Enthalpy Helmholtz energy and

The Legendre transforms currently used in thermodynamics are enthalpy, Helmholtz energy, and Gibbs energy ... 

This chapter begins with a discussion of mathematical properties of the total differential of a dependent variable. Three extensive state functions with dimensions of energy are introduced enthalpy, Helmholtz energy, and Gibbs energy. These functions, together with internal energy, are called thermodynamic potentials. Some formal mathematical manipulations of the four thermodynamic potentials are described that lead to expressions for heat capacities, surface work, and criteria for spontaneity in closed systems. 

The enthalpy, Helmholtz energy, and Gibbs energy are important functions used extensively in thermodynamics. They are state functions (because the quantities used to define them are state functions) and are extensive (because U, S, and V are extensive). If temperature or pressure are not uniform in the system, we ean apply the definitions to eonstituent phases, or to subsystems small enough to be essentially uniform, and sum over the phases or subsystems. 

We substitute this relation for dU into the differentials of enthalpy, Helmholtz energy, and Gibbs energy given by Eqs. 5.3.4-5.3.6 to obtain three more relations ... 

As mentioned above, free energy F is occasionally called the Helmholtz energy, and free enthalpy G is frequently called the Gibbs energy. These two energy functions F and G correspond to the amounts of energy that are freed from the restriction of entropy and hence can be fully utilized for irreversible processes to occur at constant temperature. 

By transforming only S we obtain the definition of the Helmholtz energy, and by transforming only V we get the definition of enthalpy. For more information, see Alberty (2001). 

The expressions in the third column of Table 7.4 may be summarized by the statement that, when an ideal gas expands isothermally, the internal energy and enthalpy stay constant, the entropy increases, and the Helmholtz energy and Gibbs energy decrease. 

However, the energy of the chemical input and output is not so easily defined. At a simple level we could say that it is the chemical energy of the H2, O2, and H2O that is in question. The problem is that chemical energy is not simply defined - and terms such as enthalpy, Helmholtz function, and Gibbs free energy are used. In recent years the useful term exergy has become quite widely used, and the concept is particularly useful in high-temperature fuel cells. There are also older (but still useful) terms such as calorific value. 

In most applications, thermodynamics is concerned with five fundamental properties of matter volume (V), pressure (/ ), temperature (T), internal energy (U) and entropy (5). In addition, three derived properties that are combinations of the fundamental properties are commonly encountered. The derived properties are enthalpy (//). Helmholtz free energy (A) and Gibbs free energy ) ... 

In addition to the fundamental variables p, V, T, U, and S that we have described so far, three other thermodynamic variables are commonly encountered enthalpy Helmholtz free energy and Gibbs free energy. They are extensive variables that do not represent fundamental properties of the... 

The value of the electric potential affecting the activation enthalpy of the electrode reaction is decreased by the difference in the electrical potential between the outer Helmholtz plane and the bulk of the solution, 2, so that the activation energies of the electrode reactions are not given by Eqs (5.2.10) and (5.2.18), but rather by the equations... 

The internal energy, enthalpy and Helmholtz energy can be expressed in an analogous manner ... 

Equation 54 implies that U is a function of S and I. a choice of variables that is not always convenient. Alternative fundamental property relations may be formulated in which other pairs of variables appear. They are found systematically through Legendre transformations (1,2), which lead to the following definitions for the enthalpy, H, Helmholtz energy,. 1. and Gibbs energy, G ... 

Conversely, if the Gibbs free energy change is known as a function of temperalure at constant pressure, the enthalpy change can be obtained by a relation which is an alternate form of the Gibbs-Helmholtz equation, and which can be derived from Equation (8). 

Key Concepts of Interfacial Properties in Food Chemistry Equation D3.5.12 G = U + PV - TS = yA + p,/j, i Equation D3.5.13 where H is the enthalpy, F the Helmholtz free energy, and G the Gibbs free energy. These basic equations can be used to derive explicit expressions for these quantities as they apply... 

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. 

From their definitions (Eq. (4.39)) based on the energy, the enthalpy, and the Gibbs and Helmholtz energies, we may set the chemical potentials to be functions of other variables, as follows ... 

In this discussion of indifferent states we have always used the entropy, energy, and volume as the possible extensive variables that must be used, in addition to the mole numbers of the components, to define the state of the system. The enthalpy or the Helmholtz energy may also be used to define the state of the system, but the Gibbs energy cannot. Each of the systems that we have considered has been a closed system in which it was possible to transfer matter between the phases at constant temperature and pressure. The differentials of the enthalpy and the Helmholtz and Gibbs energies under these conditions are... 

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