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We investigate the geometric properties of the equilibrium manifold of athermodynamic system determined by the van der Waals equations of state. We usethe formalism of geometrothermodynamics to obtain results that are invariantunder Legendre transformations, i. e., independent of the choice ofthermodynamic potential. It is shown that the equilibrium manifold is curvedwith curvature singularities situated at those points where first order phasetransitions occur. Moreover, the geodesic equations in the equilibrium manifoldare investigated numerically to illustrate the equivalence between geodesicincompleteness and curvature singularities as a criterion to define phasetransitions in an invariant manner.

A geometric approach to the thermodynamics of the van der Waals system