Page 72 - Introduction to Transfer Phenomena in PEM Fuel Cells

The specific heat C p is a function of temperature; the following equation
shows an empirical relation usable in our case:
C =α + β + γ T² Charge Transfer Phenomena 61
[2.31]
T
p
where T denotes the operating temperature of the cell; α, β and γ are the
coefficients that depend on the gas. Table 2.2 gives the values of these
coefficients [PER 08, SAI 06]:
–1
–3
–1
–2
–1
–1
Substance α (J . mol . K ) β (J . mol . K ) γ (J . mol . K )
–6
Hydrogen, H 2 29.038 -0.8356 . 10 –3 2.0097 . 10
–6
Oxygen, O 2 25.699 12.966 . 10 –3 -3.8581 . 10
–6
Water, H 2 O 30.33 9.6056 . 10 –3 1.1829 . 10
Table 2.2. Numerical values of empirical coefficients
The following equations allow us to calculate the variation of the
standard Gibbs free energy for temperatures other than 298.15 K. The index
(i) designates (anode or cathode).

For the enthalpy:
2
3
T − 298 2 T − 298 3
0
Δ H(T) = Δ H 0 + α (T 298− ) + β + γ [2.32]
i
298
2 3
For the entropy:
2
0
Δ S (T) = Δ S 0 298 + α ln   T   + β (T 298− ) + γ T − 298 2 [2.33]
i
 298  3
Knowing that:

Δ H reaction = Δ H 0 products − Δ H 0 reac tan ts [2.34]

and:

Δ S reaction = Δ S 0 products − Δ S 0 reac tan ts [2.35]