An electrolyte-supported SOFC is operated at atmospheric pressure and
\(800^{\circ} \mathrm{C}\) with the following mole fractions of the reactant and
product species: \(x_{\mathrm{H}_{2}}=\) \(0.95\) and \(x_{\mathrm{H}_{2}
\mathrm{O}}=0.05\) (anode) and \(x_{\mathrm{O}_{2}}=0.21\) (cathode). At
\(800^{\circ} \mathrm{C}\), the fuel cell has \(\Delta
\bar{g}_{\mathrm{f}}=-188.6 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\) and \(\Delta
h_{\mathrm{r}}=-248.3 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\) of
\(\mathrm{H}_{2}\), and the conductivity of the cell is \(5 \Omega^{-1} \cdot
\mathrm{m}^{-1}\). The cell active area is \(2 \times 10^{-4} \mathrm{~m}^{2}\),
and the electrolyte thickness is \(100 \mu \mathrm{m}\). If the cell is operated
at \(0.7 \mathrm{~V}\), then determine the following:
a. The inlet Nernst voltage
b. The rates at which hydrogen and oxygen are consumed
c. The electrical efficiency (fuel to electricity)