Thermodynamic functions based on the third law

We have seen that absolute values of the entropy function based on the third law can be obtained from measurements of the heat capacity and heats of transitions. A more general equation than Equation (15.9) may be written as 

The first term on the right-hand side of this equation represents the required extrapolation from 0 K to the lowest experimental temperature. The second term represents the sum of the contributions to the entropy for the change of temperature of a single phase, and the subscript i refers to the different phases. The third term represents the sum of the contributions for all of the 

For any compilation of values of these functions the standard states must be completely defined. In essentially all cases the pressure is 1 bar and for gases the state is usually the ideal gas at 1 bar. For compilations at a single temperature, the temperature is usually 298.15 K. When values at various temperatures are required, it is easier to compile values at convenient temperature intervals rather than to obtain algebraic functions of the value. In such cases the function [Se(T) — He(0)]/T is used because the interpolation between the listed values is more nearly linear than between the values of [5e(T)-tfe(0)]. 

Another set of thermodynamic functions is based on the values of the enthalpy at 298.15 K. With a knowledge of the heat capacities and changes of enthalpy for changes of phase, values of the function [ffe(T) —ffe(298)] are obtained. The corresponding function for the Gibbs energy is [( e(T) — He(298)] or [Se(T)-tfe(298)]/T. Values for these functions are obtained by 

These functions are particularly useful when the low-temperature thermal data are not available. Under such circumstances the values of Se(T) must be obtained from equilibrium measurements as indicated in Section 15.5. 

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