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In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol $G$) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy change , measured in
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force appli ...
s in SI) is the ''maximum'' amount of non-expansion work that can be extracted from a closed system (one that can exchange heat and work with its surroundings, but not matter) at fixed temperature and pressure. This maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state under these conditions, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
forces. The Gibbs energy is the thermodynamic potential that is minimized when a system reaches chemical equilibrium at constant pressure and temperature when not driven by an applied electrolytic voltage. Its derivative with respect to the reaction coordinate of the system then vanishes at the equilibrium point. As such, a reduction in $G$ is necessary for a reaction to be
spontaneous Spontaneous may refer to: * Spontaneous abortion * Spontaneous bacterial peritonitis * Spontaneous combustion * Spontaneous declaration * Spontaneous emission * Spontaneous fission * Spontaneous generation * Spontaneous human combustion * Spontan ...
under these conditions. The concept of Gibbs free energy, originally called ''available energy'', was developed in the 1870s by the American scientist Josiah Willard Gibbs. In 1873, Gibbs described this "available energy" as The initial state of the body, according to Gibbs, is supposed to be such that "the body can be made to pass from it to states of dissipated energy by reversible processes". In his 1876 magnum opus ''
On the Equilibrium of Heterogeneous Substances In the history of thermodynamics, ''On the Equilibrium of Heterogeneous Substances'' is a 300-page paper written by American chemical physicist Willard Gibbs. It is one of the founding papers in thermodynamics, along with German physicist Hermann ...
'', a graphical analysis of multi-phase chemical systems, he engaged his thoughts on chemical-free energy in full. If the reactants and products are all in their thermodynamic
standard state In chemistry, the standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions. A superscript circle ° (degree symbol) or a Plimsoll (⦵) character is use ...
s, then the defining equation is written as , where ''$H$'' is enthalpy, $T$ is absolute temperature, and ''$S$'' is entropy.

# Overview

According to the second law of thermodynamics, for systems reacting at fixed temperature and pressure without input of non-''Pressure Volume'' (PV) work, there is a general natural tendency to achieve a minimum of the Gibbs free energy. A quantitative measure of the favorability of a given reaction under these conditions is the change Δ''G'' (sometimes written "delta ''G''" or "d''G''") in Gibbs free energy that is (or would be) caused by the reaction. As a necessary condition for the reaction to occur at constant temperature and pressure, Δ''G'' must be smaller than the non-pressure-volume (non-''PV'', e.g. electrical) work, which is often equal to zero (then Δ''G'' must be negative). Δ''G'' equals the maximum amount of non-''PV'' work that can be performed as a result of the chemical reaction for the case of a reversible process. If analysis indicates a positive Δ''G'' for a reaction, then energy — in the form of electrical or other non-''PV'' work — would have to be added to the reacting system for Δ''G'' to be smaller than the non-''PV'' work and make it possible for the reaction to occur. One can think of ∆G as the amount of "free" or "useful" energy available to do non-''PV'' work at constant temperature and pressure. The equation can be also seen from the perspective of the system taken together with its surroundings (the rest of the universe). First, one assumes that the given reaction at constant temperature and pressure is the only one that is occurring. Then the entropy released or absorbed by the system equals the entropy that the environment must absorb or release, respectively. The reaction will only be allowed if the total entropy change of the universe is zero or positive. This is reflected in a negative Δ''G'', and the reaction is called an exergonic process. If two chemical reactions are coupled, then an otherwise
endergonic reaction In chemical thermodynamics, an endergonic reaction (; also called a heat absorbing nonspontaneous reaction or an unfavorable reaction) is a chemical reaction in which the standard change in free energy is positive, and an additional driving fo ...
(one with positive Δ''G'') can be made to happen. The input of heat into an inherently endergonic reaction, such as the elimination of
cyclohexanol Cyclohexanol is the organic compound with the formula HOCH(CH2)5. The molecule is related to cyclohexane by replacement of one hydrogen atom by a hydroxyl group. This compound exists as a deliquescent colorless solid with a camphor-like odor, ...
to
cyclohexene Cyclohexene is a hydrocarbon with the formula C6H10. This cycloalkene is a colorless liquid with a sharp smell. It is an intermediate in various industrial processes. Cyclohexene is not very stable upon long term storage with exposure to light ...
, can be seen as coupling an unfavourable reaction (elimination) to a favourable one (burning of coal or other provision of heat) such that the total entropy change of the universe is greater than or equal to zero, making the ''total'' Gibbs free energy change of the coupled reactions negative. In traditional use, the term "free" was included in "Gibbs free energy" to mean "available in the form of useful work". The characterization becomes more precise if we add the qualification that it is the energy available for non-pressure-volume work. (An analogous, but slightly different, meaning of "free" applies in conjunction with the Helmholtz free energy, for systems at constant temperature). However, an increasing number of books and journal articles do not include the attachment "free", referring to ''G'' as simply "Gibbs 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 Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
meeting to set unified terminologies for the international scientific community, in which the removal of the adjective "free" was recommended. This standard, however, has not yet been universally adopted. The name "free enthalpy" was also used for ''G'' in the past.

# History

The quantity called "free energy" is a more advanced and accurate replacement for the outdated term ''affinity'', which was used by chemists in the earlier years of physical chemistry to describe the ''force'' that caused chemical reactions. In 1873, Josiah Willard Gibbs published ''A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces'', in which he sketched the principles of his new equation that was 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 composed of part solid, part liquid, and part vapor, and by using a three-dimensional
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
- entropy- internal energy graph, Gibbs was able to determine three states of equilibrium, i.e., "necessarily stable", "neutral", and "unstable", and whether or not changes would ensue. Further, Gibbs stated: 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 Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
of the body... Thereafter, in 1882, the German scientist
Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Associat ...
characterized the affinity as 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. 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 Substances'' by
Gilbert N. Lewis Gilbert Newton Lewis (October 23 or October 25, 1875 – March 23, 1946) was an American physical chemist and a Dean of the College of Chemistry at University of California, Berkeley. Lewis was best known for his discovery of the covalent bond a ...
and
Merle Randall Merle Randall (January 29, 1888 – March 17, 1950) was an American physical chemist famous for his work with Gilbert N. Lewis, over a period of 25 years, in measuring reaction heat of chemical compounds and determining their corresponding free ...
led to the replacement of the term "affinity" by the term "free energy" in much of the English-speaking world.

# Definitions

The Gibbs free energy is defined as $G(p,T) = U + pV - TS,$ which is the same as $G(p,T) = H - TS,$ where: *''U'' is the internal energy (SI unit:
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force appli ...
), * ''p'' is
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
(SI unit:
pascal Pascal, Pascal's or PASCAL may refer to: People and fictional characters * Pascal (given name), including a list of people with the name * Pascal (surname), including a list of people and fictional characters with the name ** Blaise Pascal, Frenc ...
), * ''V'' is
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
(SI unit: m3), * ''T'' is the temperature (SI unit: kelvin), * ''S'' is the entropy (SI unit: joule per kelvin), * ''H'' is the enthalpy (SI unit: joule). The expression for the infinitesimal reversible change in the Gibbs free energy as a function of its "natural variables" ''p'' and ''T'', for an open system, subjected to the operation of external forces (for instance, electrical or magnetic) ''Xi'', which cause the external parameters of the system ''ai'' to change by an amount d''ai'', can be derived as follows from the first law for reversible processes: $\begin T\,\mathrmS &= \mathrmU + p\,\mathrmV - \sum_^k \mu_i \,\mathrmN_i + \sum_^n X_i \,\mathrma_i + \cdots \\ \mathrm(TS) - S\,\mathrmT &= \mathrmU + \mathrm(pV) - V\,\mathrmp - \sum_^k \mu_i \,\mathrmN_i + \sum_^n X_i \,\mathrma_i + \cdots \\ \mathrm(U - TS + pV) &= V\,\mathrmp - S\,\mathrmT + \sum_^k \mu_i \,\mathrmN_i - \sum_^n X_i \,\mathrma_i + \cdots \\ \mathrmG &= V\,\mathrmp - S\,\mathrmT + \sum_^k \mu_i \,\mathrmN_i - \sum_^n X_i \,\mathrma_i + \cdots \end$ where: *''μ''''i'' is the chemical potential of the ''i''-th chemical component. (SI unit: joules per particle or joules per mole) *''N''''i'' is the number of particles (or number of moles) composing the ''i''-th chemical component. This is one form of the Gibbs fundamental equation. In the infinitesimal expression, the term involving the chemical potential accounts for changes in Gibbs free energy resulting from an influx or outflux of particles. In other words, it holds for an open system or for a
closed Closed may refer to: Mathematics * Closure (mathematics), a set, along with operations, for which applying those operations on members always results in a member of the set * Closed set, a set which contains all its limit points * Closed interval, ...
, chemically reacting system where the ''Ni'' are changing. For a closed, non-reacting system, this term may be dropped. Any number of extra terms may be added, depending on the particular system being considered. Aside from mechanical work, a system may, in addition, perform numerous other types of work. For example, in the infinitesimal expression, the contractile work energy associated with a thermodynamic system that is a contractile fiber that shortens by an amount −d''l'' under a force ''f'' would result in a term ''f'' d''l'' being added. If a quantity of charge −d''e'' is acquired by a system at an electrical potential Ψ, the electrical work associated with this is −Ψ d''e'', which would be included in the infinitesimal expression. Other work terms are added on per system requirements. Each quantity in the equations above can be divided by the amount of substance, measured in
moles Moles can refer to: * Moles de Xert, a mountain range in the Baix Maestrat comarca, Valencian Community, Spain *The Moles (Australian band) *The Moles, alter ego of Scottish band Simon Dupree and the Big Sound People * Abraham Moles, French engin ...
, to form ''molar Gibbs free energy''. The Gibbs free energy is one of the most important thermodynamic functions for the characterization of a system. It is a factor in determining outcomes such as the voltage of an electrochemical cell, and the equilibrium constant for a
reversible reaction A reversible reaction is a reaction in which the conversion of reactants to products and the conversion of products to reactants occur simultaneously. : \mathit aA + \mathit bB \mathit cC + \mathit dD A and B can react to form C and D or, in the ...
. In isothermal, isobaric systems, Gibbs free energy can be thought of as a "dynamic" quantity, in that it is a representative measure of the competing effects of the enthalpic and entropic driving forces involved in a thermodynamic process. The temperature dependence of the Gibbs energy for an ideal gas is given by the
Gibbs–Helmholtz equation The Gibbs–Helmholtz equation is a thermodynamic equation used for calculating changes in the Gibbs free energy of a system as a function of temperature. It was originally presented in an 1882 paper entitled " Die Thermodynamik chemischer Vorgan ...
, and its pressure dependence is given by $\frac = \frac + kT\ln \frac.$ or more conveniently as its chemical potential: $\frac = \mu = \mu^\circ + kT\ln \frac.$ In non-ideal systems,
fugacity In chemical thermodynamics, the fugacity of a real gas is an effective partial pressure which replaces the mechanical partial pressure in an accurate computation of the chemical equilibrium constant. It is equal to the pressure of an ideal gas whic ...
comes into play.

# Derivation

The Gibbs free energy total differential with respect to natural variables may be derived by Legendre transforms of the internal energy. :$\mathrmU = T\,\mathrmS - p \,\mathrmV + \sum_i \mu_i \,\mathrm N_i.$ The definition of ''G'' from above is :$G = U + p V - T S$. Taking the total differential, we have :$\mathrmG = \mathrmU + p\,\mathrmV + V\,\mathrmp - T\,\mathrmS - S\,\mathrmT.$ Replacing d''U'' with the result from the first law gives :$\begin \mathrmG &= T\,\mathrmS - p\,\mathrmV + \sum_i \mu_i \,\mathrmN_i + p \,\mathrmV + V\,\mathrmp - T\,\mathrmS - S\,\mathrmT\\ &= V\,\mathrmp - S\,\mathrmT + \sum_i \mu_i \,\mathrm N_i. \end$ The natural variables of ''G'' are then ''p'', ''T'', and .

## Homogeneous systems

Because ''S'', ''V'', and ''N''''i'' are extensive variables, an Euler relation allows easy integration of d''U'': :$U = T S - p V + \sum_i \mu_i N_i.$ Because some of the natural variables of ''G'' are intensive, d''G'' may not be integrated using Euler relations as is the case with internal energy. However, simply substituting the above integrated result for ''U'' into the definition of ''G'' gives a standard expression for ''G'': :$\begin G &= U + p V - TS\\ &= \left\left(T S - p V + \sum_i \mu_i N_i \right\right) + p V - T S\\ &= \sum_i \mu_i N_i. \end$ This result shows that the chemical potential of a substance ''$i$'' is its (partial) mol(ecul)ar Gibbs free energy. It applies to homogeneous, macroscopic systems, but not to all thermodynamic systems.

# Gibbs free energy of reactions

The system under consideration is held at constant temperature and pressure, and is closed (no matter can come in or out). The Gibbs energy of any system is and an infinitesimal change in ''G'', at constant temperature and pressure, yields :$dG=dU+pdV-TdS$. By the first law of thermodynamics, a change in the internal energy ''U'' is given by :$dU=\delta Q+\delta W$ where is energy added as heat, and is energy added as work. The work done on the system may be written as , where is the mechanical work of compression/expansion done on or by the system and is all other forms of work, which may include electrical, magnetic, etc. Then :$dU=\delta Q-pdV+\delta W_x$ and the infinitesimal change in ''G'' is :$dG=\delta Q-TdS+\delta W_x$. The second law of thermodynamics states that for a closed system at constant temperature (in a heat bath), and so it follows that :$dG \le \delta W_x$ Assuming that only mechanical work is done, this simplifies to :$dG \le 0$ This means that for such a system when not in equilibrium, the Gibbs energy will always be decreasing, and in equilibrium, the infinitesimal change ''dG'' will be zero. In particular, this will be true if the system is experiencing any number of internal chemical reactions on its path to equilibrium.

## In electrochemical thermodynamics

When electric charge ''dQ''ele is passed between the electrodes of an electrochemical cell generating an emf $\mathcal$, a electrical work term appears in the expression for the change in Gibbs energy: $dG = -SdT + Vdp + \mathcal dQ_ ,$ where ''S'' is the entropy, ''V'' is the system volume, ''p'' is its pressure and ''T'' is its absolute temperature. The combination ($\mathcal$, ''Qele'') is an example of a conjugate pair of variables. At constant pressure the above equation produces a
Maxwell relation file:Thermodynamic map.svg, 400px, Flow chart showing the paths between the Maxwell relations. P is pressure, T temperature, V volume, S entropy, \alpha coefficient of thermal expansion, \kappa compressibility, C_V heat capacity at constant volu ...
that links the change in open cell voltage with temperature ''T'' (a measurable quantity) to the change in entropy ''S'' when charge is passed isothermally and
isobarically In thermodynamics, an isobaric process is a type of thermodynamic process in which the pressure of the system stays constant: Δ''P'' = 0. The heat transferred to the system does work, but also changes the internal energy (''U'') ...
. The latter is closely related to the reaction entropy of the electrochemical reaction that lends the battery its power. This Maxwell relation is: :$\left\left(\frac\right\right)_ = -\left\left( \frac \right\right)_$ If a mole of ions goes into solution (for example, in a Daniell cell, as discussed below) the charge through the external circuit is :$\Delta Q_ = -n_0 F_0 \, ,$ where ''n''0 is the number of electrons/ion, and ''F''0 is the Faraday constant and the minus sign indicates discharge of the cell. Assuming constant pressure and volume, the thermodynamic properties of the cell are related strictly to the behavior of its emf by :$\Delta H = -n_0 F_0 \left\left( \mathcal - T \frac \right\right) ,$ where Δ''H'' is the enthalpy of reaction. The quantities on the right are all directly measurable.

# Useful identities to derive the Nernst equation

During a reversible electrochemical reaction at constant temperature and pressure, the following equations involving the Gibbs free energy hold: *$\Delta_\text G = \Delta_\text G^\circ + R T \ln Q_\text$ (see chemical equilibrium), *$\Delta_\text G^\circ = -R T \ln K_\text$ (for a system at chemical equilibrium), *$\Delta_\text G = w_\text = -nF\mathcal$ (for a reversible electrochemical process at constant temperature and pressure), *$\Delta_\text G^\circ = -nF\mathcal^\circ$ (definition of $\mathcal^\circ$), and rearranging gives $\begin nF\mathcal^\circ &= RT \ln K_\text, \\ nF\mathcal &= nF\mathcal^\circ - R T \ln Q_\text, \\ \mathcal &= \mathcal^\circ - \frac \ln Q_\text, \end$ which relates the cell potential resulting from the reaction to the equilibrium constant and reaction quotient for that reaction ( Nernst equation), where * , Gibbs free energy change per mole of reaction, * , Gibbs free energy change per mole of reaction for unmixed reactants and products at standard conditions (i.e. 298K, 100kPa, 1M of each reactant and product), * , gas constant, * , absolute temperature, * , natural logarithm, * , reaction quotient (unitless), * , equilibrium constant (unitless), * , electrical work in a reversible process (chemistry sign convention), * , number of
moles Moles can refer to: * Moles de Xert, a mountain range in the Baix Maestrat comarca, Valencian Community, Spain *The Moles (Australian band) *The Moles, alter ego of Scottish band Simon Dupree and the Big Sound People * Abraham Moles, French engin ...
of electrons transferred in the reaction, * , Faraday constant (charge per mole of electrons), * $\mathcal$, cell potential, * $\mathcal^\circ$,
standard cell potential In electrochemistry, standard electrode potential E^\ominus, or E^\ominus_, is a measure of the reducing power of any element or compound. The IUPAC "Gold Book" defines it as: ''"the value of the standard emf (electromotive force) of a cell in wh ...
. Moreover, we also have $\begin K_\text &= e^, \\ \Delta_\text G^\circ &= -RT\left(\ln K_\text\right) = -2.303\,RT\left(\log_ K_\text\right), \end$ which relates the equilibrium constant with Gibbs free energy. This implies that at equilibrium $Q_\text = K_\text$ and $\Delta_\text G = 0.$

# Standard Gibbs energy change of formation

The standard Gibbs free energy of formation of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of that substance from its component elements, in their
standard state In chemistry, the standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions. A superscript circle ° (degree symbol) or a Plimsoll (⦵) character is use ...
s (the most stable form of the element at 25 °C and 100  kPa). Its symbol is Δ''f''''G''˚. All elements in their standard states (diatomic
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
gas,
graphite Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on la ...
, etc.) have standard Gibbs free energy change of formation equal to zero, as there is no change involved. : Δf''G'' = Δ''f''''G''˚ + ''RT'' ln ''Qf'', where ''Qf'' is the reaction quotient. At equilibrium, Δ''f''''G'' = 0, and ''Qf'' = ''K'', so the equation becomes : Δ''f''''G''˚ = −''RT'' ln ''K'', where ''K'' is the equilibrium constant of the formation reaction of the substance from the elements in their standard states.

# Graphical interpretation by Gibbs

Gibbs free energy was originally defined graphically. In 1873, American scientist
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 was instrumental in ...
published his first thermodynamics paper, "Graphical Methods in the Thermodynamics of Fluids", in which Gibbs used the two coordinates of the entropy and volume to represent the state of the body. In his second follow-up paper, "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces", published later that year, Gibbs added in the third coordinate of the energy of the body, defined on three figures. In 1874, Scottish physicist
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and ligh ...
used Gibbs' figures to make a 3D energy-entropy-volume thermodynamic surface of a fictitious water-like substance.James Clerk Maxwell,
Elizabeth Garber Elizabeth Garber (1939–2020) was an American historian of science known for her work on James Clerk Maxwell and the history of physics. She was a professor of history for many years at Stony Brook University. Education and career Elizabeth Anne ...
, Stephen G. Brush, and C. W. Francis Everitt (1995),
Maxwell on heat and statistical mechanics: on "avoiding all personal enquiries" of molecules
', Lehigh University Press, , p. 248.
Thus, in order to understand the concept of Gibbs free energy, it may help to understand its interpretation by Gibbs as section AB on his figure 3, and as Maxwell sculpted that section on his 3D surface figure.

*
Bioenergetics Bioenergetics is a field in biochemistry and cell biology that concerns energy flow through living systems. This is an active area of biological research that includes the study of the transformation of energy in living organisms and the study of ...
* Calphad (CALculation of PHAse Diagrams) * Critical point (thermodynamics) * Electron equivalent * Enthalpy-entropy compensation * Free entropy *
Gibbs–Helmholtz equation The Gibbs–Helmholtz equation is a thermodynamic equation used for calculating changes in the Gibbs free energy of a system as a function of temperature. It was originally presented in an 1882 paper entitled " Die Thermodynamik chemischer Vorgan ...
* Grand potential *
Non-random two-liquid model The non-random two-liquid model (abbreviated NRTL model) is an activity coefficient model that correlates the activity coefficients \gamma_i of a compound with its mole fractions x_i in the liquid phase concerned. It is frequently applied in the f ...
(NRTL model) – Gibbs energy of excess and mixing calculation and activity coefficients * Spinodal – Spinodal Curves (Hessian matrix) * Standard molar entropy * Thermodynamic free energy * UNIQUAC model – Gibbs energy of excess and mixing calculation and activity coefficients