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.

Only closed systems have so far been considered. However, mass can be varied and is an important variable for all thermodynamic functions. The introduction of mass as an independent variable into the basic differential expressions for the thermodynamic functions yields the equations that Gibbs called ‘fundamental’. It is on these equations that much of the development of the applications of thermodynamics to chemical systems is based.

Many of the problems that are met in applications require the evaluation of various derivatives and the integration of differential quantities that involve the derivatives. To be of use, the derivatives must be expressed in terms of experimentally determinable quantities.