As described the experiment has ~7g of tungsten, AMU 184.
So we have 7/184 = 0.04 Mol. That does not include the electrode, which is also tungsten, 1.6mm diameter, say 5cm long? Tunssten density is 20g/cc. We have are 2 sq mm = 0.02 cc^2 area, so total volume of 0.1cc => an extra 2g. So ignore this.
There is also a stainless steel mesh anode. Ignore possible reactions with this (though maybe we should not). It could release energy reacting with the electrolyte.
At 180kJ/mol we have 7kJ released. Suppose we use 100W input, that would be equivalent to 70s.
So if the reaction lasts a minute at this power we have max COP of 2 from tungsten reacting. The instructions claim 90-240s reaction. So this chemical effect could provide a significant error, but not by itself COP of 4.
[I have no idea what the correct enthalpy is for Tungsten in this experiment. It looks to me as though it would form Tungstate ions in the aqueous solution. I'll believe giorgio 180kCal/mol with reservations.]
However we have some other sources of error.
The power out is calibrated by looking at the temperature vs time curve for the cell with no current and initially hot electrolyte.
We have differences between heat loss (evaporation and convection followed by conduction to walls) in the two cases. for example what if the current causes small bubbles to cling to the walls of the container so partially insulating it?
The power in is calculated from DC current and voltage produced by rectifying mains. Let us suppose the cell looks like a resistive load. Pirelli says that he calculates:
P = Vdc * Idc.
However the voltage and current here will be average values =
peak value * (2 / pi)
Power will be average of the two waveforms multiplied
peak value * (1/2)
So the power input will be Vmeasured*Imeasured*(4/pi)
Actually this is overestimating input power by 30%, so his COP of 4 would in fact be COP of 5 or so.
This analysis assumes the cell looks like a resistive load.
In the case there is some nonlinear effect increasing current at higher voltage we could worse case get a very spiky current waveform with P ~ Vpeak * Iav. In that case we have
P = Vdc*Idc*(pi/2).
This underestimates the input power by a factor of 1.6, making calculated COP of 4 only 2.5.
One more error. If the voltage and current values are very variable a DC meter may give completely the wrong answer.
The errors here are potentially so large we need to use a proper power meter measurement, and log the results for proper integration.
That is all I can think of initially.
One other thought. I bet the COP quoted of 4 is the maximum value over the 90s etc run. In which case average COP though the run would be lower.
So here is what
real LENR people should do. Run the experiment as shown here carefully:
Work out average COP.
Then try to bound, or control for, the other errors.
Using a proper power meter would help.
Running calibreation after the run to see if it has changed would help.
Bounding chemical energy more properly would help.
That is only an initial set of possible errors, and I am no calorimetry expert. I would very much like to see LENR people do at least these (obvious) things.
Best wishes, Tom
Giorgio wrote:I gave it a quick look, no time to go into details.
It looks to me like they did not account for any chemical side process inside the cell.
Namely Tungsten to different Tungsten oxides will give you an average of 180 Kcal/mol. More than enough to justify the extra heat.
I applaud their effort and their openness in publishing all the details but I am afraid this experiment will not stand a more accurate replication.
Still it is great to see students and teachers getting involved in these type of experiments, especially in a country like Italy where this is absolutely uncommon.
Even if they did not discover a cold fusion route it will be an invaluable lesson for all of them on how science should work and how scientific research is able to self-correct when all the details of an experiment are openly published.
Double thumbs up to everyone involved! Back to china work now.