A tall tube, height h, stands in a pool of water. An electric current is used
to electrolyse the water; suppose a mass m moles of water is electrolysed every second.
The current required to do this is mF amps, where F is the number of coulombs of charge
required to split up one mole of water.
The electrolysis produces oxygen, which we release to the atmosphere, and hydrogen, which
we allow to diffuse up the tube. At the top of the tube we burn it, forming water.
This water has potential energy mgh, where g is the acceleration due to gravity.
To obtain this potential energy, we allow the water to fall, turning a dynamo to
produce electricity. Suppose the dynamo converts the energy of the water to
electrical energy with an efficiency 
.
Now, comparing the energy produced with the energy consumed, these are in the
ratio 
. g is fixed by the fact that we're on earth, F is fixed
by chemistry, 
is the best efficiency we can get from a dynamo, about
. So we can just increase h until this ratio is greater than 1, and we will
then have a device that produces a net profit. There is no pollution and no depletion
of valuable resources.
Comment on the feasibility of this device.