A SIMPLE ELECTRIC HEATER, WHICH HAS EFFICIENCY GREATER THAN 1

[gyulasun]

Hi George,

You can do several manipulations on mathematical equations or inequalities as long as the math rules are observed. 
On manipulations I mean you can divide by, multiply by, add to or substract numbers from both sides, the equation symbol between both sides of the equation remains correct (or the inequality symbol does not change direction),  again this is so as long as the rules for doing the manipulations are not broken (like multiplying both sides of an inequality by say a negative number).  But you surely know these, the point is this:
You again returned to those equalities and inequalities, and I wrote which ones I think to be correct for characterizing the process. 

So I can again repeat, for the last time, that this is all that I can comment on your theoretical or hypothetical math questions. Please understand this. I will not consider your posts any more when you include such attempts.

By the way, how can you expect anybody here to give opinion, to interpret your experimental results which are not known? How can help be given?

What opinion can be given on the obvious: if the input DC voltage is decreased across a resistor, the input current also decreases proportionally ? (provided a liquid resistor remains pretty closely linear in its electrical conductivity behaviour which let's suppose can be maintained).   So what?

Gyula

[George1]

Hi Gyula,
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1) You are right, of course. I will not argue with you -- experiments have to confirm theory -- no doubt about this.
2) At the same time however in our previous posts we use simple formulas, (a) which are based on experimental facts and (b) which have been working successfully for 200 years. And simple mathematical operations (not manipulations -- we would not agree with this definition) with these simple formulas unambiguously show that under certain conditions standard water-splitting electrolysis has COP > 1. That's all. Simple and clear.
3) We keep performing experiments.

George

     
 
 

[gyulasun]

Hi George,

Yes the word 'operation' is better to use here than 'manipulation' when dealing with mathematical equations or inequalities etc.  Mathematics has its own special technical terms and my word selection was not fortunate.

And I did not mean using 'manipulate' negatively (it certainly has a negative meaning too) but if you look it up in big dictionaries, it has the 'handle' or even the 'edit' meanings too. 

Good luck in performing the experiments, it surely takes time and no need for any hurry. 

Gyula

[George1]

Hi Gyula.
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Thank you for your reply. And thank you for your good will and patience. You are a real friend.
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Now let me report what we have done until now.
We found a bunch of several identical PEM water-splitting electrolyzers at a distance of 500 km from the place we live. The related manufacturer was again Proton Onsite.
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Most important specifications of this type of electrolyzer are as follows.
Name: C10 Hydrogen Generation System.
Power consumption rate: 68.9 kWh/kg.
Water consumption rate: 9L/hr.
Electrical supply: 342 to 456 VAC, 3 Phase, 50 Hz.
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And here is our step-by-step experimental procedure.
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1) We tested one single electrolyzer. The voltage applied was 400 VAC, 3 Phase, 50 Hz. The experimental results coincide in general with the above mentioned specifications.
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2) We connected two electrolyzers in parallel. After that we connected another two electrolyzers in parallel too. After that we connected in series these two couples of connected-in-parallel electrolyzers (we used long wires of big cross-section, because the electrolyzers were situated in different rooms) thus forming a series-parallel circuit consisting of four identical  electrolyzers.
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3) The voltage applied to the circuit was again 400 VAC, 3 Phase, 50 Hz. The test results were as follows.
3A) Power consumption rate: 68.9 kWh/2 kg.
3B) Water consumption rate: 18 L/hr.

4) And here is what we get for COP.
4A) 68.9 kWh/kg = 248040000 J/kg and LHV of hydrogen = 120000000 J/kg.
4B) Joule's heat = 248040000 - 120000000 = 128040000 J. ( This equality is assumed to be true according to your requirements.)
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4C) COP for the single-electrolyzer case (item 1) is given by:
COP = (128040000 + 120000000)/(248040000) = 1.
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4D) COP for the four-electrolyzers-circuit case (items 2 and 3) is given by:
COP =  (4 x ((128040000/4) + (120000000/2)))/(248040000) = 2 > 1.
Note 1. Hydrogen generation. Each single electrolyzer generated 0.5 kg/hr and the four electrolyzers generated together 2 kg/hr.
Note 2. Cooling agent consumption. The cooling agent consumption rate for each single electrolyzer decreased 4 times. But the electrolyzers were 4 (four) in number and thus the cooling agent consumption rate remained the same.
Note 3. Water consumption. Each electrolyzer consumed 4.5 L/hr but the electrolyzers were four in number and consumed together 18 L/hr.
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(Only please don't ask me how did we manage to perform all the above described experiments. It costed us a lot of money, time and effort. Three members of our team (two colleagues and I) had to cover several times a distance of of 500 km (back and forth) in order to carry out the tests. Fortunately, part of our travelling group was the mentioned-in-my-previous-posts retired Hogen 6m operator who helped us a lot by using his contacts and his technology skills.)
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So it is as if evident that whatever to do the water-splitting electrolysis has always COP > 1.
Looking forward to your answer.

George





 

[gyulasun]

Hi George,

You again ask me to comment on test results you wrote in the above post. The problem is I can see test results again which are lacking a few simple additions like I indicated in my Reply #90 for your previous test results in your Reply #87. 

Putting this otherwise,  in fact, you did not include any convincing  'proof'  other than text and readers here have no way of checking them unless they perform such test themselves. 

Please do not get offended, it is not my intention to offend anyone, just read through my Reply #90 and think it over what simple questions I posed in it back then which did not turn out from the experimental results and you still have not reflected on them, probably never will because back then you attempted again to come along with doing the mathematical operations on the equations and inequalities.   

Please understand that it is not me to whom you would need to prove the COP > 1 result with measurements, I am not an 'authority',  just a person with a certain scientific background and common sense.

It looks like nobody else is interested in this topic and I consider withdrawing too.  I am simply running out of patience towards this thread, it has been enough.  I really wish you good luck to be able to design and actually build a practical electric heater which measurably produces a COP > 1 result. 

Gyula