Use the test $i-V$ data for a $5-$cell PEM fuel cell stack are given in Table $1,$ with its single cell information

provided in Table $2,$ to answer the Problems $1$ to $2$:

Table $1$ Five$-$cell stack test

Table $2$ Single cell information

Determine:

$(1)$ The maximum power output per unit area of the fuel cell stack, in $\frac{W}{m^2}.$

$(2)$ The limit current density, in $m\frac{A}{c}{m}^2,$

$(3)$ Find the number of individual parts needed to make this $5-$cell stack, and then evaluate the total expense for

manufacturing it$.$

$(4)$ If the operating voltage is selected to be $3\mathrm{.}3V,$ evaluate the power density of the stack, in $\frac{W}{m^3}.$