Thermodynamic free energy

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The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to perform work. This unusable energy is given by the entropy of a system multiplied by the temperature of the system.

Like the internal energy, the free energy is a thermodynamic state function.

Contents

Overview

Free energy is that portion of any first-law energy that is available to perform thermodynamic work; i.e., work mediated by thermal energy. Free energy is subject to irreversible loss in the course of such work.[1] Since a first-law energy is always conserved, it is evident that free energy is an expendable, second-law kind of energy that can perform work within finite amounts of time. Several free energy functions may be formulated based on system criteria. Free energy functions are Legendre transformations 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, 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 = UTS, 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.