This is interesting for it combines both the thermodynamic concept of a minimum Gibbs function for equilibrium and minimum mechanical potential energy for equilibrium.

In these papers, Gibbs showed how the first two laws of thermodynamics could be measured graphically and mathematically to determine both the thermodynamic equilibrium of chemical reactions as well as their tendencies to occur or proceed.

The relation between the equilibrium constant, K, and the Gibbs free energy for an electrochemical cell is expressed as follows:

When Gibbs submitted his long paper on the equilibrium of heterogeneous substances to the Academy, both Elias Loomis and Hubert Anson Newton protested that they did not understand Gibbs's work at all, but they helped to raise the money needed to pay for the typesetting of the many equations and mathematical symbols in the paper.

By studying the interactions of homogeneous substances in contact, i. e., bodies, being in composition part solid, part liquid, and part vapor, and by using a three-dimensional volume-entropy-internal energy graph, Gibbs was able to determine three states of equilibrium, i. e., " necessarily stable ", " neutral ", and " unstable ", and whether or not changes will ensue.

This type of reaction is an invariant reaction, because it is in thermal equilibrium ; another way to define this is the Gibbs free energy equals zero.

An equilibrium constant, K, is related to the standard Gibbs free energy, ΔG < sup > Image: StrikeO. png </ sup > by

relating the Gibbs energy to a chemical equilibrium constant, the van't Hoff equation can be derived.

By studying the interactions of homogeneous substances in contact, i. e. bodies, being in composition part solid, part liquid, and part vapor, and by using a three-dimensional volume – entropy – internal energy graph, Gibbs was able to determine three states of equilibrium, i. e. " necessarily stable ", " neutral ", and " unstable ", and whether or not changes will ensue.

Gibbs energy ( also referred to as ∆ G ) is also the chemical potential that is minimized when a system reaches equilibrium at constant pressure and temperature.

By studying the interactions of homogeneous substances in contact, i. e., bodies, being in composition part solid, part liquid, and part vapor, and by using a three-dimensional volume-entropy-internal energy graph, Gibbs was able to determine three states of equilibrium, i. e., " necessarily stable ", " neutral ", and " unstable ", and whether or not changes would ensue.

* When the temperature ( T ), pressure ( p ) and external parameters of a closed system are held constant, the Gibbs free energy ( G ) decreases and reaches a minimum value at equilibrium.

Another potential, the Gibbs free energy ( G ), is minimized at thermodynamic equilibrium in a system with surroundings at controlled constant temperature and pressure:

Gibbs theorized that, analogous to the equilibrium of the simple Watt governor ( which depends on the balancing of two torques: one due to the weight of the “ balls ” and the other due to their rotation ), thermodynamic equilibrium for any work producing thermodynamic system depends on the balance of two entities.

These formulations are ubiquitous today in the natural sciences in the form of the Gibbs ' free energy equation, which is used to determine the equilibrium of chemical reactions ; also known as Gibbs equilibrium.

* In endergonic reactions and exergonic reactions it is the sign of the Gibbs free energy that determines the equilibrium point, and not enthalpy.

According to Gibbs free energy equation, the relation between dissociation equilibrium constant, K < sub > d </ sub >, and the components of free energy was built.

The concentrations of reactants and products in an equilibrium mixture are determined by the analytical concentrations of the reagents ( A and B or C and D ) and the equilibrium constant, K. The magnitude of the equilibrium constant depends on the Gibbs free energy change for the reaction.

Specimens are allowed to reach moisture equilibrium with a standard atmosphere of Af and Af and then laid out without tension on a flat, polished surface, care being taken that the fabric is free from wrinkles or creases.

* Carbonate / bicarbonate / carbonic acid equilibrium in water: pH of solutions, buffer capacity, titration and species distribution vs. pH computed with a free spreadsheet

The time to reach equilibrium depends on such parameters as temperature, pressure and the materials involved, and is determined by the minimum free energy.

With hinged, fixed or free end support conditions the deflected shape in neutral equilibrium of an initially straight column with uniform cross section throughout its length always follows a partial or composite sinusoidal curve shape, and the critical load is given by

Léon Walras, one of the founders of the neoclassical school of economics who helped formulate the general equilibrium theory, argued that free competition could only be realized under conditions of state ownership of natural resources and land.

General equilibrium theory has demonstrated, with varying degrees of mathematical rigor over time, that under certain conditions of competition, the law of supply and demand predominates in this ideal free and competitive market, influencing prices toward an equilibrium that balances the demands for the products against the supplies.

Some models in econophysics have shown that when agents are allowed to interact locally in a free market ( i. e. their decisions depend not only on utility and purchasing power, but also on their peers ' decisions ), prices can become unstable and diverge from the equilibrium, often in an abrupt manner.

The condition for this is that the chemical potential of the solvent ( since only it is free to flow toward equilibrium ) on both sides of the membrane is equal.

The equilibrium constant for this dissociation can be predicted by the change in Gibb's free energy of this reaction.

One of the few cases in which neoclassical economists support government provision of goods or intervention in markets, markets for public goods, which may attract free rider problems, will not come to rest at the appropriate equilibrium when left to the invisible hand alone.

Additionally, many theories were developed which showed that the free market would produce the socially optimum equilibrium with regard to production of goods and services, such as the fundamental theorems of welfare economics and general equilibrium theory, which helped prove further that government intervention could only result in making society worse off ( see Pareto efficient ).

Moreover, when there is not diffusive equilibrium, i. e., when there is a tendency for molecules to diffuse from one region to another, then there is a certain free energy released by each net-diffusing molecule.

These potentials contain free parameters such as atomic charge, van der Waals parameters reflecting estimates of atomic radius, and equilibrium bond length, angle, and dihedral ; these are obtained by fitting against detailed electronic calculations ( quantum chemical simulations ) or experimental physical properties such as elastic constants, lattice parameters and spectroscopic measurements.

At chemical equilibrium or in phase equilibrium the total sum of chemical potentials is zero, as the free energy is at a minimum.

At equilibrium free energy is at its minimum for the system, that is, dG = 0.

The Judgment took place because the Christian church had lost its charity and faith, resulting in a loss of spiritual free will that threatened the equilibrium between heaven and hell in everyone ’ s life

In most interpretations, classical economists such as Adam Smith maintained that the free market would tend towards economic equilibrium through the price mechanism.

The free market's strength was not creating a static or a general equilibrium but instead in organising resources to meet individual desires and discovering the best methods to carry the economy forward.

Notice that at equilibrium the surface adopts a shape such that an element of volume at any location on its surface has the same potential energy as at any other.

If rotation is arrested, the energy stored in fashioning the concave surface must be dissipated, for example through friction, before an equilibrium flat surface is restored.

Introducing the catalyst to the system would result in reaction to move to the new equilibrium, producing energy.

Non-spontaneous reactions run so slowly that they are considered to require the input of some type of additional energy ( such as extra heat, light or electricity ) in order to proceed to completion ( chemical equilibrium ) at human time scales.

The Liouville measure restricted to the energy surface Ω is the basis for the averages computed in equilibrium statistical mechanics.

It may also get dissipated into other microscopic motions within the matter, coming to thermal equilibrium and manifesting itself as thermal energy in the material.

The electromagnetic radiation in an opaque cavity at thermal equilibrium is effectively a form of thermal energy, having maximum radiation entropy.

In particular, in the Born – Oppenheimer and harmonic approximations, i. e. when the molecular Hamiltonian corresponding to the electronic ground state can be approximated by a harmonic oscillator in the neighborhood of the equilibrium molecular geometry, the resonant frequencies are determined by the normal modes corresponding to the molecular electronic ground state potential energy surface.

Mathematically, the total electromagnetic energy density ( radiation energy density ) in thermodynamic equilibrium from Planck's law is

In the spring-mass system, oscillations occur because, at the static equilibrium displacement, the mass has kinetic energy which is converted into potential energy stored in the spring at the extremes of its path.

In particular, the photon model accounted for the frequency dependence of light's energy, and explained the ability of matter and radiation to be in thermal equilibrium.

Even at equilibrium molecules are constantly in motion and, once in a while, a molecule in the liquid phase gains enough kinetic energy to break away from the liquid phase and enter the gas phase.

When in thermal equilibrium, then, it is seen that the lower energy state is more populated than the higher energy state, and this is the normal state of the system.

The onset of nuclear fusion leads relatively quickly to a hydrostatic equilibrium in which energy released by the core exerts a " radiation pressure " balancing the weight of the star's matter, preventing further gravitational collapse.

In normal media at thermal equilibrium, absorption exceeds stimulated emission because there are more electrons in the lower energy states than in the higher energy states.

In the classical account strictly and purely in terms of cyclic processes, the spatial interior of the ' working body ' of a cyclic process is not considered ; the ' working body ' thus does not have a defined internal thermodynamic state of its own because no assumption is made that it should be in thermodynamic equilibrium ; only its inputs and outputs of energy as heat and work are considered.