Thermodynamic free energy

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Thermodynamic free energy

In thermodynamics

Thermodynamics

In physics, thermodynamics is the study of the conversion of heat energy into different forms of energy ; different energy conversions into heat energy; and its relation to macroscopic variables such as temperature, pressure, and volume....
, the term thermodynamic free energy refers to the amount of work

Work (thermodynamics)

In thermodynamics, work is the quantity of energy transferred from one system to another without an accompanying transfer of entropy. It is a generalization of the concept of mechanical work in mechanics....
that can be extracted from a system

System

System is a set of interacting or interdependent entities, real or abstract, forming an integrated whole.The concept of an "integrated whole" can also be stated in terms of a system embodying a set of relationships which are differentiated from relationships of the set to other elements, and from relationships between an element of the se...
, and is helpful in engineering

Engineering

Engineering is the discipline and profession of applying Technology and science knowledge and utilizing natural laws and physical resources in order to design and implement materials, structures, machines, devices, systems, and process that safely realize a desired objective and meet specified criteria....
applications. It is a subtraction of the entropy

Entropy

In many branches of science, entropy is a measure of the disorder of a system. The concept of entropy is particularly notable as it is applied across physics, information theory and mathematics....
of a system multiplied by a reference temperature (giving the "unusable energy") from the total energy, yielding a thermodynamic

Thermodynamics

State function

In thermodynamics, a state function, state quantity, or a function of state, is a physical quantity of a system that depends only on the current Thermodynamic state, not on the way in which the system got to that state....
which represents the "useful energy

Exergy

In thermodynamics, the exergy of a System is the maximum Mechanical work possible during a Thermodynamic process that brings the system into Thermodynamic equilibrium with a heat reservoir....
".

hort, free energy is that portion of any First-Law

First law of thermodynamics

In thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the conservation of energy. Succinctly, the first law of thermodynamics states:...
energy that is available for doing thermodynamic work

Work (thermodynamics)

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Encyclopedia

In thermodynamics

Thermodynamics

Work (thermodynamics)

System

Engineering

Entropy

Thermodynamics

State function

Exergy

In thermodynamics, the exergy of a System is the maximum Mechanical work possible during a Thermodynamic process that brings the system into Thermodynamic equilibrium with a heat reservoir....
".

Overview

In short, free energy is that portion of any First-Law

First law of thermodynamics

Work (thermodynamics)

Irréversible

Irr?versible is a film screenwriter, film director, film editor, and cinematographer by Gaspar No?. It stars Monica Bellucci and Vincent Cassel....
loss in the course of such work and First-Law energy is always conserved, it is evident that free energy is an expendable, Second-Law

Second law of thermodynamics

The second law of thermodynamics is an expression of the universal law of increasing entropy, stating that the entropy of an isolated system which is not in Thermodynamic equilibrium will tend to increase over time, approaching a maximum value at equilibrium....
kind of energy that can make things happen within finite amounts of time.

The free energy functions

Function (mathematics)

The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. A function associates a single output to each input element drawn from a fixed Set , such as the real numbers , although different inputs may have the same output....
are Legendre transforms

Legendre transformation

In mathematics, it is often desirable to express a functional relationship as a different function, whose argument is the derivative of f , rather than x ....
of the internal energy

Internal energy

In thermodynamics, the internal energy of a thermodynamic system, or a physical body with well-defined dimension, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules and the potential energy associated with the vibrational and electricity energy of atoms within molecules or crysta...
. For processes involving a system at constant pressure

Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
p and temperature

Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
T, the Gibbs free energy

Gibbs free energy

In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating Work obtainable from an isothermal, Isobaric process thermodynamic system....
is the most useful because, in addition to subsuming any entropy change due merely to heat flux

Flux

In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.*In the study of transport phenomena , flux is defined as the amount that flows through a unit area per unit time....
, it does the same for the pdV work needed to "make space for additional molecules" produced by various processes. (Hence its utility to solution

Solution

In chemistry, a solution is a homogeneous mixture composed of two or more substances. In such a mixture, a solute is dissolved in another substance, known as a solvent....
-phase

Phase (matter)

In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, refractive index, and chemical composition....
chemists, including biochemists.) The Helmholtz free energy

Helmholtz free energy

In thermodynamics, the Helmholtz free energy is a thermodynamic potential which measures the ?useful? work obtainable from a closed system thermodynamic thermodynamic system at a constant temperature and volume....
has a special theoretical

Theory

For a more detailed account of theories as expressed in formal language as they are studied in mathematical logic see Theory A theory, in the general sense of the word, is an analytic structure designed to explain a set of observations....
importance since it is proportional to the logarithm

Logarithm

In mathematics, the logarithm of a number to a given base is the Power or exponent to which the base must be raised in order to produce the number....
of the partition function

Partition function (statistical mechanics)

In statistical mechanics, the partition function Z is an important quantity that encodes the statistics properties of a system in thermodynamic equilibrium....
for the canonical ensemble

Canonical ensemble

A canonical ensemble in statistical mechanics is a statistical ensemble representing a probability distribution of microscopic states of the system....
in statistical mechanics

Statistical mechanics

Statistical mechanics is the application of probability theory, which includes Mathematics tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force....
. (Hence its utility to physicists

Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
; and to gas

Gas

In physics, a gas is a state of matter, consisting of a collection of particles without a definite shape or volume that are in more or less random motion....
-phase chemists and engineers, who do not want to ignore pdV work.)

The (historically earlier) Helmholtz free energy

Helmholtz free energy

Thermodynamic temperature

Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is an ?absolute? scale because it is the measure of the fundamental property underlying temperature: its null or zero point, absolute zero, is the temperature at which the particle constitue...
, and S is the entropy

Entropy

Reversible process (thermodynamics)

In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy....
work done on, or obtainable from, a system at constant T. Thus its appellation "work content

Work content

In thermodynamic analysis of chemical reactions, the term free energy denotes either of two related concepts of importance expressing the total amount of energy which is used up or released during a chemical reaction....
", 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, and it can increase at most by the amount of work done on a system.

The Gibbs free energy

Gibbs free energy

Enthalpy

In thermodynamics and chemistry, the enthalpy is a quotient or description of thermodynamic potential of a system, which can be used to calculate the heat transfer during a quasistatic process taking place in a closed system thermodynamic system under constant pressure....
. (H = U + pV, where p is the pressure and V is the volume.)

There has been historical controversy:

In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, “free energy” most often refers to the Helmholtz free energy
Helmholtz free energy

In thermodynamics, the Helmholtz free energy is a thermodynamic potential which measures the ?useful? work obtainable from a closed system thermodynamic thermodynamic system at a constant temperature and volume....
, denoted by F.
In chemistry
Chemistry

Chemistry is the science concerned with the composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions....
, “free energy” most often refers to the Gibbs free energy
Gibbs free energy

In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating Work obtainable from an isothermal, Isobaric process thermodynamic system....
.

Since both fields use both functions, a compromise

Compromise

In arguments, compromise is a concept of finding agreement through communication, through a mutual acceptance of terms?often involving variations from an original Objective or desire....
has been suggested, using A to denote the Helmholtz function, with 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.

Application

The experiment

Experiment

In scientific inquiry, an experiment is a method of investigating causal relationships among variables. An experiment is a cornerstone of the empiricism approach to acquiring data about the world and is used in both natural sciences and social sciences....
al 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 Maxwell relations

Maxwell relations

Maxwell's relations are a set of equations in thermodynamics which are derivable from the definitions of the thermodynamic potentials. The Maxwell relations are statements of equality among the second derivatives of the thermodynamic potentials....
. Work other than pdV may be added, e.g., for electrochemical

Electrochemistry

Electrochemistry is a branch of chemistry that studies chemical reactions which take place in a solution at the interface of an electron Electrical conductor and an ionic conductor , and which involve electron transfer between the electrode and the electrolyte or species in solution....
cells, or f ?dx work in elastic

Elastomer

An elastomer is a polymer with the property of elasticity. The term, which is derived from elastic polymer, is often used interchangeably with the term rubber, and is preferred when referring to vulcanization....
materials and in muscle

MUSCLE

MUSCLE is public domain, multiple sequence alignment software for protein and nucleotide sequences.MUSCLE is integrated into UGENE bioinformatics tool as a plugin....
contraction. Other forms of work which must sometimes be considered are stress

Stress (physics)

In continuum mechanics, stress is a measure of the average amount of force exerted per unit area. It is a measure of the intensity of the total internal forces acting within a body across imaginary internal surfaces, as a reaction to external applied forces and body forces....
-strain

Strain (materials science)

In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal Deformation s of a Continuum mechanics....
, magnetic

Magnetism

In physics, magnetism is one of the phenomena by which materials exert attractive or repulsive forces on other materials. Some well-known materials that exhibit easily detectable magnetic properties are nickel, iron, cobalt, and their alloys; however, all materials are influenced to greater or lesser degree by the presence of a magnetic fiel...
, as in adiabatic

Adiabatic process

In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid....
demagnetization

Magnetization

Magnetization is defined as the quantity of magnetic moment per unit volume. The origin of the magnetic moments responsible for magnetization can be either microscopic electric currents resulting from the motion of electrons in atoms, or the spin of the electrons or the nuclei....
used in the approach to absolute zero

Absolute zero

Absolute zero is a temperature marked by a 0 entropy configuration. It is the coldest temperature theoretically possible, and cannot be reached, by artificial or natural means....
, and work due to electric polarization

Dipole

In physics, there are two kinds of dipoles :*An electric dipole is a separation of positive and negative charge. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some, usually small, distance....
. These are described by tensor

Tensor

A tensor is an object which extends the notion of Scalar , Vector , and Matrix . The term has slightly different meanings in mathematics and physics....
s.

In most cases of interest there are internal degrees of freedom

Degrees of freedom (physics and chemistry)

Degrees of freedom is a general term used in explaining dependence on parameters, and implying the possibility of counting the number of those parameters....
and processes, such as chemical reaction

Chemical reaction

A chemical reaction is a process that always results in the interconversion of chemical substances. The substance or substances initially involved in a chemical reaction are called reactants....
s and phase transition

Phase transition

In thermodynamics, a phase transition is the transformation of a thermodynamic system from one phase to another.At phase-transition point, physical properties may undergo abrupt change- for instance, volume of the two phases may be vastly different....
s, which create entropy. Even for homogeneous "bulk" materials, the free energy functions depend on the (often suppressed) composition

Chemical compound

A chemical compound is a Chemical substance consisting of two or more different chemical element Chemical bond together in a fixed mass ratio that can be split into simpler substances....
, as do all proper thermodynamic potentials

Thermodynamic potentials

A thermodynamic potential is a scalar potential function used to represent the thermodynamic state of a physical system. One main thermodynamic potential which has a physical interpretation is the internal energy, U....
(extensive functions), including the internal energy.

N_i is the number of molecules (alternatively, moles

Mole (unit)

The mole is a Units of measurement of amount of substance: it is an SI base unit, and one of the few units used to measure this physical quantity....
) of type i in the system. If these quantities do not appear, it is impossible to describe compositional changes. The differential

Differential (mathematics)

In mathematics, and more specifically, in differential calculus, the term differential has several interrelated meanings....
s for reversible processes

Reversible process (thermodynamics)

In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy....
are (assuming only pV work)

where µ_i is the chemical potential

Chemical potential

In thermodynamics, physics and chemistry, chemical potential, symbolized by ?, is a term introduced by the American engineer, chemist and mathematical physicist Willard Gibbs, which he defined as follows:...
for the i-th component

Component (thermodynamics)

In thermodynamics, a component is a chemically distinct constituent ofa system. Calculating the number of components in a system is necessary, for example, when applying Gibbs phase rule in determination of the number of degrees of freedom of a system....
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

Life

Life is a characteristic of organisms that exhibit certain biological processes such as chemical reactions or other events that results in a transformation....
creatures.

Any decrease in the Gibbs function of a system is the upper limit for any isothermal

Isothermal process

An isothermal process is a thermodynamic process in which the temperature of the system stays constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir , and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange....
, isobaric

Isobaric process

An isobaric process is a thermodynamic process in which the pressure stays constant: The term derives from the Greek isos, "equal," and barus, "heavy." The heat transferred to the system does work but also changes the internal energy of the system:...
work that can be captured in the surroundings

Surroundings

Surroundings are the area around a given physical or geographical Point or place. The exact definition depends on the field. Surroundings can also be used in geography and mathematics, as well as philosophy, with the literal or metaphorically extended definition....
, or it may simply be dissipated

Dissipation

In physics, dissipation embodies the concept of a dynamical system where important mechanical modes, such as waves or oscillations, lose energy over time, typically due to the action of friction or turbulence....
, appearing as T times a corresponding increase in the entropy of the system and/or its surrounding.

Thermodynamic free energy

Overview

Application

See also