  In this work we employ a recently devised metric within the
Geometrothermodynamics program to study ordinary thermodynamic systems. The new
feature of this metric is that, in addition to Legendre symmetry, it exhibits
invariance under a change of representation. This metric was derived in a
previous work by the authors while addressing the problem of the conformal
structure of the thermodynamic metrics for different representations. Here, we
present an thorough analysis for the ideal gas, the van der Waals fluid, the
one dimensional Ising model and some other systems of cosmological interest.
