G is the most useful for processes involving a system at constant pressure p and temperature T, because, in addition to subsuming any entropy change due merely to heat, a change in G also excludes the p dV work needed to "make space for additional molecules" produced by various processes.
Gibbs free energy change therefore equals work not associated with system expansion or compression, at constant temperature and pressure, hence its utility to solution-phase chemists, including biochemists.
The Helmholtz free energy has a special theoretical importance since it is proportional to the logarithm of the partition function for the canonical ensemble in statistical mechanics.
(Hence its utility to physicists; and to gas-phase chemists and engineers, who do not want to ignore p dV work.)
The basic definition of "energy" is a measure of a body's (in thermodynamics, the system's) ability to cause change.
In the adiabatic 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.
In 1824, for example, the French physicist 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
, in which the change in A (or G) determines the amount of energy ‘free’ for work under the given conditions, specifically constant temperature.
This is the result of a 1988 IUPAC meeting to set unified terminologies for the international scientific community, in which the adjective ‘free’ was supposedly banished.
[10][11][12] This standard, however, has not yet been universally adopted, and many published articles and books still include the descriptive ‘free’.
In most cases of interest there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which create entropy.
Under these conditions, it simplifies to Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as
The path integral Monte Carlo method is a numerical approach for determining the values of free energies, based on quantum dynamical principles.
Under other conditions, free-energy change is not equal to work; for instance, for a reversible adiabatic expansion of an ideal gas,
It is important to note that for heat engines and other thermal systems, the free energies do not offer convenient characterizations; internal energy and enthalpy are the preferred potentials for characterizing thermal systems.
According to the second law of thermodynamics, for any process that occurs in a closed system, the inequality of Clausius, ΔS > q/Tsurr, applies.
Thus, a negative value of the change in free energy is a necessary condition for a process to be spontaneous; this is the most useful form of the second law of thermodynamics in chemistry.
The quantity called "free energy" is a more advanced and accurate replacement for the outdated term affinity, which was used by chemists in previous years to describe the force that caused chemical reactions.
The term affinity, as used in chemical relation, dates back to at least the time of Albertus Magnus.
[13] From the 1998 textbook Modern Thermodynamics[14] by Nobel Laureate and chemistry professor Ilya Prigogine we find: "As motion was explained by the Newtonian concept of force, chemists wanted a similar concept of ‘driving force’ for chemical change.
Chemists called the ‘force’ that caused chemical reactions affinity, but it lacked a clear definition."
During the entire 18th century, the dominant view with regard to heat and light was that put forth by Isaac Newton, called the Newtonian hypothesis, which states that light and heat are forms of matter attracted or repelled by other forms of matter, with forces analogous to gravitation or to chemical affinity.
In 1875, after quantifying the heats of reaction for a large number of compounds, Berthelot proposed the principle of maximum work, in which all chemical changes occurring without intervention of outside energy tend toward the production of bodies or of a system of bodies which liberate heat.
Based on these and other ideas, Berthelot and Thomsen, as well as others, considered the heat given out in the formation of a compound as a measure of the affinity, or the work done by the chemical forces.
By 1865, the German physicist Rudolf Clausius had shown that this equivalence principle needed amendment.
Thus, we might naively reason that one can entirely convert the initial combustion heat of the chemical reaction into the work of pushing the piston.
In 1873, Willard Gibbs published A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces, in which he introduced the preliminary outline of the principles of his new equation able to predict or estimate the tendencies of various natural processes to ensue when bodies or systems are brought into contact.
Hence, in 1882, after the introduction of these arguments by Clausius and Gibbs, the German scientist Hermann von Helmholtz stated, in opposition to Berthelot and Thomas' hypothesis that chemical affinity is a measure of the heat of reaction of chemical reaction as based on the principle of maximal work, that affinity is not the heat given out in the formation of a compound but rather it is the largest quantity of work which can be gained when the reaction is carried out in a reversible manner, e.g., electrical work in a reversible cell.
According to chemistry historian Henry Leicester, the influential 1923 textbook Thermodynamics and the Free Energy of Chemical Reactions by Gilbert N. Lewis and Merle Randall led to the replacement of the term "affinity" by the term "free energy" in much of the English-speaking world.