Helmholtz relation

By combining Eq. (1) with the Gibbs-Helmholtz relation we obtain... 

Heras [10] has shown how to use the relation written above to recover Jefimenko s formulas [11,12]. Helmholtz relation generalized to spacetime can... 

The AT driving force is the isobaric equivalent of the isothermal Ag in Equation (3.10). The Gibbs-Helmholtz relation may be applied to... 

Finally, once E and H are determined by integration of (1.18.13) or via heat capacities, F and G may be found by the Gibbs-Helmholtz relation (1.18.33), thus closing the loop. The reader is well advised to ponder the methodology of thermodynamics, because it is through this general approach that the theory is particularly powerful in the analysis of phenomena. Other aspects of this structure will be pointed out in later sections. 

Standard Gibbs energies of adsorption are often encountered. When A j G is accurately known as a function of temperature, standard enthalpies and entropies of adsorption can also be obtained, using the appropriate Gibbs Helmholtz relations (sec. 1.2.15). 

Glbbs-Helmholtz relations 1.2.41, 1.2.15, 1.2.61, 1.2.78, 3.156 Gibbs-Kelvln equation see Kelvin equation Glbbs-Thomson equation see Kelvin equation glass,... 

For the implied infinitesimal changes of y with T the factor RTF remains constant. Generally, however, the derivative dy/dT also depends on T. From (4.3.22) S° will eventually be obtained as a function of x and T. As, for each T, F is accessible as a function of x, it is also possible to derive the surface excess entropy as a function of the monolayer composition. Accurate data are, as before, a prerequisite. From S the surface excess enthalpy = TS is obtainable. Alternatively, one can differentiate y /T with respect to the temperature, obtaining the enthalpy directly using the appropriate Gibbs-Helmholtz relation. 

If the c.m.c. is known as a function of T, the micelllzation enthalpy can immediately be derived, using the following Gibbs -Helmholtz relation (see [1.2.15.8a]... 

Equations (4.8) and (4.9) can also be written in terms of the average affinity and average heat of reaction. We start from the Gibbs-Helmholtz relation (4.33) and apply this to one state in which = 1, and another in which T and V have the same values but = 0 ... 

The classical expression due to Helmholtz, relating the streaming potential to the zeta potential, , and measurable quantities may be simply obtained as follows. Fig. 2 represents a capillary tube of radius r with a fixed surface charge of density, [Pg.437]

The enthalpy of formation is obtained from enthalpies of combustion, usually made at 298.15 K while the standard entropy at 298.15 K is derived by integration of the heat capacity as a function of temperature from T = 0 K to 298.15 K according to equation fB 1.27.16). The Gibbs-Helmholtz relation gives the variation of the Gibbs energy with temperature... 

An alternative approach that may be applied to determine AH (Hupu) involves combination of equation 4 with the Gibbs-Helmholtz relation which leads to the following formula 18,19) ... 

Thus for the closed system we have the following Helmholtz relation ... 

In some textbooks (3.197) is rewritten by using the changes of enthalpy Ah and the Gibbs free energy Ag before and after the reaction, and the Gibbs-Helmholtz relation is given by... 

This formula is often called the Wolfsberg-Helmholtz relation. 

By deriving the expression [1.28] relative to the amount , of component i, we obtain the second Helmholtz relation ... 

To calculate enthalpy, we will use either the definition of Gibbs entropy, or the first Helmholtz relation [1.29]. We obtain the following ejq)ressions for excess molar enthalpy ... 

Derive relations for the physical properties of materials whose magnetization follows the Curie-Weiss law M = AxM-ol T + ), where is a parameter, called the Weiss constant. Check on the expression (5.8.14) by basing your derivation on the Gibbs-Helmholtz relation and solving the first-order differential equation. 

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