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( Thermodynamic free energy)
In thermodynamics, the term thermodynamic free energy is 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". 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 ?G) 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.)
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