Page 520 - Advanced thermodynamics for engineers

21.2 THEORY OF FUEL CELLS 513

Now, from the Van’t Hoff equation
d Q p
Þ¼ (21.44)
ðln K p r 2
dT <T
Substituting from Eqn (21.44) into Eqn (21.43) gives

vE <T Q p E Q p E
¼ þ ¼ þ (21.45)
vT z i F <T 2 T z i FT T
p
Equation (21.45) shows that the change of emf is related to the heat of reaction, Q p .Now,for
exothermic reactions Q p is negative, and this means that the emf of a cell based on an exothermic
reaction decreases with temperature. This is in line with the effect of temperature on the degree of
dissociation in a combustion process, as discussed in Chapter 12.

21.2.4.1 Examples

Example 1
A Pb–Hg fuel cell operates according to the following equation
Pb þ Hg Cl 2 /PbCl 2 þ 2Hg
2
and the heat of reaction, Q p ¼ 95,200 kJ/kmol Pb. The cell receives heat transfer of 8300 kJ/
kmol Pb from the surroundings. Calculate the potential of the cell, and evaluate the electrical
work produced per kilogram of reactants, assuming the following atomic weights: Pb – 207; Hg –
200; Cl – 35.
Solution
This problem can be solved by a macroscopic approach to the cell as a closed system. Applying the
First Law gives
zFEdn ¼ dU dQ trans þ TdS pdV
¼ dG dQ trans
0
Now this value of energy transfer has to be used in Eqn (21.34) in place of DG , giving
T
0

DG dQ trans 95200 8300
T
E ¼ ¼ ¼ 0:5363 V
zF 2 96487
The quantity of work obtained per kg of reactants is given in the following way. Assume the
potential of the cell is not reduced by drawing a current, then the charge transferred through the cell per
kmol Pb is 2F (because the valency of lead is 2). Hence the work done per kmol Pb is
dW ¼ 2 96485 0:5363 ¼ 103500 kJ=kmol Pb
giving the work per unit mass of reactants as
dW 103500
¼ ¼ 152:9kJ=kg
m react 207 þ 2 ð200 þ 35Þ
Example 2
A hydrogen–oxygen fuel cell operates at a constant temperature of 227 C and the hydrogen and

oxygen are fed to the cell at 40 bar, and the water is taken from it at the same pressure. Evaluate the
emf at this condition, and the heat transfer from the cell.