Thermodynamic free energy

Lore & Background

The Gibbs free energy, defined as G = H − TS, is most useful for processes at constant pressure and temperature, as it excludes p dV work needed to 'make space for additional molecules.' The Helmholtz free energy, defined as A = U − TS, is completely general and its decrease is the maximum work a system can do at constant temperature. Historically, 'free energy' has been used for either quantity, with physics often referring to Helmholtz and chemistry to Gibbs.

Reader's Guide

Thermodynamic free energy is central to understanding the direction and limits of chemical and physical processes. It distinguishes between the total first-law energy of a system and the portion available to perform useful work at constant temperature. The Gibbs free energy is particularly valuable for solution-phase chemists and biochemists because it accounts for work not associated with expansion or compression at constant pressure and temperature. The Helmholtz free energy holds special theoretical importance in statistical mechanics, as it is proportional to the logarithm of the partition function for the canonical ensemble. Both functions are Legendre transforms of the internal energy, and their changes indicate whether a process is spontaneous. The concept resolves the apparent paradox that while first-law energy is conserved, free energy is subject to irreversible loss, making it a second-law kind of energy. The derivative forms of the free energy functions show that spontaneous changes involve available energy for work and unavailable energy related to temperature change. The values of Gibbs and Helmholtz free energies are usually quite similar, and the intended function is often implicit in manuscripts and presentations.

Did You Know?

• The change in free energy is the maximum amount of work a system can perform at constant temperature.
• Only relative free energy values, or changes in free energy, are physically meaningful.
• The Helmholtz free energy is proportional to the logarithm of the partition function for the canonical ensemble in statistical mechanics.
• The term 'free energy' has historically been used for either Gibbs or Helmholtz free energy, depending on the field.