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Entropy and fuel cells 139

9.4 Misconceptions

Two misconceptions with respect to the operation of fuel cells need
to be carefully addressed. The first issue is the incorrect claim(s) about the
possibility of fuel cell efficiency being >100%, when the entropy of the
reaction products is greater than that of the reactants. This misconception
has been addressed to some extent by others, e.g., Ref. [4]. The second
misconception is with respect to inaccurate calculations, which have led
to a claim that the upper bound of fuel cell efficiency is limited to the Car-
not efficiency.

9.4.1 First issue: η>1!
To resolve the first issue, it should be noted that an efficiency >100% in any
fuel-to-power conversion system is in violation of the conservation of
energy. For further elaboration, let us reconsider Fig. 9.5. As discussed pre-
viously, the maximum efficiency monotonically increases with Λ and
reaches the 100% limit at a certain value of Λ. The results for the maximum
efficiency in Fig. 9.5 are calculated at the regime of fully reversible, i.e., the
total entropy generation rate is zero.
It is mathematically correct that a further increase in Λ beyond the 100%
efficiency limit (e.g., Λ¼7.2 in hydrogen-air fuel cell) would yield a max-
imum power output greater than the total input energy provided we con-
tinue to assume that the system still operates at the reversible limit. However,
since an efficiency of >100% violates the energy conservation principle, we
conclude that the reversible operation would no longer be possible, and
the generation of entropy would be unavoidable. For instance, it is impos-
sible for the hydrogen-air fuel cell to operate at fully reversible limit for any
value of Λ >7.2 (see Fig. 9.5) so the maximum efficiency may approach
100% while the system produces entropy.

9.4.2 Second issue
Shown in Fig. 9.5 is also the efficiency of a Carnot engine operating between
the same low temperature (T R ¼298.15K) and the high temperature (T P )of
the fuel cell. It is obvious that for each mole of hydrogen consumed in the
cell and fixed reactants temperature, an increase in the air amount supplied to
the cell would lower the temperature of the reaction products, hence the
corresponding Carnot efficiency would also decrease. Fig. 9.5 clearly shows