Hydrogen is usually produced from water by a high-temperature catalytic reaction or by electrolysis. A 100% efficient electrolytic plant would require about 34,000 kcal of electric energy to produce 1 kg of hydrogen.

An automobile engine can be modified to operate on hydrogen instead of gasoline. the amount of energy received by the engine upon burning 1 kg of hydrogen is about 34,000 kcal, but only 40% of this energy is converted by the engine into motive power.

(a) Assuming a 50% efficient electrolytic plant driven by electricity produced by the local utility with a 35% efficient nuclear power plant, what fraction of the nuclear power is finally converted into motive power by the hydrogen engine?

(b) Is it correct to view hydrogen as an energy “source” in the same sense as we view coal and oil as energy sources?

(c) If electricity for the 50% efficient electrolytic production of hydrogen comes from 10% efficient photovoltaic solar cells in a region where the insolation is 4 kWh/m2 per day, what cell area (in square meters) is required to produce sufficient hydrogen to drive the car 500 km per week?

(d) Assume a capital investment of $1100 per kilowatt of electric power produced by the nuclear power plant, and $300 per kilowatt of electric power consumed by the electrolytic hydrogen plant; a yearly cost (except fuel cost) of 25% of the investment; a nuclear fuel cost of 0.6 cent/kWh; and the energy conversion efficiencies specified in part (a). What is the cost (in cents/kWh) of producing hydrogen if the nuclear and electrolytic plants are operated for 8000 h/yr?

(e) Repeat part (d) assuming that the electrolytic plant is operated only for 3000 h/yr corresponding to the periods of low electric power demand. Accordingly, only three-eighths of the nonfuel cost of the nuclear plant should be allocated to the hydrogen production. Compare your results in parts (d) and (e) with a cost of gasoline about 8 cents/kWh.