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Information about Thermodynamic Free Energy

Thermodynamic potentials
Internal energy
Helmholtz free energy
Enthalpy
Gibbs free energy
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In thermodynamics, the term thermodynamic 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 subtraction of the entropy of a system ("useless energy") from the total energy, yielding a thermodynamic state function which represents the "useful energy".

Overview

In short, free energy is that portion of any First-Law energy that is available for doing thermodynamic work; i.e., work mediated by thermal energy. Since free energy is subject to irreversible 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 kind of energy that can make things happen within finite amounts of time.

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 a 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.

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 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.)

The (historically earlier) Helmholtz free energy is defined as A = U − TS, where U is the internal energy, T is the absolute temperature, and S is the entropy. Its change is equal to the amount of reversible work done on, or obtainable from, a system at constant T. Thus its appellation "work content", and the designation A from arbeit, the German word for work. Since it makes no reference to any quantities involved in work (such as P and V), the Helmholtz function is completely general: its decrease is the maximum amount of work which can be done by a system, and it can increase at most by the amount of work done on a system.

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.)

There has been historical controversy: 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 sometimes still in use, and the correct free energy function is often implicit in manuscripts and presentations.

Application

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 electrochemical 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 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.

NameDefinitionNatural variables
Helmholtz free energy
Gibbs free energy


Ni is the number of molecules (alternatively, moles) of type i in the system. If these quantities do not appear, it is impossible to describe compositional changes. The differentials for reversible processes are (assuming only PV work)





where μi is the chemical potential for the i-th component in the system. The second relation is especially useful at constant T and P, conditions which are easy to achieve experimentally, and which approximately characterize living creatures.



Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and/or its surrounding.

See also

thermodynamic potentials are parameters associated with a thermodynamic system and have the dimensions of energy. They are called "potentials" because in a sense, they describe the amount of potential energy in a thermodynamic system when it is subjected to certain constraints.
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In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and
..... Click the link for more information.
In thermodynamics, the Helmholtz free energy is a thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic system at a constant temperature.
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In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the "useful" work
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In thermodynamics, the Gibbs free energy (IUPAC recommended name: Gibbs energy or Gibbs function) is a thermodynamic potential which measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system.
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Thermodynamics (from the Greek θερμη, therme, meaning "heat" and δυναμις, dynamis, meaning "power") is a branch of physics that studies the effects of changes in temperature, pressure, and volume on
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In physics, mechanical work is the amount of energy transferred by a force. Like energy, it is a scalar quantity, with SI units of joules. Heat conduction is not considered to be a form of work, since there is no macroscopically measurable force, only microscopic forces occurring
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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.
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System (from Latin systēma, in turn from Greek σύστημα systēma) is a set of entities, real or abstract, where each entity interacts with, or is related to, at least one other
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Engineering is the applied science of acquiring and applying knowledge to design, analysis, and/or construction of works for practical purposes. The American Engineers' Council for Professional Development, also known as ECPD,[1] (later ABET [2]
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Ice melting - a classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice.
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Thermodynamics (from the Greek θερμη, therme, meaning "heat" and δυναμις, dynamis, meaning "power") is a branch of physics that studies the effects of changes in temperature, pressure, and volume on
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In thermodynamics, a state function, or state quantity, is a 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. A state function describes the equilibrium state of a system.
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The first law of thermodynamics is an expression of the universal law of conservation of energy, and identifies heat transfer as a form of energy transfer. The most common enunciation of the first law of thermodynamics is:


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Irreversible may refer to:
  • Irreversibility, in thermodynamics, a process that is not reversible
  • Irréversible, a 2002 film

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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 equilibrium will tend to increase over time, approaching a maximum value at equilibrium.
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Biochemistry is the study of the chemical processes in living organisms.[1] The word "biochemistry" comes from the Greek word βιοχημεία biochēmeia, which means "the chemistry of life.
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In thermodynamics, the Gibbs free energy (IUPAC recommended name: Gibbs energy or Gibbs function) is a thermodynamic potential which measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system.
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chemical reaction is a process that results in the interconversion of chemical substances.[1] The substance or substances initially involved in a chemical reaction are called reactants.
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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 equilibrium will tend to increase over time, approaching a maximum value at equilibrium.
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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.
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function expresses dependence between two quantities, one of which is given (the independent variable, argument of the function, or its "input") and the other produced (the dependent variable, value of the function, or "output").
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Legendre transform of the original function, after Adrien-Marie Legendre.

The Legendre transform of a function is defined as follows:



The notation indicates the maximization of the expression with respect to the variable while p
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In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and
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Process (lat. processus - movement) is a naturally occurring or designed sequence of changes of properties or attributes of an object or system[1][2][3][4][5][6][7].
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In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. This is in contrast to a variable, which is not fixed.

Unspecified constants

The most widely mentioned sort of constant
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Pressure (symbol: p) is the force per unit area applied on a surface in a direction perpendicular to that surface.

Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
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trillion fold).]]

Temperature is a physical property of a system that underlies the common notions of hot and cold; something that is hotter generally has the greater temperature. Temperature is one of the principal parameters of thermodynamics.
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In thermodynamics, the Gibbs free energy (IUPAC recommended name: Gibbs energy or Gibbs function) is a thermodynamic potential which measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system.
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