From the postulates in Chapter 2, we have already seen that from U(S, V, N1, …, Nm) or S(U, V, N1, …, Nm) we can derive all of the thermodynamic information about a system. For example, we can find mechanical or thermal equations of state. However, we also know that it is sometimes convenient to use other independent variables besides entropy and volume. For example, when we perform an experiment at room temperature open to the atmosphere, we are manipulating temperature and pressure, not entropy and volume. In this case, the more natural independent variables are T and P. Then, the following question arises: Is there a function of (T, P, N1, …, Nm) that contains complete thermodynamic information? In other words, is there some function, say G(T, P, N1, …, Nm), from which we could derive all the equations of state? It turns out that such functions do exist, and that they are very useful for solving practical problems.
In the first section we show how to derive such a function for any complete set of independent variables using something called Legendre transforms. In this book we introduce three widely used potentials: the enthalpy H (S, P, N1, …, Nm), the Helmholtz potential F (T, V, N1, …, Nm), and the Gibbs free energy G (T, P, N1, …, Nm). These functions which contain complete thermodynamic information using independent variables besides S, V, and N1, …, Nm are called generalized thermodynamic potentials.