Infinite Energy With Fuel Cells?

[NanakiXIII]

I've got a problem. I tried to see what would happen when putting a fuel cell and electrolysis in a circle. I end up with infinite energy, so I must be doing something wrong.

Electrolysis

4 H2O -> 4 H+ + 4 OH-
4 H+ + 4 e- -> 4 H -> 2 H2 || The H2 is lead to the fuel cell anode
4 OH- -> O2 + 2 H2O + 4 e- || The O2 is lead to the fuel cell cathode, the electrons continue down the circuit to the fuel cell cathode

The electrons complete the circuit

Fuel Cell

2 H2 -> 4 H+ + 4 e- || The electrons are lead to the external circuit - electrolysis
4 H+ + 4 e- + O2 -> 2 H2O + heat || The circle is complete, the water can be lead to be electrolysed again


Now that all works out, you have an infinite circle with no particular use. Or do you? Where the protons, electrons and oxygen reunite into water, heat is produced. Thus you have infinite heat. Not possible, I'd think. What am I missing?

 

[Gokul43201]

What about the work done in electrolysing water in the first place ?

You need to apply some potential difference V, and drive some current I. You are doing work at a rate of VI per second.

 

[mrjeffy321]

the efficency of electrolysizing water into hydrogen and oxygen gas is roughly 50% I think, also, the efficency of a fuel cell taking that gas and recombining it into water is only about 50% aswell.
so if you start out giving it a certain amount of energy to start it off, after each cycle, there is only 1/4 of the previous total left (50% of 50%). it won't take long for the amount of energy remaining to be less than what is needed to break the water apart, so the cycle will stop. the problem is all the heat loss, both in electrolysis and in the fuel cell, energy, in the form of heat, is lost and unless you keep replenishing it, everything will come to a stop.

 

[NanakiXIII]

I see, thanks.