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If you do the physics, you loose more energy than you gain. The are losses in energy conversion, mechanical to electrical energy (alternator/belt - heat) and electrical-chemical losses in electrolysis (breaking the H and O bonds in the water). Accurately accounting for these conversion losses will show that you have no gain. Currently there is no way of invalidating the laws of thermodynamics, it would be nice to produce a perpetual motion machine out of my Yaris. If you can get the hydrogen for free you may have something - perhaps as a waste product from manufacturing. Perhaps I should get some chickens and use the poop to generate methane and bottle it to run my car, as I side product I get fresh eggs and meat. Blast, I still have to buy the chicken feed.
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