freeenergy

Free energy is a term used in physics and engineering with several related meanings. In thermodynamics, it refers to specific thermodynamic potentials that quantify the amount of energy available to do useful work under defined conditions. The two most common are the Helmholtz free energy F and the Gibbs free energy G. The Helmholtz free energy is defined as F = U − TS, where U is internal energy, T is temperature, and S is entropy. The Gibbs free energy is G = H − TS = U + pV − TS, where H is enthalpy and pV is pressure–volume work. These potentials indicate the system’s capacity to perform non-expansion work under fixed volume and temperature (F) or fixed pressure and temperature (G).

Spontaneity and equilibrium: For a closed system at constant temperature and volume, a process tends to decrease F (ΔF ≤ 0); at constant temperature and pressure, spontaneous change tends to decrease G (ΔG ≤ 0). The equilibrium state corresponds to the minimum of the appropriate free energy under the given constraints.

Maximum useful work: The decrease in free energy provides an upper bound on reversible work obtainable from the system beyond any PV work: at constant T and V, the maximum non-PV work is −ΔF; at constant T and P, it is −ΔG.

Beyond physics, the term “free energy” is also used in popular culture to denote energy that can be extracted without cost. Claims of perpetual motion or energy-from-nothing devices are not supported by credible evidence and conflict with the laws of thermodynamics, as energy conservation and entropy considerations forbid such mechanisms.

Historically, the concepts emerged from the work of Gibbs and Helmholtz in the 19th century and remain central to thermodynamics, chemistry, and engineering.