Free energy of a system

Mark, A. E., van Gunsteren, W. F. Decomposition of the free energy of a system in terms of specific interactions. Implications for theoretical and experimental studies. J. Mol. Biol. 240 (1994) 167-176... 

If J, are the free energies of a system before and after dissociation at a constant temperature, the maximum external work obtainable is — 4/ This may be calculated directly. Let us take the case of nitrogen peroxide ... 

How does free energy allow us to predict spontaneity while ignoring the surroundings To answer this question, we examine the change in free energy of a system, A Gsys = A Hsys -A(T If we hope to use A G ys to... 

These relationships interrelate the parameters pressure, volume and temperature with the Gibbs free energy of a system. It may be pointed out that the results embodied in these equations are applicable to closed systems only. 

Assume that we are interested in how the free energy of a system changes as a function of an order parameter, , which changes between 0 and i. A direct approach to this problem is to carry out MD or MC simulations long enough to obtain a sufficiently accurate estimate of the probability density function, ( ), of finding the system in a state corresponding to . Then, it follows from (1.22) of... 

The change in free energy of a system between two states (A,B) (AG,) is calculated after each step of the transformation. Since the free energy is a state function the total free energy change, AG, is the sum of the intermediate AG,s. An intermediate state22 of the system is defined as,... 

The change in the free energy of a system, AG, at constant temperature is given by the equation AG = AH - TAS. In this equation, as in most chemistry equations, the temperature, T, must be in Kelvin degrees. The symbol AH represents the change in enthalpy. The symbol AS represents the change in entropy. 

The Gibbs free energy of a system (Gtotai) is composed of all the Gibbs free energies of the various phases in the system, defined by the chemical potentials of their components. Algebraically, this is expressed as... 

For pyrotechnic reactions, many of which proceed at constant pressure and temperature, the two quantities that define the free energy of a system are the entropy, as discussed above, and the enthalpy, H, which represents the heat content of a system. 

Thermodynamically, we would like to know which material minimizes the free energy of a system containing gaseous 02 and a solid at the specified conditions. A useful way to do this is to define the grand potential associated with each crystal structure. The grand potential for a metal oxide containing NM metal atoms and No oxygen atoms is defined by... 

The chemical potential is defined as the increase in free energy of a system on adding an infinitesimal amount of a component (per unit number of molecules of that component added) when T, p and the composition of all other components are held constant. Clearly, from this definition, if a component i in phase A has a higher chemical potential than in phase B (that is, xf > pf) then the total free energy will be lowered if molecules are transferred from phase A to B and this will occur in a spontaneous process until the chemical potentials equalize, at equilibrium. It is easy to see from this why the chemical potential is... 

From a thermodynamic consideration by Gibbs,225 one can expect surface segregation to occur if the total free energy of a system can be lowered by segregation of a species to the surface. For a dilute solution of B in A, this condition is described as... 

The negative sign in Equation 14-4 indicates that the free energy of a system decreases when the work is done on the surroundings. 

A short discussion of thermodynamics is necessary to place the topic of equilibrium into proper perspective. From the viewpoint of thermodynamics a system is in equilibrium when the free energy G is equal to zero. Free energy is the energy available to do work. The free energy of a system depends upon the enthalpy (heat content), H and the entropy(disorder or randomness of the molecules), S. 

The change in the free energy of a system is defined as AG = AH — T AS, where T is the absolute temperature. A reaction at constant pressure and temperature can occur spontaneously if, and only if, AG is negative. The maximal amount of useful work that can be obtained from a reaction is equal to — AG. 

A common lattice defect is a vacant lattice site or vacancy. The presence of a vacancy increases the enthalpy by Ahf and the entropy by As/. Because the free energy of a system is lowered by increased entropy, there is an equilibrium fraction of vacant lattice, xv, which increases with temperature. At equilibrium, A gf = Ahf — T A Sf = 0, so A hf = —T Asf. From statistical mechanics, ASf = —klnx , so... 

Phase diagrams are related to how the Gibbs free energy of a system varies with composition, temperature, and pressure. Equilibrium corresponds to the state of lowest free energy. The Gibbs free energy of a system, G, is defined as G = H — TS, where H is the enthalpy of the system, S is the entropy of the system, and T is the temperature. The enthalpy or heat content is given by... 

Free Energy of a System in Terms of Specific Interactions. Implications for Theoretical and Experimental Studies. 

The thermodynamic characteristics of solutions are often expressed by means of excess functions. These are the amounts by which the free energy, entropy, enthalpy, etc. exceed those of a hypothetical ideal solution of the same composition (Denbigh, 1981). The excess free energy is closely related to the activity coefficients. The total free enthalpy (Gibbs free energy) of a system is ... 

In the DLVO framework, the free energy of a system of two overlapped double layers is composed of an electrostatic energy, an entropic contribution due to the ions in the double layer, and a chemical term, where applicable.4... 

The free energy of a system composed of various substances is dependent on the quantities of individual species present, as well as temperature and pressure. However, the free energy of the system as a whole is not the summation of the free energies of each species in the pure state because species may behave differently in the mixture as compared to the pure state. Thus, the free energy of the mixture is given by ... 

The variation of the free energy of a system (gas) with respect to pressure at constant temperature is given by ... 

The equation (V-4) expresses the difference in free energy of a system after reaction and before it. on the assumption that the individual components are in arbitrary states. By a similar equation we can express the change in the standard free energy of the samo reaction when both reactants and reaction products are in the standard state ... 

Let us consider a part of discrete system with random fluxes. Since the free energy of a system with random fluxes is very large (in comparison with system close equilibrium), subsystems possessing the most large energy cannot be neglected, and one should evaluate their parameters. The minimum of available energy of subsystems with random fluxes can be approximately assumed equal zero. 

In Chap. 10 it will be shown that the Gibbs free energy of a system is made up of two components such that... 

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