Page 311 - Renewable Energy Devices and System with Simulations in MATLAB and ANSYS

298 Renewable Energy Devices and Systems with Simulations in MATLAB and ANSYS ®
®

R T Π a v i
o
E = E cell − ln products (12.1)
v i
nF Π a reactants
where
E is the open-circuit voltage of the fuel cell at no load
o
R is the universal gas constant (R = 8.314472(15) J/K/mol)
T is the absolute temperature
F is the Faraday constant (the number of coulombs per mole of electrons is F = 9.64853399 ×
10 C/mol)
4
n is the number of moles of electrons transferred in the cell reaction
a is the chemical activity for the relevant species (for ideal gas, a = p /p , where p and p are,
i
i
o
o
i
respectively, the partial pressure of species i and the standard state pressure, that is, 1 atm)
v denotes the stoichiometric coefficient of ith species involved in the chemical reaction (in this
i
case the stoichiometric coefficient of O is ½)
2
In case of a hydrogen–oxygen fuel cell system, n = 2, and therefore, Equation 12.1 reduces to
R T  1 
o − ln (12.2)
E = E cell  12 
/
2 F  pp O 2 
H 2
This expression gives the ideal thermodynamic potential or maximum theoretical voltage across
the cell. It is also known as the open-circuit voltage at standard temperature and pressure with no
current drawn from the cell.
When the activities of H and O are both unity, that is, the partial pressure of both H and O is
2
2
2
2
1 atm, the expression reduces to
o
E = E clle (12.3)
o
The E cell decreases with increase in temperature. Therefore, at standard pressure conditions,
= = 1 atm, the open-circuit voltage of an SOFC is lower than that of a PEMFC.
p H 2 p O 2
To calculate the fuel cell efficiency, some thermodynamic parameters, that is, Gibbs free energy
G, enthalpy H, and entropy S, need to be defined and determined as a result of the chemical
reaction.
Entropy is another thermodynamic property that is a measure of a system’s thermal energy per
unit temperature that is unavailable for doing useful work:

Q
∆ = (12.4)
S
T
where
Q is the heat or thermal energy
T is the absolute temperature of the system

In the case of a fuel cell (chemical reactions), entropy appears in the form of rejected or
released heat in the process. Chemical reactions act as a source of enthalpy H and generate an
amount of electrical energy W and reject an amount of thermal energy (heat) Q as shown in
e
Figure 12.5.