Thermodynamic free energy

In useful energy".

Overview

In short, free energy is that portion of any Second-Law kind of energy that can make things happen within finite amounts of time.

In solution 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 gas-phase chemists and engineers, who do not want to ignore pdV work.)

The (historically earlier) 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 enthalpy. (H = U + pV, where p is the pressure and V is the volume.)

There has been historical controversy:

• In physics, “free energy” most often refers to the Helmholtz free energy, denoted by F.
• In Gibbs free energy, 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 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 polarization. These are described by tensors.

In most cases of interest there are internal degrees of freedom and processes, such as chemical reactions and thermodynamic potentials (extensive functions), including the internal energy.

Name	Definition	Natural variables
Helmholtz free energy
Gibbs free energy

N_i is the number of molecules (alternatively, reversible processes are (assuming only pV work)

where μ_i is the 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 dissipated, appearing as T times a corresponding increase in the entropy of the system and/or its surrounding.

See also

• Gibbs free energy
• Helmholtz free energy
• Exergy
• Merle Randall