Helmholtz free energy, definition

The definitions of enthalpy, H, Helmholtz free energy. A, and Gibbs free energy, G, also give equivalent forms of the fundamental relation (3) which apply to changes between equiUbrium states in any homogeneous fluid system ... 

The problem at hand is the evaluation of the activity coefficient defined in Eq. (76). It will be assumed that only pairwise interactions between the defects need be considered at the low defect concentrations we have in mind. (The theory can be extended to include non-pairwise forces.23) Then the cluster function R(n) previously defined in Eq. (78) is the sum of all multiply connected diagrams, in which each bond represents an /-function, which can be drawn among the set of n vertices, the /-function being defined by Eqs. (66), (56), and (43). The Helmholtz free energy of interaction of two defects appearing in this definition can be written as... 

Wilson and Cunningham developed the PFGC equation of state on the basis of the following definition of the Helmholtz free energy... 

Begin with the definition of the Helmholtz free energy... 

It is also useful to define the chemical potential in terms of the partition function. By the definition of p,k in Eq. 9.24 and the Helmholtz free-energy expression of Eq. 8.114,... 

For definiteness, consider barrierless adsorption-desorption reaction (2). In the variational TST, the position qf of transition complex TCad in the reaction path (see Figures 9.1 and 9.2) corresponds to a maximum of the Helmholtz free energy cf(qr) of the trial transition complex TCad( r) considered as a function of the reaction coordinate. 

In Frame 4, as equation (4.2), equation (15.2) was established as a definition of an ideal gas on the basis of the simplest qualitative argument and not by classical thermodynamic arguments. Just for the record we note here that the relationship can be established by the following route (which involves introduction of the Helmholtz free energy, A and use of the Maxwell... 

Using Eq. (24) for the Helmholtz free energy and the thermodynamic definition of the surface tension c,... 

In the last equations A(n) is the Helmholtz free energy of the total NVT system fully defined by the vector n = nm, n 2,... providing the molecular number in each tiny volume and iq) is the chemical potential at a given iq position, i.e., within the corresponding tiny volume. Note that the molecular number can be used as a continuous variable, given the fact that for any thermodynamic property in a macroscopic system the variation due to a single molecule is virtually equivalent to a differential. From the definition of the chemical potential and probability density in the r) space p(t, ti), we readily have... 

Using Stirling s formula, the definition of the Helmholtz free energy F = -kT In and standard thermodynamic relations, several useful formulae may be deduced from the expression for Zn in Equation 12. The chemical potential (/x) is given by... 

The natnral variables S and V of [/ are transformed to T and V by Legendre transformation of U to the energy fnnction A, called the Helmholtz free energy, or Helmholtz energy. By definition. 

It can readily be shown (Davies Rideal 1963) that, provided the viscosity of the liquid is not very high, the surface tension is equal to the Helmholtz free energy per unit area of surface, and hence also has the equivalent dimensions of energy per unit area. From the definition of the Helmholtz free energy applied at the surface, it also is easily demonstrated that the surface tension decreases with increasing liquid temperature that is,... 

There is another free energy state function, the Helmholtz free energy (F), defined as F = E - 715. Comparing this to the definition of G, we see that internal energy has replaced enthalpy in the definition. Under what conditions would this free energy tell us whether or not a process is spontaneous ... 

The equation above is the fundamental equation for an open system. Similarly, using enthalpy H, Helmholtz free energy A, and Gibbs free energy G definitions, we can derive three more fundamental equations... 

From the definition of y and Equation (1.32) at constant T and V, the change in Helmholtz free energy for the creation of an increment of planar interfacial area dA for a unary two-phase system will be equal to the work done on the system,... 

Equation (2.25) shows that the temperature dependence of the surface energy is determined by the surface entropy, which should generally be positive. Thus, the surface energy decreases as the temperature is increased. From the definition of the Helmholtz free energy. Equation (1.28), the surface Helmholtz firee energy, internal energy and entropy are related by... 

Here, U is the internal energy and T the temperature. On another hand, there is a definition of the Helmholtz free-energy from a statistical approach [12]. Given a system with an energy spectrum , the Helmholtz free-energy is defined as ... 

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