Helmholtz free energy

chemistry

Also known as: Helmholtz function

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July 23, 2026

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In thermodynamics, Helmholtz free energy (F) is a state function representing the energy available to do work in a system at constant temperature and volume. It is defined as the internal energy (U) minus the product of temperature (T) and entropy (S): (F = U - TS).1

The change in Helmholtz free energy ((\Delta F)) indicates the spontaneity of a process. If (\Delta F) is negative, the process will occur spontaneously. This concept is crucial for understanding processes in open systems, where energy and matter can be exchanged with the environment.12

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free energy
…expressed in two forms: the Helmholtz free energy F, sometimes called the work function, and the Gibbs free energy G. If U is the internal energy of a system, PV the pressure-volume product, and TS the temperature-entropy product (T being the temperature above absolute zero
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…expressed in two forms: the Helmholtz free energy F, sometimes called the work function, and the Gibbs free energy G. If U is the internal energy of a system, PV the pressure-volume product, and TS the temperature-entropy product (T being the temperature above absolute zero
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thermodynamics
Thermodynamic potentials
…expressed in terms of the Helmholtz free energy F and the Gibbs free energy G, named after the 19th-century German physiologist and physicist Hermann von Helmholtz and the contemporaneous American physicist Josiah Willard Gibbs. The key conceptual step is to separate a system from its heat reservoir. A system is…
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…expressed in terms of the Helmholtz free energy F and the Gibbs free energy G, named after the 19th-century German physiologist and physicist Hermann von Helmholtz and the contemporaneous American physicist Josiah Willard Gibbs. The key conceptual step is to separate a system from its heat reservoir. A system is…
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mechanics of solids
Thermodynamic considerations
Alternatively, one may introduce the Helmholtz free energy f per unit mass, where f = e − θs = f([ε], θ), and show that σ_ij = ρ₀∂f([ε], θ)/∂ε_ij. The latter form corresponds to the variables with which the stress-strain relations were written above. Sometimes ρ₀f is called the strain energy…
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Alternatively, one may introduce the Helmholtz free energy f per unit mass, where f = e − θs = f([ε], θ), and show that σ_ij = ρ₀∂f([ε], θ)/∂ε_ij. The latter form corresponds to the variables with which the stress-strain relations were written above. Sometimes ρ₀f is called the strain energy…
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