Nafion membrane, a commercial product of DuPont, is most commonly used as Nafion membrane, a commercial product of DuPont, is most commonly used as electrolyte in proton

exchange membrane fuel cells $($PEMFCs$)$ with hydrogen and air. The proton conductivity of Nafion

membrane was reported as follows. $($Note that the exponential applies to the square$-$bracket only,

and the last term $(0\mathrm{.}005139-0\mathrm{.}00326)$ is outside of the exponential.$)$

${}_e(\frac{S}{c}m)=$exp$[1268(\frac{1}{303}-\frac{1}{T})](0\mathrm{.}005139-0\mathrm{.}00326)$

where ${}_e$ is the proton conductivity in $\frac{S}{c}m,T$ is the temperature in Kelvin, and $$ is the water

content $($you will learn more about water content later in this course$).$ The water content $$ varies

from $0$ in the completely dry condition to $14$ in the wet $($fully saturated$)$ condition.

For part $(1)$ and part $(2),$ use a computer software of your favorite $($MS$-$Excel, Matlab, Mathe$-$

matica, etc.$)$ and export your plots as the image files $($such as JPEG, PNG$,$ PDF$,$ etc.$).$

Make $($and properly format$)$ a plot of the proton conductivity change $($in vertical axis$)$ with

temperature $($in horizontal axis$)303KT363K$ when $=5$ and $=14($two lines in

one plot$).$ Try to make professional$-$looking plot that can be used in an official report or

publications.

Make $($and properly format$)$ a plot of the proton conductivity change $($in vertical axis$)$ with

water content $($in horizontal axis$)314$ when $T=353K.$ Try to make professional$-$

looking plot that can be used in an official report or publications.

At the temperature $T=353K$ and water content $=12,$ how much is the proton conductivity

of this membrane in $\frac{S}{c}m?$

If you use the membrane with $10cm10cm=100c{m}^2$ area and $50m$ thickness $($see the

figure$),$ how much is the resistance across the membrane at the condition above?

If $i=1\frac{A}{c}{m}^2$ of ionic current density is passing through the membrane at the condition

above, how much is the voltage drop across the membrane due to the ohm's law?electrolyte in proton

exchange membrane fuel cells $($PEMFCs$)$ with hydrogen and air. The proton conductivity of Nafion

membrane was reported as follows. $($Note that the exponential applies to the square$-$bracket only,

and the last term $(0\mathrm{.}005139\backslash$lambda $0\mathrm{.}00326)$ is outside of the exponential.$)$