996/pdf/6804x0957.pdf |archive-date=9 October 2022 |url-status=live |journal=[[Pure and Applied Chemistry|Pure Appl. Chem.]] |volume=68 |pages=957–100 0|year=1996 |first1=H. P. |last1=Lehmann |first2=X. |last2=Fuentes-Arderiu |first3=L. F. |last3=Bertello |doi=10.1351/pac199668040957 |issue=4|s2cid=95196393 }}</ref> This standard, however, has not yet been universally adopted, and many published articles and books still include the descriptive ‘free’.{{Citation needed|date=August 2010}}