Figuring out electrolysis at higher temps and pressures

[Ronin2004]

Ok so I am working my way around fuel cell technology and i was trying to see the energy requirements for the breaking of the water into hyrdogen and oxygen. I was looking at http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/electrol.html
and it outlines the thermodynamic process for the amount of energy that is required to convert water to hydrogen and Oxygen but that's only at stp The question I have is how do you caclulate the energy requirements if you have different temps and pressures.

I am looking up thermo tables and I get a enthapy for water at various pressures and temps but the problem I am having is finding the entropy of H2 and O2 at the same temps and pressures all i can find is STP entropy. Is there an way to find the values instead of doing the intergration of Dq/T.

And is caclulating the the gibs free energy the best way to see how much work is required to split water
G=H-TS

 

[carmatic]

with regards to the entropy of hydrogen and oxygen gas at different temperatures and pressures... can you not treat them as ideal gasses to calculate the entropy value at your temperature and pressure?

 

[Ronin2004]

Yeah i think that might work if i hold Volume to be a constant but pouring through my thermo textbook i found this formula

S2 - S1 = Cp * ln ( T2 / T1) - R * ln ( p2 / p1)

so this will give me a change in entropy related to a temp and pressure. I can now get enthalpy at various temps and pressures using this formula.

dH=Cp*dT

Now given that i can look up Cp of ideal gases in thermo tables and i can get both H values and S values. What does i use for the second temperature and pressure. When we try eletrolysis at higher temps and pressures does They hydrogen and Oxygen released at same temp and pressure or does it go stp

Is using gibs free energy a good way of calculating the energy needed to split water
dG=dH-Tds

 

[izzyadonai]

don't fuel cells bond hydrogen and oxygen rather than disassociate them?
are you thinking of a way to recycle the water produced by the cell?

 

[carmatic]

hmm, the temperature change upon electrolysis is a good question...

is it not true that the gibbs free energy is what splits the water molecule, while the rest of the energy you put in is turned into heat in the system?

its been awhile since i last did thermodynamics, so I am more than a little unpracticed in these things by now

 

[Ronin2004]

Yeah I am pretty sure that is it. Gibbs free Energy is the total energy used. Usually You just Use Enthalpy to determine the change but the TdS is the thermal energy from the reaction. So the higher the temp the higher the TdS which means the less energy needed from the enthalpy which is usually your voltage source. So if it was hot enough it would require no energy and water would just naturally split. But if H and S are both functions of Temperature then how do I calculate them. I think I can Use the formula

dS=S(T2)-S(T1)-R LN(P2/P1)
where S(t) is from the tables and is the change of entropy at different temps but one atm