Helmholtz energy function

Gibbs and Helmholtz energy functions and open systems... 

The only two functions actually required in thermodynamics are the energy function, obtained from the first law of thermodynamics, and the entropy function, obtained from the second law of thermodynamics. However, these functions are not necessarily the most convenient functions. The enthalpy function was defined in order to make the pressure the independent variable, rather than the volume. When the first and second laws are combined, as is done in this chapter, the entropy function appears as an independent variable. It then becomes convenient to define two other functions, the Gibbs and Helmholtz energy functions, for which the temperature is the independent variable, rather than the entropy. These two functions are defined and discussed in the first part of this chapter. 

Fld and AFex are the ideal Helmholtz energy functional and excess Helmholtz energy functional, respectively. The ideal Helmholtz energy, as a functional of pp(Q) and ps(q), can be written as... 

Here subscripts p and s represent polymer and solvent, respectively, Q is the coordinate of all polymers with configurations inherited and q is that of all solvent molecules, V, t(Q) is the intrinsic energy function. If all the potential terms in addition to the intrinsic energy of r connected segments are taken into account, the real Helmholtz energy functional... 

The advantage of this approach over kinematically extended continua is twofold first, the additional parameter is abstract and does not require special assumptions of the local kinematics as it is necessary in micropolar continua, for example. As a consequence, the corresponding boundary conditions can be formulated more flexibly. Second, the coupling between the macroscopic balance of momentum and the additional balance of equilibrated forces is obtained consti-tutively, via the free Helmholtz energy function and not via the free energy function in combination with measures of deformation assumed a priori. Therefore, such an approach allows for size effects in both ways - either smaller is stiffer" or smaller is weaker depending on the boundary conditions. 

According to the definition of the Helmholtz energy function, we can easily deduce that the pressure is given by the opposite of the derivative of this Helmholtz energy with regard to volume ... 

The most common form of wide-range accurate equation being developed today is that of a dimensionless Helmholtz energy function, which can be written as... 

Each equation of state has been fitted to an equation in the form of a dimensionless Helmholtz energy function using multiproperty fitting of the most accurate experimental data. The Helmholtz function ensures that all the properties are thermodynamically consistent and enables the calculations to be performed by differentiation alone. The properties which can be calculated are ... 

Finally, the modeling of the solution, i.e. the establishing of the excess molar Helmholtz energy function, involves expressing the value of the coefficients ky from relation [3.56], and most of the existing models differ only in this evaluation. 

The Helmholtz energy function (Hermann Ludwig Ferdinand von Helmholtz, Germany, 1821-1894)is A. 

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