I'm pretty sure you're mistaken. The battery you describe violates the Second Law of Thermodynamics (no system can ever be 100% efficient). Both batteries and f

I'm pretty sure you're mistaken. The battery you describe violates the Second Law of Thermodynamics (no system can ever be 100% efficient). Both batteries and fuel cells (and any other open physical system) will lose some energy as waste heat in doing their work (producing electricity).