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

$(1)$ Assume that every single cell of the PEMFC stack is steadily operated at $80C$ and the water product is in

gaseous phase, determine its ideal $($reversible$)$ open circuit voltage $(V_{\text{i}\text{d}\text{e}\text{a}\text{l}})$ and the efficiency limit of a single

cell.

$(2)$ Find the cell operational open circuit voltage $(V_{oc}),$ in $V,$ based on the data given in Table $1.$

$(3)$ Estimate the overpotential caused by the internal current or the fuel crossover for a single cell, in V$.$

$(4)$ One way of measuring the internal current and the fuel crossover is to measure the consumption of

reactant gases at open circuit. For the PEMFC stack described herein, determine the stack open circuit

consumption of hydrogen fuel.

$[$Hint: stack operational open circuit voltage No$.$ of cells