  Thermodynamic length is a metric distance between equilibrium thermodynamic
states that asymptotically bounds the dissipation induced by a finite time
transformation of a thermodynamic system. By means of thermodynamic length, we
first evaluate the departures from ideal to real gases in geometric
thermodynamics with and without Legendre invariance. In particular, we
investigate ideal and real gases in the Ruppeiner and geometrothermodynamic
formalisms. Afterwards, we formulate a strategy to relate thermodynamic lengths
to efficiency of thermodynamic systems in both the aforementioned frameworks in
the working assumption of small deviations from ideality. In this respect, we
propose a geometric efficiency definition built up in analogy to quantum
thermodynamic systems. We show the result that this efficiency is higher for
geometrothermodynamic fluids. Moreover, we stress this efficiency could be used
as a novel geometric way to distinguish ideal from non-ideal thermal behaviors.
In such a way, it could be useful to quantify deviations from ideality for a
variety of real gases. Finally, we discuss the corresponding applications of
our recipe to classical thermodynamic systems, noticing that our findings could
help geometrically grasping the nature of different metrizations on manifolds
of equilibrium thermal states.
