Page 141 - Entrophy Analysis in Thermal Engineering Systems

Entropy and fuel cells 135

9.2.1 Hydrogen-air fuel cell
A more realistic analysis should account for the fact that oxygen is not freely
available in the nature. We consider a hydrogen fuel cell, which uses air,
comprising 21% oxygen and 79% nitrogen (mole basis) as the oxidizer.
Thus, the overall cell reaction obeys

ð
ð
H 2 + Λ O 2 +3:76N 2 Þ ! H 2 O+ Λ 0:5ÞO 2 +3:76ΛN 2 (9.17)
where Λ ( 0.5) is a stoichiometric coefficient.
As the products cool down to the surrounding temperature, a portion of
water vapor may condense and the rest is left as vapor in the products mix-
ture. The derivation procedure for the maximum fuel cell power is the same
as described in the previous section. The following expression is obtained for

.
_ W FC
max

ð
¼ H R H P,0 + T 0 S P,0 S R Þ (9.18)
_ W FC
max
where the reactants include hydrogen, oxygen, and nitrogen, and the prod-
ucts comprise water (liquid and gas), unused oxygen, and nitrogen.
9.2.2 Fuel cell operating on methane

Like oxygen, hydrogen is not freely available in the nature. One would then
need to account for production of hydrogen from a primary fuel. For exam-
ple, hydrogen can be produced through steam reforming of a hydrocarbon
fuel. Assume that methane is the fuel that is reformed with steam to produce
carbon monoxide and hydrogen.
CH 4 +H 2 O ! 3H 2 + CO (9.19)

Additional hydrogen may be produced by converting carbon monoxide to
carbon dioxide through water-gas shift reaction.

CO + H 2 O ! H 2 +CO 2 (9.20)
The reforming reaction, Eq. (9.19), is endothermic whereas the water-gas
shift reaction is exothermic. It can be deduced from Eqs. (9.19) and
(9.20) that for each mole of methane, the net reforming plus shift reaction
requires two moles of steam to produce four moles of hydrogen.
(9.21)
CH 4 +2H 2 O ! 4H 2 +CO 2
where the overall reaction is endothermic with a reaction enthalpy of
165kJ/mol at 298K.