  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 the 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 intriguing 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.
