Combining the Irreversibilities

It is useful to construct an equation that brings together all these irreversibilities. We can do so and arrive at the following equation for the operating voltage of a fuel cell at a current density i. 

E is the reversible OCV given by equations 2.1 and 3.1 in is the internal and fuel crossover equivalent current density described in Section 3.5 

A is the slope of the Tafel line as described in Section 3.4.2 io is either the exchange current density at the cathode if the cathodic overvoltage is much greater than the anodic or it is a function of both exchange cnrrent densities as given in equation 3.5 m and n are the constants in the mass-transfer overvoltage equation 3.10 as discussed in Section 3.7 

Although correct, this equation is often simplified in a useful and practical way. The crossover cnrrent i is usually very small, and althongh useful for explaining the initial 

Because the second half of this equation is a constant, we can deal with this by postulating a real, practical, open circuit voltage oc that is given by the equation 

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