  In this paper we show that the vanishing of the scalar curvature of
Ruppeiner-like metrics does not characterize the ideal gas. Furthermore, we
claim through an example that flatness is not a sufficient condition to
establish the absence of interactions in the underlying microscopic model of a
thermodynamic system, which poses a limitation on the usefulness of Ruppeiner's
metric and conjecture. Finally, we address the problem of the choice of
coordinates in black hole thermodynamics. We propose an alternative energy
representation for Kerr-Newman black holes that mimics fully Weinhold's
approach. The corresponding Ruppeiner's metrics become degenerate only at
absolute zero and have non-vanishing scalar curvatures.
