In short,<unk>  is that portion of any First-Law energy that is available for doing thermodynamic  work; i.e., work mediated by thermal energy. Since<unk>  is subject to irreversible loss in the course of such work and First-Law energy is always conserved, it is evident that<unk>  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<unk>  change (denoted by<unk>  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<unk>  functions are Legendre transforms of the internal energy. For processes involving a system at constant pressure p and temperature T, the Gibbs<unk>  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<unk>  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<unk>  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<unk>  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:
In physics,<unk> ” most often refers to the Helmholtz<unk> , denoted by F.
In chemistry,<unk> ” most often refers to the Gibbs<unk> , 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 sometimes still in use, and the correct<unk>  function is often implicit in manuscripts and presentations.
Free energy
Potential energy
Gas constant
Gibbs free energy
Saturation 
Concentration
Molecular mass
Chemical symbol