Jules Verne's Flaws

A lithium-ion battery stores 160Wh/Kg, see http://www.electronics-lab.com/articles/Li_Ion_reconstruct/. The electric power required to electrolyze hydrogen equivalent in energy content to 1.04 US gallons of gasoline is about 33 kWh, assuming perfect efficiency, see http://www.stardrivedevice.com/electrolysis.html and http://www.hionsolar.com/n-heq1.html. The resulting quantity of gas has an energy content of about 38 kWh (137 MJ), see Gasoline#Energy_content (note that this is more than the energy that was input, which is not possible according to the laws of conservation of energy--as noted above the estimate for the energy required to electrolyze the water assumed 100% efficiency, which is not realistic). The energy required to heat hydrogen is 14.3 joules per gram per degree, see Specific_heat#Heat_capacity. The total energy stored in 300 Kg of lithium-ion batteries would be about 48kWh, which could theoretically electrolyze hydrogen containing 55 kWh (198 MJ). This would be sufficient to heat about 275 kilos of hydrogen by 50 degrees. The specific volume of hydrogen is about 12 m3/Kg at 1 atmosphere and 20 degrees, see http://www1.eere.energy.gov/hydrogenandfuelcells/tech_validation/pdfs/fcm01r0.pdf. The balloon described by Verne had a volume of 90 thousand cubic feet (2548 m3), see chapter 7 of his book. So it would require about 212 Kg of hydrogen to fill the balloon completely; Verne states that the hydrogen weighed about 125 Kg, which is consistent with starting with a balloon that was only half-full, in order to allow for expansion. Given that the energy contained in the battery could only heat the 125 Kg of hydrogen by 50 degrees twice, it is clear that there was nowhere near enough energy in the battery to sustain a five week flight, and this because the gas would cool over time and would need to be heated many times over (not to mention the fact that Verne states that the hydrogen was heated by more than 100 degrees more than once--again, well beyond the capacity of even a modern high-performance battery).