The Gibbs function, which depends on the intensive variables T and P , is easier
to obtain experimentally than any other thermodynamical potential. However, textbooks usually
first introduce the internal energy, as a function of the extensive variables V and S, and then
proceed, by Legendre transformations, to obtain the Gibbs function. Here, taking liquid water as an
example, we show how to obtain the internal energy from the Gibbs function. The two fundamental
equations (Gibbs function and internal energy) are examined and their output compared. In both
cases complete thermodynamical information is obtained and shown to be practically the same,
emphasizing the equivalence of the two equations. The formalism of the Gibbs function is entirely
analytical, while that based on the internal energy is, in this case, numerical. Although it is well
known that all thermodynamic potentials contain the same information, usually only the ideal gas
is given as an example. The study of real systems, such as liquid water, using numerical methods,
may help students to obtain a deeper insight into thermodynamic
