For other uses of this term, see Free energy (disambiguation).

The free energy is a measure of the amount of mechanical (or other) work that can be extracted from a system, and is helpful in engineering applications. It is a linear combination of the energy and the entropy of a system, yielding a thermodynamic state function which represents the "useful energy". It uses a mathematical "trick" to produce a function which automatically accommodates any entropy change due to heat exchanged with the surroundings. In short, free energy is that portion of any First-Law energy that is available for doing work. In other words, it is an expendable, Second-Law energy. This article needs to be cleaned up to conform to a higher standard of quality. ... The internal energy of a system (abbreviated E or U) is the total kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the total potential energy associated with the vibrational and electric energy of atoms within molecules or crystals. ... This page develops the Helmholtz free energy from the point of view of thermal and statistical physics. ... Enthalpy (symbolized H, also called heat content) is the sum of the internal energy of matter and the product of its volume multiplied by the pressure. ... In thermodynamics the Gibbs free energy is a thermodynamic potential and is therefore a state function of a thermodynamic system. ... Various meanings of the term free energy include: In thermodynamics the term free energy denotes the total amount of energy in a system which can be converted into work. ... Work (abbreviated W) is the energy transferred by a force to a moving object. ... In thermodynamics, free energy is a measure of the amount of mechanical work that can be extracted from a system. ... A system is an assemblage of inter-related elements comprising a unified whole. ... Engineering applies scientific and technical knowledge to solve human problems. ... The word linear comes from the Latin word linearis, which means created by lines. ... In thermodynamics and statistical mechanics, the thermodynamic entropy (or simply the entropy) S is a key physical variable in describing a thermodynamic system. ... Thermodynamics (from the Greek thermos meaning heat and dynamis meaning power) is a branch of physics that studies the effects of temperature, pressure, and volume changes on physical systems at the macroscopic scale. ... In thermodynamics, a state function, or thermodynamic potential, is any property of a system that depends only on the current state of the system, not on the way in which the system got to that state. ... Mathematics is often defined as the study of topics such as quantity, structure, space, and change. ... A red-hot iron rod cooling after being worked by a blacksmith. ... In a thermodynamics problem, the surroundings, or environment, are anything not part of the system. ... The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: // Description The essence of the First Law of Thermodynamics declares: energy cannot be destroyed. ... The second law of thermodynamics, in a concise form, states that the total entropy of any thermodynamically isolated system tends to increase over time, approaching a maximum value. // General description In a general sense, the second law says that the differences between systems in contact with each other tend to...

In solution chemistry and biochemistry, the Gibbs free energy change (denoted by ΔG) is commonly used merely as a surrogate for (−T times) the entropy produced by spontaneous chemical reactions in situations where there is no work done; or at least no "useful" work; i.e., other than PdV. As such, it serves as an particularization of the second law of thermodynamics, giving it the physical dimensions of energy, even though the inherent meaning in terms of entropy would be more to the point. It serves little purpose to say that the (Gibbs) free energy decreases if this is merely a reflection of the fact that the entropy increases. In fact, it tends to give credence to the mistaken notion that there is a principle of minimum energy, while there is no such law of nature. Chemistry (derived from the Arabic word kimia, alchemy, where al is Arabic for the) is the science that deals with the properties of organic and inorganic substances and their interactions with other organic and inorganic substances. ... Biochemistry is the study of the chemistry of life, a bridge between biology and chemistry that studies how complex chemical reactions give rise to life. ... In thermodynamics the Gibbs free energy is a thermodynamic potential and is therefore a state function of a thermodynamic system. ... A chemical reaction is a process that results in the interconversion of chemical substances . ... The second law of thermodynamics, in a concise form, states that the total entropy of any thermodynamically isolated system tends to increase over time, approaching a maximum value. // General description In a general sense, the second law says that the differences between systems in contact with each other tend to... Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ... The neutrality of this article is disputed. ... A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations. ...

The free energy functions are Legendre transforms of the internal energy. For processes involving a system at constant pressure P and temperature T, the Gibbs free energy is the most useful because, in addition to subsuming any entropy change due merely to heat flux, it does the same for the PdV work needed to "make space for additional molecules" produced by various processes. (Hence its utility to solution-phase chemists, including biochemists.) The Helmholtz free energy is has a special theoretical importance since it is proportional to the logarithm of the partition function for the canonical ensemble in statistical mechanics. (Hence its utility to physicists; and to gas-phase chemists and engineers, who do not want to ignore PdV work.) Partial plot of a function f. ... In mathematics, two differentiable functions f and g are said to be Legendre transforms of each other if their first derivatives are inverse functions of each other: f and g are then said to be related by a Legendre transformation. ... The internal energy of a system (abbreviated E or U) is the total kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the total potential energy associated with the vibrational and electric energy of atoms within molecules or crystals. ... Look up Process in Wiktionary, the free dictionary Process (lat. ... In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ... Pressure (symbol: p) is the force per unit area acting on a surface in a direction perpendicular to that surface. ... Temperature is the physical property of a system which underlies the common notions of hot and cold; the material with the higher temperature is said to be hotter. ... In thermodynamics the Gibbs free energy is a thermodynamic potential and is therefore a state function of a thermodynamic system. ... In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks. ... Look up Process in Wiktionary, the free dictionary Process (lat. ... Dissolving table salt in water In chemistry, a solution is a homogeneous mixture of one or more substances (the solutes) dissolved in another substance (the solvent). ... In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i. ... This page develops the Helmholtz free energy from the point of view of thermal and statistical physics. ... Theory has a number of distinct meanings in different fields of knowledge, depending on the context and their methodologies. ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... In statistical mechanics, the partition function Z is an important quantity that encodes the statistical properties of a system in thermodynamic equilibrium. ... A canonical ensemble in statistical mechanics is an ensemble of dynamically similar systems, each of which can share its energy with a large heat reservoir, or heat bath. ... Statistical mechanics is the application of statistics, which includes mathematical 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. ... A black hole concept drawing by NASA. Physics (from the Greek, φυσικός (physikos), natural, and φύσις (physis), nature) is the science of the natural world dealing with the fundamental constituents of the universe, the forces they exert on one another, and the results produced by these forces. ... A gas is one of the four main phases of matter (after solid and liquid, and followed by plasma), that subsequently appear as a solid material is subjected to increasingly higher temperatures. ...

The (historically earlier) Helmholtz free energy is defined as A = U − TS, where U is the internal energy, T is the absolute temperature, and S is the entropy. Its change is equal to the amount of reversible work done on, or obtainable from, a system at constant T. Thus its appellation "work content", and the designation A from 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. This page develops the Helmholtz free energy from the point of view of thermal and statistical physics. ... Thermodynamic temperature is a measure, in kelvins (K) of temperature for thermodynamics, with a uniquely defined zero point at absolute zero. ... In thermodynamics and statistical mechanics, the thermodynamic entropy (or simply the entropy) S is a key physical variable in describing a thermodynamic system. ... 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. ... moved from free energy 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. ...

The Gibbs free energy G = H − TS, where H is the enthalpy. (H = U + PV, where P is the pressure and V is the volume.) In thermodynamics the Gibbs free energy is a thermodynamic potential and is therefore a state function of a thermodynamic system. ... Enthalpy (symbolized H, also called heat content) is the sum of the internal energy of matter and the product of its volume multiplied by the pressure. ...

There has been historical controversy:

• Among physicists, “free energy” most often refers to the Helmholtz free energy, denoted by F.
• Among chemists, “free energy” most often refers to the Gibbs free energy, also denoted by F.

Since both fields use both functions, a compromise has been suggested, using A to denote the Helmholtz function, with G for the Gibbs function. While A is preferred by IUPAC, F is still in use. A black hole concept drawing by NASA. Physics (from the Greek, φυσικός (physikos), natural, and φύσις (physis), nature) is the science of the natural world dealing with the fundamental constituents of the universe, the forces they exert on one another, and the results produced by these forces. ... This page develops the Helmholtz free energy from the point of view of thermal and statistical physics. ... Chemistry (derived from the Arabic word kimia, alchemy, where al is Arabic for the) is the science that deals with the properties of organic and inorganic substances and their interactions with other organic and inorganic substances. ... In thermodynamics the Gibbs free energy is a thermodynamic potential and is therefore a state function of a thermodynamic system. ... This article needs to be cleaned up to conform to a higher standard of quality. ... The International Union of Pure and Applied Chemistry (IUPAC) is an international non-governmental organization devoted to the advancement of chemistry. ...

The experimental usefulness of these functions is restricted to conditions where certain variables (T, and V or external P) are held constant, although they also have theoretical importance in deriving Maxwell relations. Work other than PdV may be added, e.g., for electrochemcial cells, or f ˑdx work in elastic materials and in muscle contraction. Other forms of work which must sometimes be considered are stress-strain, magnetic, as in adiabatic demagnetization used in the approach to absolute zero, and work due to electric polarization. These are described by tensors. In the scientific method, an idiot is a person with a lot of issues who doesn;t know anything, for example, me The word is derived from the Latin id- + iot, issues. // An experiment in baking As a simple example, consider that many bakers have noticed that the amount of... Maxwells relations are a set of equations in Thermodynamics which are derivable from the definitions of the four thermodynamic potentials. ... English chemists Jonh Daniell (left) and Michael Faraday(right), both are credited to as founders of electrochemistry as is known today. ... The term elastomer is often used interchangeably with the term rubber, and is preferred when referring to vulcanisates. ... A top-down view of skeletal muscle Muscle is a contractile form of tissue. ... Figure 1  Stress tensor In physics, stress is a measure of the internal distribution of force per unit area within a body that balances and reacts to the loads applied to it. ... In any branch of science dealing with materials and their behaviour, strain is the geometrical expression of deformation caused by the action of stress on a physical body. ... In physics, magnetism is one of the phenomena by which materials exert an attractive or repulsive force on other materials. ... In thermodynamics, an adiabatic process is a process in which no heat is gained or lost in the working fluid. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Absolute zero is a fundamental lower bound on the temperature of any macroscopic system. ... The Earths magnetic field, which is approximately a dipole. ... In mathematics, a tensor is a generalized quantity or a certain kind of geometrical entity that includes all the ideas of scalars, vectors, matrices and linear operators. ...

In most cases of interest there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which create entropy. Even for homogeneous "bulk" materials, the free energy functions depend on the (often suppressed) composition, as do all proper thermodynamic potentials (extensive functions), including the internal energy. // Degrees of freedom in mechanics In mechanics, for each particle belonging to a system, and for each independent direction in which movement is possible, two degrees of freedom, are defined, one describing the particles momentum in that direction, the other describing the particles position along an axis defined... A chemical reaction is a process that results in the interconversion of chemical substances . ... In physics, a phase transition, (or phase change) is the transformation of a thermodynamic system from one phase to another. ... A chemical compound is a chemical substance formed from two or more elements, with a fixed ratio determining the composition. ... This article needs to be cleaned up to conform to a higher standard of quality. ... In physics and chemistry, an extensive quantity (also referred to as an extensive variable) is a physical quantity whose value is proportional to the size of the system it describes. ...

Name	Definition	Natural variables
Helmholtz free energy
Gibbs free 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 reversible processes are (assuming only PV work) This page develops the Helmholtz free energy from the point of view of thermal and statistical physics. ... In thermodynamics the Gibbs free energy is a thermodynamic potential and is therefore a state function of a thermodynamic system. ... The mole (symbol: mol) is the SI term identifying the number of particles in a given amount of matter. ... In mathematics, the word differential has various meanings: In calculus, a differential is an infinitesimal change in the value of a function. ... 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. ...

where μ_i is the chemical potential for the i-the component in the system. The second relation is especially useful at constant T and P, conditions which are easy to achieve experimentally, and which approximately characterize living creatures. The precise meaning of the term chemical potential depends on the context in which it is used. ... In thermodynamics, a component is a chemically distinct constituent of a system. ... Look up life and living in Wiktionary, the free dictionary. ...

Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and/or its surrounding. An isothermal process is a thermodynamic process in which the temperature of the system stays constant; ΔT = 0. ... An isobaric process is a thermodynamic process in which the pressure stays constant; . The heat transferred to the system does work but also changes the internal energy of the system: according to the first law of thermodynamics, where W is work done by the system, E is internal energy, and... In a thermodynamics problem, the surroundings, or environment, are anything not part of the system. ... A wave that loses amplitude is said to dissipate. ...

External links

• Free Energy in Relation to Entropy.
• Free Energy as a Second-Law Energy.