- Thermodynamic free energy
thermodynamics, the term thermodynamic free energy refers to the amount of work that can be extracted from a system, and is helpful in engineeringapplications. It is a subtraction of the entropyof a system ("useless energy") from the total energy, yielding a thermodynamic state functionwhich represents the "useful energy".
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
irreversibleloss 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.
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 energyis the most useful because, in addition to subsuming any entropy change due merely to heat flux, it does the same for the "p"d"V" work needed to "make space for additional molecules" produced by various processes. (Hence its utility to solution-phase chemists, including biochemists.) The Helmholtz free energyhas a special theoretical importance since it is proportional to the logarithmof the partition function for the canonical ensemblein statistical mechanics. (Hence its utility to physicists; and to gas-phase chemists and engineers, who do not want to ignore "p"d"V" work.)
The (historically earlier)
Helmholtz free energyis 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.
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:
physics, “free energy” most often refers to the " Helmholtz free energy", denoted by "F".
chemistry, “free energy” most often refers to the " Gibbs free energy".
Since both fields use both functions, a
compromisehas 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.
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 "p"d"V" may be added, e.g., for electrochemical cells, or "f ˑ"d"x" work in elastic materials and in musclecontraction. Other forms of work which must sometimes be considered are stress-strain, magnetic, as in adiabatic de magnetizationused 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.
"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)
where μ"i" is the
chemical potentialfor 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.
Gibbs free energy
Helmholtz free energy
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