Page 69 - Introduction to Transfer Phenomena in PEM Fuel Cells

58 Introduction to Transfer Phenomena in PEM Fuel Cells
2.2.5. Effect of pressure
The preceding equations are valid for a pressure equal to the atmospheric
pressure. However, the battery can operate at different pressures, ranging
from atmospheric pressure to several bars [BAR 05, SPI 07]. For a process
considered isothermal, the change of free energy of Gibbs can be written as:
dG = V ⋅ dP [2.13]
m
where:

3
–1
– V m is the molar volume, in [m .mol ];
– P is the pressure, in [Pa].
For an ideal gas, we write:

PV = RT [2.14]
m
Replacing equation [2.13] in [2.14], we find:

dP
dG = RT [2.15]
P
Then, after integration:

 P 
0
G = G + RTln   [2.16]
 P 0 
0
where (G ) and (P 0) are respectively the Gibbs free energy and pressure at
standard pressure and temperature. During a chemical reaction of the
following type:

+
jA kB → mC nD [2.17]
+
The change in Gibbs’ free energy is a function of the products and
reactants, so that:

Δ= mG + nG − jG − kG B [2.18]
G
C
A
D