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Potential energy of water from electrolysis

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Could I please have help with something: If I generated hydrogen via electrolysis from water, sent it high up a long tube then converted it back to water (via a cell or motor to reclaim energy) then, taking into account inefficiencies (or assume no energy loss), where does the energy come from to give the potential energy from? I can't work this out from applying gas laws (eg PV=nRt)and force/work/mass and buoyancy relationships. Please help. Thank you.

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