**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Helmholtz free energy

Summary

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 (isothermal). 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 in which temperature is held constant. At constant temperature, the Helmholtz free energy is minimized at equilibrium.
In contrast, the Gibbs free energy or free enthalpy is most commonly used as a measure of thermodynamic potential (especially in chemistry) when it is convenient for applications that occur at constant pressure. For example, in explosives research Helmholtz free energy is often used, since explosive reactions by their nature induce pressure changes. It is also frequently used to define fundamental equations of state of pure substances.
The concept of free energy was developed by Hermann von Helmholtz, a German physicist, and first presented in 1882 in a lecture called "On the thermodynamics of chemical processes". From the German word Arbeit (work), the International Union of Pure and Applied Chemistry (IUPAC) recommends the symbol A and the name Helmholtz energy. In physics, the symbol F is also used in reference to free energy or Helmholtz function.
The Helmholtz free energy is defined as
where
F is the Helmholtz free energy (sometimes also called A, particularly in the field of chemistry) (SI: joules, CGS: ergs),
U is the internal energy of the system (SI: joules, CGS: ergs),
T is the absolute temperature (kelvins) of the surroundings, modelled as a heat bath,
S is the entropy of the system (SI: joules per kelvin, CGS: ergs per kelvin).
The Helmholtz energy is the Legendre transformation of the internal energy U, in which temperature replaces entropy as the independent variable.
The first law of thermodynamics in a closed system provides
where is the internal energy, is the energy added as heat, and is the work done on the system.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related courses (31)

Related concepts (20)

Related lectures (186)

Related MOOCs (2)

Ontological neighbourhood

Internal energy

The internal energy of a thermodynamic system is the energy contained within it, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accounting for the gains and losses of energy due to changes in its internal state, including such quantities as magnetization. It excludes the kinetic energy of motion of the system as a whole and the potential energy of position of the system as a whole, with respect to its surroundings and external force fields.

Thermodynamic potential

A thermodynamic potential (or more accurately, a thermodynamic potential energy) is a scalar quantity used to represent the thermodynamic state of a system. Just as in mechanics, where potential energy is defined as capacity to do work, similarly different potentials have different meanings. The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term fundamental functions. One main thermodynamic potential that has a physical interpretation is the internal energy U.

Gibbs free energy

In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol ) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as where p is pressure, T is the temperature, U is the internal energy, V is volume, H is the enthalpy, and S is the entropy.

MSE-639: Statistical methods in atomistic computer simulations

The course gives an overview of atomistic simulation methods, combining theoretical lectures and hands-on sessions. It
covers the basics (molecular dynamics and monte carlo sampling) and also more adv

MSE-421: Statistical mechanics

This course presents an introduction to statistical mechanics geared towards materials scientists. The concepts of macroscopic thermodynamics will be related to a microscopic picture and a statistical

CH-420: Understanding advanced molecular simulation

This course introduces advanced molecular simulation techniques such as Monte Carlo and Molecular dynamics in different ensembles, free energy calculations, rare events, Configurational-bias Monte Car

Correlation Functions in Quantum Field Theory

Explores correlation functions in QFT, Wick theorem, perturbation theory, and thermal free energy.

Variational Method in RFIM

Explores the variational method in the Random Field Ising Model, discussing the cost function, algorithmic questions, Gibbs inequality, and the Gibbs free energy.

Swelling of Hydrogels

Explores hydrogels' swelling, osmotic pressure, deformation, and free energy in polymer chains.

Thermodynamics

Ce cours vous apportera une compréhension des concepts fondamentaux de la thermodynamique du point de vue de la physique, de la chimie et de l’ingénierie. Il est scindé un deux MOOCs. Première partie:

Thermodynamics

Ce cours vous apportera une compréhension des concepts fondamentaux de la thermodynamique du point de vue de la physique, de la chimie et de l’ingénierie. Il est scindé un deux MOOCs. Première partie:

Related units (6)

Related people (36)

Related publications (232)

, , , , , , , , ,

Nicola Marzari, Nicéphore Arthur François Bonnet

The present work proposes an extension to the approach of [Xi, C; et al. J. Chem. Theory Comput. 2022, 18, 6878] to calculate ion solvation free energies from first-principles (FP) molecular dynamics (MD) simulations of a hybrid solvation model. The approa ...

Urs von Gunten, Florian Frédéric Vincent Breider, Yishuai Pan

N-Nitrosamines are potential human carcinogens frequently detected in natural and engineered aquatic systems. This study sheds light on the role of carbonyl compounds in the formation of N-nitrosamines by nitrosation of five secondary amines via different ...

2024, ,

Advanced geotechnical engineering applications, such as shale gas extraction, CO2 geological sequestration, and geological radioactive waste storage, often involve various types of shales located at significant depths. Shales exhibit mechanical properties ...