Free energy Helmholtz, defined

The excess energy associated with an interface is formally defined in terms of a surface energy. This may be expressed in terms either of Gibbs, G, or Helmholtz, A, free energies. In order to circumvent difficulties associated with the unavoidably arbitrary position of the surface plane, the surface energy is defined as the surface excess [7,8], i.e the excess (per unit area) of the property concerned consequent upon the presence of the surface. Thus Gibbs surface free energy is defined by... 

Application to Macromolecular Interactions. Chun describes how one can analyze the thermodynamics of a particular biological system as well as the thermal transition taking place. Briefly, it is necessary to extrapolate thermodynamic parameters over a broad temperature range. Enthalpy, entropy, and heat capacity terms are evaluated as partial derivatives of the Gibbs free energy function defined by Helmholtz-Kelvin s expression, assuming that the heat capacities integral is a continuous function. 

We then introduce two new energy functions called free energy / (Helmholtz energy) for the independent variables temperature T and volume V, and free enthalpy G (Gibbs energy) for the independent variables temperature T and pressure p as defined, respectively, in Eqs. 3.21 and 3.22 ... 

Instead of using volume and temperature as independent variables. however we more often wish to use pressure and temperature. In this case, instead of using t he Helmholtz free energy, it is more convenient to use the Gibbs free energy G. defined bv the equations... 

In order to express Eq. (6-7) in a more concise fashion, it is useful to define an extensive function of state. A, the work function or Helmholtz free energy. The Helmholtz free energy is defined by the relation... 

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 ... 

For such theory, a,p,y,d,2., and are expansion coefficients that are extracted from the experimentally measured quasistatic hysteretic response of a single-crystal. Physically, the first three terms of the right hand side of the first row of the Helmholtz free energy expressoin defines the equilibrium, stress and electric field free variants of the system. The fourth term couples an externally specified electric field to the local state of polarization of the solid. Such contribution biases the stability of those variants that are closer (or parallel) to the applied field. The fifth term... 

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 ... 

If the Helmholtz free energy is defined as A = U - TS then changes in the Helmholtz free energy at constant temperature are given by,... 

A similar energy function, the Helmholtz free energy A, can sometimes be found in the literature. The Helmholtz free energy is defined based on internal energy U in the same way as the G function is defined based on enthalpy H... 

Another useful set of variables is T,V,n. .. uc. The corresponding thermodsmamic potential is the Helmholtz free energy F defined by... 

The chemical potential p, of the adsorbate may be defined, following standard practice, in terms of the Gibbs free energy, the Helmholtz energy, or the internal energy (C/,). Adopting the last of these, we may write... 

Themodynamic State Functions In thermodynamics, the state functions include the internal energy, U enthalpy, H and Helmholtz and Gibbs free energies, A and G, respectively, defined as follows ... 

The Gibbs-Helmholtz equation can be used to calculate the standard free energy of formation of a compound. This quantity, AGf, is analogous to the enthalpy of formation, AH . It is defined as the free energy change per mole when a compound is formed from the elements in their stable states at 1 atm. 

The Helmholtz free energy A is the second of the three derived thermodynamic properties. It is defined as... 

In Chapter 1, we describe the fundamental thermodynamic variables pressure (p), volume (V), temperature (T), internal energy ((/), entropy (5), and moles (n). From these fundamental variables we then define the derived variables enthalpy (//), Helmholtz free energy (A) and Gibbs free energy (G). Also included in this chapter is a review of the verbal and mathematical language that we will rely upon for discussions and descriptions in subsequent chapters. 

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... 

Define, now, a new thermodynamic function, the Helmholtz free energy A,... 

The A defined in Equation 5.30 is not to be confused with the Helmholtz free energy. Should the A frequencies be limited to the external hindered translations and rotations, vi g = vi g = 0, and this is an additional simplification. In some molecules, however, there are isotope sensitive low lying internal modes (often internal rotations or skeletal bends). In that cases both terms in Equation 5.30 contribute. 

Protein stability has generally been defined in terms of the free energy change between the native and the unfolded states (AGu). This parameter of unfolding can be used to decipher stability of the native state across a wide temperature range.43 The relation that incorporates all of the terms described above is the modified Gibbs-Helmholtz equation and is a function of temperature. 

As U, T, and S are state functions, the quantity (U— TS) also must be a state function. This quantity is sufficiently important that it is given the name Helmholtz function, or Helmholtz free energy, which is defined as... 

In a finite, one component, system defined by the number of molecules, N, the volume, V, and the temperature, T, the Helmholtz free energy of formation, of a stable droplet is written... 

The application of the second law to chemical equilibrium is facilitated by the introduction of two more state functions. These are defined as (a) the Helmholtz free energy... 

The potential I speak of is usually called the potential of average force. Insofar as it is to be identified to a thermodynamic potential it is a local Helmholtz free energy as a function of the coordinate positions of all the atoms (or radicals) that must change relative positions in the reaction it may be defined by... 

Alternatively, the chemical potential may be defined in terms of the Helmholtz free energy as... 

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