Maxwell relationship temperature-dependent function

For the purpose of satisfying the Maxwell relationship more precisely, an adjustment was made on the temperature-dependent function fa(T). The final expression obtained for fa(T) is as follows ... 

Before turning to the surface enthalpy we would like to derive an important relationship between the surface entropy and the temperature dependence of the surface tension. The Helmholtz interfacial free energy is a state function. Therefore we can use the Maxwell relations and obtain directly an important equation for the surface entropy ... 

The amount of indirect evidence for the correctness of the Maxwell distribution law is overwhelming. The relationship of the distribution law to the rate of a chemical reaction has already been mentioned briefly (Section 4.10). We shall see later that the functional f orm of the experimentally determined temperature dependence of the rate constant agrees with the dependence we expect from the Maxwell distribution. This agreement may be regarded as indirect evidence for the correctness of both the Maxwell distribution and our ideas concerning reaction rates. 

In this chapter, wc introduce two more methods of thermodynamics. The first is Maxwell relations. With Maxwell relations you can find the entropic and energetic contributions to the stretching of rubber, the expansion of a surface or a film, or the compression of a bulk material. Second, we use the mathematics of homogeneous functions to develop the Gibbs-Duhem relationship. This is useful for finding the temperature and pressure dependences of chemical equilibria. 

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