Why does gas from an electrolytic cell underwater provide work as it rises?

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imhungry
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A friend has asked a question of me that has me wishing that my days of thermodynamics were not so long in the past. He and some colleagues have been making electrolytic cells for high production of hydrogen and oxygen from water. In demonstrating one to me he posed an experiment that on the surface seems to produce free energy, which we all know is impossible.

They have tested the cell under pressure and found that it's gas production and the amount of electricity used are no different than at normal atmospheric pressure. He proposed the following setup. Place the electrolytic cell 30 meters under the water (or what ever, the depth does not matter). Flip the switch and hydrogen and oxygen are produced , no surprise there. The energy content of the gasses is not the issue. The gasses can also provide work when they rise to the surface. The amount of gas produced and the amount of electricity used depth is the same as produced at the surface so that part of the equation is a wash. The work provided by placing the cell beneath water and harnessing energy from the rising gas is the part that I cannot account for.

What am I missing?
 

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Hi imhungry, welcome to PF!

With respect to your colleague, I question the claim that gas production was not decreased under higher pressure. Higher pressure should shift the reaction equilibrium and require more voltage, as we know from thermo. Is it possible that decreased gas production or higher required voltage was not detectable within error at the pressure they tried? Was the testing pressure 2 atm or 1000 atm, for example?
 
Thanks Mapes,

I don't know what pressures he tested at but your response is in line with my first thoughts on the issue. My guess is that his tests were at low (a few atmospheres) levels. I will "pressure" him into giving more details.
 
I would be curious to know how easy electrolysis becomes if the pressure is just above the vapor pressure.