Maxwell relations Helmholtz energy

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 ... 

Another important equation, the Gibbs-Helmholtz equation, is derived from the Maxwell relations. A chemist may use this equation to determine the enthalpy change in a reaction, and a pharmaceutical scientist may use it to calculate colligative properties (i.e., freezing point depression and boiling point elevation). The expression for free energy with respect to temperature at constant pressure is given by Equation (1.105) ... 

Equation (7.9) is an example of a Maxwell relation. Derive the other two Maxwell relations associated with the Helmholtz free energy of a rubber. 

This conclusion has ramifications since the differential of the Helmholtz free energy A =E TS is given by dA = —Zdz — SdT, the cross-differentiation with respect to z and T gives rise to a Maxwell relation of the form (dZ/dT) = (dS/dzh, whence Eq. (1.13.5) may be rewritten as... 

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