Do you agree the mathematical expression for molar rate of D2O vapor in a electrolytic cell is correct or not?

Mv / (Mv+Md+Mo) = P / P' .................................... (1)

Please, I just proved mathematically that this is perfectly correct.

Do you really not understand the math?

I tried to make the math as clear as possible. Is there anything more I need to explain in my details?

Read my comment once more and ask any question you would like

I had already told you (1) that "*In your math, you repeated what I had already explained in my last jpeg, so no problem believing you, but this only applies to the vapor that saturates the gas bubbles produced by electrolysis.*"

You see? I too try to write as clear as possible. But, just in case, I try to explain what it means with other words.

It means that I believe in all your equations from [1] to [4] (*), but only if they are correctly applied for calculating the sensible and latent heat carried away by the vapor that saturates the electrolytic gas, which doesn't include the vapor produced by direct boiling.

(*) I use the square brackets to distinguish equations from links

Ascoli, please remember that the energy input in an electrolytic cell IS electricity.

Electricity provides the energy both to heat the water AND to produce electrolytic gas.

And electrolyte is the resistor where some of the electric energy is lost as heat.

Are you of the opinion that there are other energy sources than electricity that produced the bubbles ?

But of course is we have some excess heat produced by LENR then...

No, I'm of the opinion that, near or at boiling, the heat from electricity, which is the only form of energy required to explain the results reported in the 1992 paper (and IMO in all the other LENR reports), is mainly removed by the latent heat associated to the steam generated by **two completely different mechanisms**: (a) the **saturation of the gas bubbles** produced by electrolysis and (b) the vapor bubbles produced by **direct boiling** on the hot surfaces of the electrodes, the latter being by far the most important. The "*Enthalpy content of the gas stream*" term in the calorimeter model described in equation [1] of (2), as well as in Appendix 3 of (3), accounts only for the enthalpy carried away by the vapor produced by the first mechanism.

If you replaced the cathode with a resistor and the Anode with a resistor, you would still run current through the electrolyte, and (4) would work.

If you replace the anode and cathode with single resistive heating, there would be no current going through the electrolyte and (4) would be zero BECAUSE (4) is developed for an electrolytic cell NOT for pure resistive heating.

I was talking about the second case, of course, and you confirm that your equation [4] can't accounts for the vapor produced by Joule heating. You should remember that at boiling conditions, most of the electric energy is dissipated by Joule effect in the electrolyte and in the electrodes.

Please note that the formula for total molar rate of D2O vapor rate -

Mv= (3/4) * (I/F) * P / (P'-P) ..................................... (3)

Gives very differenet results at 40 degC and at 80 degC. Why? Because the vapor pressure P increase from 10 kPa to 50 kPa over the temperature range.

I know, but this variation has nothing to do with boiling. Consider these two opposite situations:

A) when cell temperature increases from 40°C to 60°C the vapor content in gas bubbles triples (the saturation pressure goes from 78.5 mbar to 245 mbar), but in both cases there is no boiling at all;

B) at boiling condition, if the cell voltage (V) increases by 10%, the current (I) also increases by 10%, it means that the gas stream increases by 10% and hence the vapor carried away by them increases by 10%. However, the electric power (V*I) dissipated inside the cell increases by 21% and, since the water is already at his maximum temperature, all this extra power should be removed by increasing the total vapor flux by 21%.

Do you see why the vapor produced by these two mechanisms (the saturation of the electrolytic bubbles and the direct boiling) are completely decoupled?

(1) F&P's experiments – 30 years after CF announcement

(2) https://www.lenr-canr.org/acrobat/Fleischmancalorimetra.pdf

(3) https://www.lenr-canr.org/acrobat/Fleischmancalorimetr.pdf