  The well-known Gouy-Stodola theorem states that a device produces maximum
useful power when working reversibly, that is with no entropy production inside
the device. This statement then leads to a method of thermodynamic optimization
based on entropy production minimization. Exergy destruction (difference
between exergy of fuel and exhausts) is also given by entropy production inside
the device. Therefore, assessing efficiency of a device by exergy analysis is
also based on the Gouy-Stodola theorem. However, assumptions that had led to
the Gouy-Stodola theorem are not satisfied in several optimization scenarios,
e.g. non-isothermal steady-state fuel cells, where both entropy production
minimization and exergy analysis should be used with caution. We demonstrate,
using non-equilibrium thermodynamics, a few cases where entropy production
minimization and exergy analysis should not be applied.
