TheInfoList

The thermodynamic free energy is a concept useful in the
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

of chemical or thermal processes in
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...

and science. The change in the free energy is the maximum amount of
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...
that a
thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, whic ...
can perform in a process at constant temperature, and its sign indicates whether a process is thermodynamically favorable or forbidden. Since free energy usually contains
potential energy In physics, potential energy is the energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, but not created or destroyed. The unit of measure ...

, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful. The free energy is a thermodynamic
state function In the thermodynamics of equilibrium, a state function, function of state, or point function is a function defined for a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form ...
, like the
internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that ca ...
,
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant p ...

, and
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

. Free energy is that portion of any first-law energy that is available to perform thermodynamic
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...
at constant
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ...

, ''i.e.'', work mediated by
thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concepts, such as the internal energy of a system; heat or sensible heat, which are defined as types of energy transfer (as is ...
. Free energy is subject to irreversible loss in the course of such work. Since first-law energy is always conserved, it is evident that free energy is an expendable, second-law kind of energy. Several free energy functions may be formulated based on system criteria. Free energy
functions Function or functionality may refer to: Computing * Function key A function key is a key on a computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations automatically. Modern comp ...
are Legendre transforms of the
internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that ca ...
. The
Gibbs free energy In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qua ...
is given by , where ''H'' is the
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant p ...

, ''T'' is the
absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of ...

, and ''S'' is the
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

. , where ''U'' is the internal energy, ''p'' is the
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

, and ''V'' is the volume. ''G'' is the most useful for
processes A process is a series or set of Action (philosophy), activities that interact to produce a result; it may occur once-only or be recurrent or periodic. Things called a process include: Business and management *Business process, activities that pro ...
involving a system at
constant Constant or The Constant may refer to: Mathematics * Constant (mathematics) In mathematics, the word constant can have multiple meanings. As an adjective, it refers to non-variance (i.e. unchanging with respect to some other Value (mathematics ...
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

''p'' and
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ...

''T'', because, in addition to subsuming any entropy change due merely to
heat In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these ...

, a change in ''G'' also excludes the 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 Solution may refer to: * Solution (chemistry) Image:SaltInWaterSolutionLiquid.jpg, upMaking a saline water solution by dissolving Salt, table salt (sodium chloride, NaCl) in water. The salt is the solute and the water the solvent. In chemistry ...
-
phase Phase or phases may refer to: Science * State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter) In the physical sciences, a phase is a region of space (a thermodynamic system A thermodynamic system is a ...
chemists, including biochemists.) The historically earlier
Helmholtz free energy In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quan ...
is defined as . 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 done ''by'' a system at constant temperature, and it can increase at most by the amount of work done ''on'' a system isothermally. The Helmholtz free energy has a special
theoretical A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, G ...

importance since it is proportional to the
logarithm In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no ...

of the partition function for the
canonical ensemble In statistical mechanics In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, i ...
in
statistical mechanics In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
. (Hence its utility to
physicist A physicist is a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical method of acquiring knowledge that has characterized the development of science since at leas ...

s; and to
gas Gas is one of the four fundamental states of matter In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space ...

-phase chemists and engineers, who do not want to ignore work.) Historically, the term 'free energy' has been used for either quantity. In
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scie ...

, ''free energy'' most often refers to the Helmholtz free energy, denoted by ''A'' (or ''F''), while in
chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in the real world. T ...

, ''free energy'' most often refers to the Gibbs free energy. The values of the two free energies are usually quite similar and the intended free energy function is often implicit in manuscripts and presentations.

# 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 meters 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 (). 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 utilisation. 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 in order 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 $T$ and the change in entropy $S$ of a body (entropy is a measure of disorder in a system). The difference between the change in internal energy, which is $\Delta U$, 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: free energy $A=U-TS$ This expression has commonly been interpreted to mean that work is extracted from the internal energy $U$ while $TS$ 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 $\Delta U=0$ and the expansion work $w=-T\Delta S$ is derived exclusively from the $TS$ term supposedly not available to perform work. But it is noteworthy that the derivative form of the free energy: $dA=-SdT-PdV$ (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) $-PdV$ and the unavailable energy $-SdT$. Similar expression can be written for the Gibbs free energy change. In the 18th and 19th centuries, the
theory of heat The history of thermodynamics is a fundamental strand in the history of physics, the history of chemistry, and the history of science in general. Owing to the relevance of thermodynamics in much of science and technology, its history is finely wov ...
, i.e., that heat is a form of energy having relation to vibratory motion, was beginning to supplant both the
caloric theory The caloric theory is an obsolete scientific theory In Science#History, science, a theory is superseded when a scientific consensus once widely accepted it, but current science considers it inadequate, incomplete, or debunked (i.e., wrong). Such ...
, 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 In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these ...

was beginning to be distinguished into different classification categories, such as “free heat”, “combined heat”, “radiant heat”,
specific heat In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quant ...
,
heat capacity Heat capacity or thermal capacity is a physical property A physical property is any property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on t ...
, “absolute heat”, “latent caloric”, “free” or “perceptible” caloric (''calorique sensible''), among others. In 1780, for example,
Laplace Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath A polymath ( el, πολυμαθής, ', "having learned much"; Latin Latin (, or , ) is a classical language belonging to the I ...

and
Lavoisier Antoine-Laurent de Lavoisier ( , ,; 26 August 17438 May 1794), When reduced without charcoal, it gave off an air which supported respiration and combustion in an enhanced way. He concluded that this was just a pure form of common air and th ...

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 ''Vis viva'' (from the Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the ...
, 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. 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
compression Compression may refer to: Physical science *Compression (physics), size reduction due to forces *Compression member, a structural element such as a column *Compressibility, susceptibility to compression *Gas compression *Compression ratio, of a co ...
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 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 Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branch ...

coined the phrase ‘free energy’ for the expression , in which the change in ''A'' (or ''G'') determines the amount of
energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ...

‘free’ for
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...
under the given conditions, specifically constant temperature. 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.’ 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. 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 The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering OrganizationsNational Adhering Organizations in chemistry are the organizations that work as the authoritative power over chemist ...
meeting to set unified terminologies for the international scientific community, in which the adjective ‘free’ was supposedly banished. This standard, however, has not yet been universally adopted, and many published articles and books still include the descriptive ‘free’.

# Application

Just like the general concept of energy, free energy has a few definitions suitable for different conditions. In physics, chemistry, and biology, these conditions are thermodynamic parameters (temperature $T$, volume $V$, pressure $p$, etc.). Scientists have come up with several ways to define free energy. The mathematical expression of Helmholtz free energy is: :$A = U-TS$ This definition of free energy is useful for gas-phase reactions or in physics when modeling the behavior of isolated systems kept at a constant volume. For example, if a researcher wanted to perform a combustion reaction in a bomb calorimeter, the volume is kept constant throughout the course of a reaction. Therefore, the heat of the reaction is a direct measure of the free energy change, $q=\Delta U$. In solution chemistry, on the other hand, most chemical reactions are kept at constant pressure. Under this condition, the heat $q$ of the reaction is equal to the enthalpy change $\Delta H$ of the system. Under constant pressure and temperature, the free energy in a reaction is known as Gibbs free energy $G$. :$G = H-TS$ These functions have a minimum in chemical equilibrium, as long as certain variables ($T$, and $V$ or $p$) are held constant. In addition, they also have theoretical importance in deriving Maxwell relations. Work other than may be added, e.g., for
electrochemical Electrochemistry is the branch of physical chemistry Physical chemistry is the study of macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying ...

cells, or work in elastic materials and in
muscle Skeletal muscles (commonly referred to as muscles) are organs An organ is a group of tissues with similar functions. Plant life and animal life rely on many organs that co-exist in organ systems. A given organ's tissues can be broadly cat ...

contraction. Other forms of work which must sometimes be considered are stress- strain,
magnetic Magnetism is a class of physical attributes that are mediated by magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For in ...

, as in de
magnetization In classical electromagnetism Classical electromagnetism or classical electrodynamics is a branch of theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and s ...
used in the approach to
absolute zero Absolute zero is the lowest limit of the thermodynamic temperature Thermodynamic temperature is the measure of ''absolute temperature'' and is one of the principal parameters of thermodynamics. A thermodynamic temperature reading of zero deno ...
, and work due to electric
polarization Polarization or polarisation may refer to: In the physical sciences *Polarization (waves), the ability of waves to oscillate in more than one direction, in particular polarization of light, responsible for example for the glare-reducing effect of ...

. These are described by
tensor In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...

s. In most cases of interest there are internal
degrees of freedom Degrees of Freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or other physical ...
and processes, such as
chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and t ...

s and
phase transition In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in ...
s, which create entropy. Even for homogeneous "bulk" materials, the free energy functions depend on the (often suppressed)
composition Composition or Compositions may refer to: Arts * Composition (dance), practice and teaching of choreography * Composition (music), an original piece of music and its creation *Composition (visual arts) The term composition means "putting togethe ...
, as do all proper
thermodynamic potentials A thermodynamic potential (or more accurately, a thermodynamic potential energy)ISO/IEC 80000-5, Quantities an units, Part 5 - Thermodynamics, item 5-20.4 Helmholtz energy, Helmholtz functionISO/IEC 80000-5, Quantities an units, Part 5 - Thermodyna ...

( extensive functions), including the internal energy. $N_i$ 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 for processes at uniform pressure and temperature are (assuming only $pV$ work): :$\mathrm dA = - p\,\mathrm dV - S\,\mathrm dT + \sum_i \mu_i \,\mathrm dN_i\,$ :$\mathrm dG = V\,\mathrm dp - S\,\mathrm dT + \sum_i \mu_i \,\mathrm dN_i\,$ where ''μ''''i'' is the
chemical potential In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is governed ...

for the ''i''th
component Component may refer to: In engineering, science, and technology Generic systems *System components, an entity with discrete structure, such as an assembly or software module, within a system considered at a particular level of analysis *Lumped ele ...
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 Living or The Living may refer to: Common meanings *Life, a condition that distinguishes organisms from inorganic objects and dead organisms ** extant taxon, Living species, one that is not extinct *Personal life, the course of an individual human ...

creatures. Under these conditions, it simplifies to :$\left(\mathrm dG\right)_ = \sum_i \mu_i \,\mathrm dN_i\,$ Any decrease in the Gibbs function of a system is the upper limit for any
isothermal In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature ''T'' of a Thermodynamic system, system remains constant: Δ''T'' = 0. This typically occurs when a system is in contact with an outside the ...

, work that can be captured in the surroundings, or it may simply be dissipated, appearing as $T$ 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.

## Work and free energy change

For a reversible isothermal process, Δ''S'' = ''q''rev/''T'' and therefore the definition of ''A'' results in : $\Delta A = \Delta U - T \Delta S = \Delta U - q_\text = w_\text$ (at constant temperature) This tells us that the change in free energy equals the reversible or maximum work for a process performed at constant temperature. Under other conditions, free-energy change is not equal to work; for instance, for a reversible adiabatic expansion of an ideal gas, Importantly, for a heat engine, including the , the free-energy change after a full cycle is zero, while the engine produces nonzero work. 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.

## Free energy change and spontaneous processes

According to the
second law of thermodynamics The second law of thermodynamics establishes the concept of entropy Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term an ...
, for any process that occurs in a closed system, the inequality of Clausius, Δ''S'' > ''q''/''T''surr, applies. For a process at constant temperature and pressure without non-''PV'' work, this inequality transforms into $\Delta G < 0$. Similarly, for a process at constant temperature and volume, $\Delta A < 0$. 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. In chemical equilibrium at constant ''T'' and ''p'' without electrical work, d''G'' = 0.

# History

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 reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and t ...

s. The term affinity, as used in chemical relation, dates back to at least the time of
Albertus Magnus Albertus Magnus (c. 1200 – November 15, 1280), also known as Saint Albert the Great or Albert of Cologne, was a German German(s) may refer to: Common uses * of or related to Germany * Germans, Germanic ethnic group, citizens of Germany ...

. From the 1998 textbook ''Modern Thermodynamics'' Chapter 4, Section 1, Paragraph 2 (page 103) by Nobel Laureate and chemistry professor
Ilya Prigogine Viscount Ilya Romanovich Prigogine (; russian: Илья́ Рома́нович Приго́жин; 28 May 2003) was a physical chemist and Nobel laureate noted for his work on dissipative structures, complex systems, and irreversibility. B ...
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." During the entire 18th century, the dominant view with regard to heat and light was that put forth by
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

, 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 the 19th century, the French chemist
Marcellin Berthelot Pierre Eugène Marcellin Berthelot (; 1827–1907) was a French chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist A scientist is a person who conducts Scientific m ...

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 thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these ...

. In addition to this, in 1780
Antoine Lavoisier Antoine-Laurent de Lavoisier ( , ,; 26 August 17438 May 1794), When reduced without charcoal, it gave off an air which supported respiration and combustion in an enhanced way. He concluded that this was just a pure form of common air and t ...

and
Pierre-Simon Laplace Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar A scholar is a person who pursues academic and intellectual activities, particularly those that develop expertise in an area of Studying, study. A ...

laid the foundations of
thermochemistry Thermochemistry is the study of the heat energy which is associated with chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter ...
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 In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quant ...
and
latent heat Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any su ...
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' lawImage:Hess cycle.svg, A representation of Hess' law (where H represents enthalpy) Hess's law of constant heat summation, also known as Hess' law, is a relationship in physical chemistry named after Germain Henri Hess, Germain Hess, a Switzerland, Sw ...
. 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 In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
. 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 James Prescott Joule (; 24 December 1818 11 October 1889) was an English physicist A physicist is a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical m ...

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 the
mechanical equivalent of heat In the history of science The history of science is the study of the development of science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), ...
and was a precursory form of the
first law of thermodynamics The first law of thermodynamics is a version of the law of conservation of energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department o ...
. By 1865, the German physicist
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German German(s) may refer to: Common uses * of or related to Germany * Germans, Germanic ethnic group, citizens of Germany or people of German ancestry * For citize ...
had shown that this equivalence principle needed amendment. That is, one can use the heat derived from a
combustion reaction Combustion, or burning, is a high-temperature exothermic redox chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical A chemical s ...
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 State may refer to: Arts, entertainment, and media Literature * ''State Magazine'', a monthly magazine published by the U.S. Department of State * The State (newspaper), ''The State'' (newspaper), a daily newspaper in Columbia, South Carolina, Un ...
of the engine cycle to the next, e.g., from ($P_1,V_1$) to ($P_2,V_2$). Clausius originally called this the “transformation content” of the body, and then later changed the name to
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

. 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 Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics Thermodynamics is ...

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, part liquid, and part vapor, and by using a three-dimensional
volume Volume is a scalar quantity expressing the amount Quantity or amount is a property that can exist as a multitude Multitude is a term for a group of people who cannot be classed under any other distinct category, except for their shared fact ...
-
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

-
internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that ca ...
graph, 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 In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is governed ...

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: In this description, as used by Gibbs, ''ε'' refers to the
internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that ca ...
of the body, ''η'' refers to the
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

of the body, and ''ν'' is the
volume Volume is a scalar quantity expressing the amount Quantity or amount is a property that can exist as a multitude Multitude is a term for a group of people who cannot be classed under any other distinct category, except for their shared fact ...
of the body. Hence, in 1882, after the introduction of these arguments by Clausius and Gibbs, the German scientist
Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branch ...

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 In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qua ...
''G'' at ''T'' = constant, ''P'' = constant or
Helmholtz free energy In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quan ...
''A'' 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 The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that ca ...
). Thus, ''G'' or ''A'' 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 RandallMerle Randall (January 29, 1888 – March 17, 1950) was an American physical chemist Physical chemistry is the study of macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the ...
led to the replacement of the term “affinity” by the term “free energy” in much of the English-speaking world.

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Exergy In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qua ...
*
Second law of thermodynamics The second law of thermodynamics establishes the concept of entropy Entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term an ...
*
Superconductivity Superconductivity is a set of physical properties observed in certain materials where electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current An electric current is a st ...

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Merle RandallMerle Randall (January 29, 1888 – March 17, 1950) was an American physical chemist Physical chemistry is the study of macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the ...

# References

{{DEFAULTSORT:Thermodynamic Free Energy Energy (physics) State functions