What is the free energy and from where come the power ?
hermodynamic free energy
From Wikipedia, the free encyclopedia
The thermodynamic free energy is the amount of work that a thermodynamic system can perform.
The concept is useful in thethermodynamics of chemical or thermal processes in engineering and
science. The free energy is the internal energy of a system less the amount of energy that cannot
be used to perform work. This unusable energy is given by the entropy of a system multiplied by
the temperature of the system. Like the internal energy, the free energy is a thermodynamic state
Free energy is that portion of any first-law energy that is available to perform thermodynamic
course of such work.[1] Since first-law energy is always conserved, it is evident that free energy
is an expendable, second-law kind of energy that can perform work within finite amounts of time.
Several free energy functions may be formulated based on system criteria. Free energy functions
subsuming any entropy change due merely to heat, it does the same for the pdV work needed
to "make space for additional molecules" produced by various processes. (Hence its utility to
chemists and engineers, who do not want to ignore pdV work.)
The historically earlier Helmholtz free energy is defined as A = U − TS, where U is the internal
energy, T is the absolute temperature, and S is the entropy. Its change is equal to the amount of
reversible work done on, or obtainable from, a system at constant T. Thus its appellation "work
content", and the designation A from Arbeit, the German word for work. Since it makes no reference
to any quantities involved in work (such as p and V), the Helmholtz function is completely general :
its decrease is the maximum amount of work which can be doneby a system, and it can increase at
The Gibbs free energy G = H − TS, where H is the enthalpy. (H = U + pV, where p is the pressure and V is the volume.)
most by the amount of work done on a system.
Historically, these energy terms have been used inconsistently. In physics, free energy most often
refers to the Helmholtz free energy, denoted by F, while in chemistry, free energymost often refers to
Since both fields use both functions, a compromise has been suggested, using A to denote the Helmholtz function and G for the Gibbs function. While A is preferred by IUPAC, F is sometimes still in
use, and the correct free energy function is often implicit in manuscripts and presentations.
the Gibbs free energy.
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.[2] 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 compression of a gas, the
absolute heat remained constant by the observed rise of temperature, indicating 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 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 E − TS, in which the change in F (or G) determines
Thus, in traditional use, the term “free” was attached to Gibbs free energy, i.e., for systems at constant
pressure and temperature, or to Helmholtz free energy, i.e., for systems at constant volume and
temperature, to mean ‘available in the form of useful work.’[4] With reference to the Gibbs free energy,
we add the qualification that it is the energy free for non-volume work.[5]
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 energy). 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.[6] This standard, however, has not yet been universally adopted,
and many published articles and books still include the descriptive ‘free’.[citation needed]
[edit]
The experimental usefulness of these functions is restricted to conditions where certain variables
(T, and V or external p) are held constant, although they also have theoretical importance in deriving
In most cases of interest there are internal degrees of freedom and processes, such as chemical
reactions and phase transitions, which create entropy. Even for homogeneous "bulk" materials, the free
energy functions depend on the (often suppressed) composition, as do all proper thermodynamic
potentials (extensive functions), including the internal energy.
| Name | Symbol | Formula | Natural variables |
|---|---|---|---|
| Helmholtz free energy | F, A | U − TS | T,V,{Ni} |
| Gibbs free energy | G | U + pV − TS | T,p,{Ni} |
Ni is the number of molecules (alternatively, moles) of type i in the system. If these quantities do not
appear, it is impossible to describe compositional changes. The differentials forreversible processes are
(assuming only pV work)
where μi is the chemical potential for the i-th component in the system. The second relation is
especially useful at constant T and p, conditions which are easy to achieve experimentally, and which
approximately characterize living creatures.
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 asT times a
corresponding increase in the entropy of the system and/or its surrounding.
An example is surface free energy, the amount of increase of free energy when the area of surface
increases by every unit area.
The path integral Monte Carlo method is a numerical approach for determining the values of free
energies, based on quantum dynamical principles.
[edit]
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
From the 1998 textbook Modern Thermodynamics[7] by Nobel Laureate and chemistry professor Ilya rigogine we find: "As motion was explained by the Newtonian concept of force, chemists wanted a similar concept of ‘driving force’ for chemical change. Why do chemical reactions occur, and why do
they stop at certain points? Chemists called the ‘force’ that caused chemical reactions affinity, but it
lacked a clear definition."
Magnus in 1250.
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
In the 19th century, the French chemist Marcellin Berthelot and the Danish chemist Julius Thomsen
had attempted to quantify affinity using heats of reaction. 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
In addition to this, in 1780 Antoine Lavoisier and Pierre-Simon Laplace laid the foundations of
thermochemistry by showing that the heat given out in a reaction is equal to the heat absorbed in
the reverse reaction. They also investigated the specific heat and latent heat of a number of
substances, and amounts of heat given out in combustion. In a similar manner, in 1840 Swiss chemist
Germain Hess formulated the principle that the evolution of heat in a reaction is the same whether
the process is accomplished in one-step process or in a number of stages. This is known as Hess' law.
With the advent of the mechanical theory of heat in the early 19th century, Hess’s law came to be
viewed as a consequence of the law of conservation of energy.
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. This view, however, was not entirely correct. In 1847, the English physicist James Joule showed
that he could raise the temperature of water by turning a paddle wheel in it, thus showing that heat and
mechanical work were equivalent or proportional to each other, i.e., approximately, 
.
.
This statement came to be known as themechanical equivalent of heat and was a precursory form of
By 1865, the German physicist Rudolf Clausius had shown that this equivalence principle needed
amendment. That is, one can use the heat derived from a combustion reaction in a coal furnace to
boil water, and use this heat to vaporize steam, and then use the enhanced high-pressure energy
of the vaporized steam to push a piston. 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. Clausius
showed, however, that we must take into account the work that the molecules of the working body,
i.e., the water molecules in the cylinder, do on each other as they pass or transform from one step of or
state of the engine cycle to the next, e.g., from (P1,V1) to (P2,V2). Clausius originally called this the
“transformation content” of the body, and then later changed the name to entropy. Thus, the heat used
to transform the working body of molecules from one state to the next cannot be used to do external
work, e.g., to push the piston. Clausius defined this transformation heat as dQ = TdS.
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. By studying the interactions
of homogeneous substances in contact, i.e., bodies, being in composition part solid,
Gibbs was able to determine three states of equilibrium, i.e., "necessarily stable", "neutral", and
"unstable", and whether or not changes will ensue. In 1876, Gibbs built on this framework by
introducing the concept of chemical potential so to take into account chemical reactions and states
of bodies that are chemically different from each other. In his own words, to summarize his results in
1873, Gibbs states:
pressure p and temperature T, this equation may be written :
δ(ε − Tη + pν) = 0
when δ refers to the variation produced by any variations in the state of
is divided between the different states. The condition of stable equilibrium
is that the value of
Hence, in 1882, after the introduction of these arguments by Clausius and Gibbs, the German
In this description, as used by Gibbs, ε refers to the internal energy of the body, η refers to the entropy
of the body, and ν is the volume of the body.
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. The maximum work is thus regarded as
the diminution of the free, or available, energy of the system (Gibbs free energy G at T = constant,
P = constant or Helmholtz free energy F at T = constant, V = constant), whilst the heat given out is
usually a measure of the diminution of the total energy of the system (Internal energy). Thus, G or F is
the amount of energy “free” for work under the given conditions.
Up until this point, the general view had been such that: “all chemical reactions drive the system to a
state of equilibrium in which the affinities of the reactions vanish”. Over the next 60 years, the term
affinity came to be replaced with the term free energy. 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.
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