$($a$)$ Calculate $E_{\text{t}\text{h}\text{e}\text{r}\text{m}\text{o}}$ for a PEMFC running on atmospheric pressure $H_2$ and air at $330K.$

$($b$)$ Calculate $a_c$ and $b_c($the constants for the natural log form of the Tafel equation for the cathode of

this PEMFC$)$ if $i_0={10}^{-3}\frac{A}{c}{m}^2,n=2,$ and $=0\mathrm{.}5.$

$($c$)$ Calculate $AS{R}_{\text{o}\text{h}\text{m}\text{i}\text{c}}$ if the membrane has a conductivity of $0\mathrm{.}1{}^{-1}*c{m}^{-1}$ and a thickness of $100m.$

Assume that there are no other contributions to cell resistance.

$($d$)$ Calculate the effective binary diffusion coefficient for $O_2$ in air in the cathode electrode. Neglect

the effect of water vapor $($consider only $O_2$ and $N_2)$ and assume the cathode electrode has a

porosity of $20\%$ and a tortuosity of $1\mathrm{.}5.$

$($e$)$ Calculate the limiting current density in the cathode given $=500m.$

$($f$)$ To complete your model, assume $c($the geometric constant in the concentration loss equation$)$

has a value of $0\mathrm{.}10V.$ Assume $i_{\text{l}\text{e}\text{a}\text{k}}=5m\frac{A}{c}{m}^2.$ Neglect all anode effects. Plot the three

overpotentials versus the current density.

$($g$)$ Plot the actual voltage and power density curves $($versus the current density$)$ for your model.

$($h$)$ What is the maximum power density for your simulated fuel cell? At what current density does

the power density maximum occur?

$($i$)$ Assuming $90\%$ fuel utilization, what is the total efficiency of your simulated fuel cell at the

maximum power density point? Final Answer :$42\%$