# Advanced Math A bipolar alkaline water electrolyzer stack module comprises 160 electrolytic cells that have an effective cell area of 2 m^2. At nominal operation, the current density for a single cell of the electrolyzer stack is 0.40 A/cm^2. The nominal operating temperature of the water electrolyzer stack is 70^circ C and pressure 1 bar. The voltage over a single electrolytic cell is 1.96 V at nominal load and 1.78 V at 50% of nominal load. The Faraday efficiency of the water electrolyzer stack is 95% at nominal current density, but at 50% of nominal load, the Faraday efficiency decreases to 80%. (Give your answer to at least three significant digits.) Calculate the nominal stack voltage: Answer in V Calculate the nominal stack current: Answer in A Calculate the nominal power on t

Question
Upper Level Math
A bipolar alkaline water electrolyzer stack module comprises 160 electrolytic cells that have an effective cell area of $$\displaystyle{2}{m}^{{2}}$$. At nominal operation, the current density for a single cell of the electrolyzer stack is 0.40 $$\displaystyle\frac{{A}}{{c}}{m}^{{2}}$$. The nominal operating temperature of the water electrolyzer stack is $$\displaystyle{70}^{\circ}$$ C and pressure 1 bar. The voltage over a single electrolytic cell is 1.96 V at nominal load and 1.78 V at 50% of nominal load. The Faraday efficiency of the water electrolyzer stack is 95% at nominal current density, but at 50% of nominal load, the Faraday efficiency decreases to 80%.
Calculate the nominal stack voltage:
Calculate the nominal stack current:
Calculate the nominal power on the water electrolyzer stack:

2020-11-17
Step 1
given
nominal cell potential =1.96 V
number of cell =160
$$\displaystyle{c}{u}{r}{r}{e}{n}{t}{d}{e}{n}{s}{i}{t}{y}={0.40}\frac{{A}}{{c}}{m}^{{2}}={0.40}{x}×{10}^{{4}}\frac{{A}}{{m}^{{2}}}$$
$$\displaystyle{c}{e}{l}{l}{a}{c}{t}{i}{v}{e}{a}{r}{e}{a}={2}{m}^{{2}}$$
Step 2
Explanation
formula for finding
$$\displaystyle{n}{o}\min{a}{l}{s}{t}{a}{c}{k}{v}{o}{<}{a}\ge={n}{o}\min{a}{l}{c}{e}{l}{l}{p}{o}{t}{e}{n}{t}{i}{a}{l}\times\nu{m}{b}{e}{r}{o}{f}{c}{e}{l}{l}{s}$$</span>
substitute the values
$$\displaystyle{n}{o}\min{a}{l}{s}{t}{a}{c}{k}{v}{o}{<}{a}\ge={1.96}{V}\times{160}{n}{o}\min{a}{l}{s}{t}{a}{c}{k}{v}{o}{<}{a}\ge={313.6}{V}$$</span>
formula for finding
$$\displaystyle{n}{o}\min{a}{l}{s}{t}{a}{c}{k}{c}{u}{r}{r}{e}{n}{t}={c}{u}{r}{r}{e}{n}{t}{d}{e}{n}{s}{i}{t}{y}\times{c}{e}{l}{l}{a}{v}{t}{i}{c}{e}{a}{r}{e}{a}$$
substitute the values
Step 3
$$\displaystyle{n}{o}\min{a}{l}{s}{t}{a}{c}{k}{c}{u}{r}{r}{e}{n}{t}={\left({0.40}×{10}^{{4}}\frac{{A}}{{m}^{{2}}}\right)}×{2}{m}^{{2}}$$ nominal stack current=8000 A
formula for finding
$$\displaystyle{n}{o}\min{a}{l}{p}{o}{w}{e}{r}{o}{n}{t}{h}{e}{w}{a}{t}{e}{r}{s}{t}{a}{c}{k}={n}{o}\min{a}{l}{v}{o}{<}{a}\ge\times{n}{o}\min{a}{l}{c}{u}{r}{r}{e}{n}{t}$$</span>
substitute the values
$$\displaystyle{n}{o}\min{a}{l}{p}{o}{w}{e}{r}{o}{n}{t}{h}{e}{w}{a}{t}{e}{r}{s}{t}{a}{c}{k}={313.6}{V}\times{8000}{A}={2508.8}{K}{W}$$

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