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In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature . The change in the Helmholtz energy during a process is equal to the maximum amount of work that the system can perform in a thermodynamic process ...
The Gibbs–Helmholtz equation is a thermodynamic equation used to calculate changes in the Gibbs free energy of a system as a function of temperature.It was originally presented in an 1882 paper entitled "Die Thermodynamik chemischer Vorgänge" by Hermann von Helmholtz.
This follows from the first and second laws of thermodynamics and is called the principle of minimum energy. The following three statements are directly derivable from this principle. When the temperature T and external parameters of a closed system are held constant, the Helmholtz free energy F decreases and reaches a minimum value at equilibrium.
Historically, the term 'free energy' has been used for either quantity. In physics, free energy most often refers to the Helmholtz free energy, denoted by A (or F), while in chemistry, free energy most often refers to the Gibbs free energy. The values of the two free energies are usually quite similar and the intended free energy function is ...
Derivation of Maxwell Relation from Helmholtz Free energy. The differential form of Helmholtz free energy is = = (), = From symmetry of second derivatives = and therefore that = The other two Maxwell relations can be derived from differential form of enthalpy = + and the differential form of Gibbs free energy = in a similar way.
In the special case of entropy, entropy is given by = ( + ) = () = where A is the Helmholtz free energy defined as A = U − TS, where U = E is the total energy and S is the entropy, so that = = .
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. [1] [2] Most modern equations of state are formulated in the Helmholtz free energy.
The Helmholtz free energy is a useful quantity when studying thermodynamic transformations in which the temperature is held constant. Although the reduction in the number of variables is a useful simplification, the main advantage comes from the fact that the Helmholtz free energy is minimized at equilibrium with respect to any unconstrained ...