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The output voltage of fuel cell is given by Nernst equation as [8–11]:

(2.1)

Table 2.1 Fuel cell resource comparison (courtesy: DOE, US Government).

Figure 2.2 PAFC characteristics.

Figure 2.3 PAFC average cell voltage vs current density.

Where:

V_dc = Fuel cell output voltage (Volt)

E = Thermodynamic potential of fuel cell (Volt) which is expressed by:

(2.2)

E⁰ = Potential of unit cavity in fuel cell = 1.229 V

PH₂, PO₂ & PH₂O = Particle pressure of Hydrogen, Oxygen and vapor (atm)

T = Cell temperature (K)

R = Universal gas constant = 8.31441 J/mol-K

F = Faraday constant = 94,685 C/mol

n = Number of electrons participating in the reaction

V₀ = Ohmic voltage drop (Volt) which is given by:

(2.3)

I = Cell current (Amp)

R_int = Internal resistance between electrodes which is given by:

l = Length between two electrodes (Meter)

V_a = Summation of activation voltage drop and concentration voltage drop (Volt) which is expressed by:

(2.4)

α = Electron transfer co-efficient

i = Current density (A/m²)

i₀ = Exchange current density (A/m²)

i_L = Limiting current density (A/m²)

є = Electrical permittivity of electrolyte

A = Effective surface area between electrodes and electrolyte (sq. meter). It is very large due to corrugated porous surface of the electrodes.

l = Distance between two layers of electrodes. It is very small (nanometer).

V_C = Voltage across the Capacitor ‘C’. It is given by:

(2.5)

Figure 2.4 PAFC equivalent circuit.

There are three operating regions for this fuel cell. The first region is activation region where the voltage drop is due to the slowness of the chemical reactions at electrode. It is considered as R_a. The second region represents the ohmic losses due to the internal resistance of the fuel cell. It is represented by R_o. The third region represents the change in concentration of reactants as the fuel is used. It is represented by R_c. By considering these three operating regions of fuel cell, an equivalent DC circuit model is obtained as shown in Figure 2.4.