Thermodynamic free energy
Free energy measures work available at constant temperature.
Thermodynamic free energy is a state function that measures the maximum work a system can perform at constant temperature, with its sign indicating whether a process is thermodynamically favorable. Only changes in free energy are physically meaningful, as free energy depends on a chosen zero point. It represents the portion of first-law energy available to perform work mediated by thermal energy, but it is subject to irreversible loss during such work, making it an expendable, second-law kind of energy. Several free energy functions exist, formulated as Legendre transforms of internal energy. The Gibbs free energy, defined as enthalpy minus the product of temperature and entropy, is most useful for processes at constant pressure and temperature, as its change excludes work needed to make space for additional molecules and equals work not associated with expansion or compression. The Helmholtz free energy, defined as internal energy minus the product of temperature and entropy, is completely general: its decrease is the maximum work obtainable from a system at constant temperature, and it is proportional to the logarithm of the partition function in statistical mechanics. Historically, the term "free energy" has referred to either quantity, with physics typically using Helmholtz and chemistry using Gibbs. The concept of "free" energy derives from the difference between internal energy change and energy lost as heat, representing useful work. However, the common interpretation that work is extracted only from internal energy while the entropy term represents unavailable energy is incorrect, as seen in isothermal expansion of an ideal gas where expansion work comes from that term.
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- Thermodynamics
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- Gibbs free energy and Helmholtz free energy as measures of useful work at constant temperature
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. Thermodynamic free energy is a state function representing the maximum work a system can perform at constant temperature, with its sign indicating whether a process is thermodynamically favorable. Because free energy includes potential energy, it is not absolute and depends on a chosen zero point; only changes in free energy are physically meaningful. It is the portion of first-law energy available for work mediated by thermal energy, subject to irreversible loss, making it an expendable, second-law kind of energy. Several free energy functions exist as Legendre transforms of internal energy. The Helmholtz free energy, denoted A or F, is proportional to the logarithm of the partition function in statistical mechanics, giving it special theoretical importance. The Gibbs free energy change equals work not associated with system expansion or compression, hence its utility in solution-phase chemistry and biochemistry. The term "free energy" historically emerged during the 18th and 19th centuries as heat theory evolved, distinguishing "free heat" from other classifications like "combined heat" and "latent caloric."
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.
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