A SIMPLE ELECTRIC HEATER, WHICH HAS EFFICIENCY GREATER THAN 1

[George1]

Here is a continuation/variation of our previous post of October 18, 2020, 05:28:00. (Please look at besslerwheel.com/forum. Almost the same text in the related topic of the same title.)
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1) Let us assume again that the energy consumed by the standard water-splitting electrolyzer is just equal to the sum of (a) the Joule's heat and (b) the heat, generated by the burning/exploding of the released hydrogen. Therefore we can write down the equality
V x I x t = (I x I x R x t) + (Z x I x t x (HHV)) (1)
where
V = DC source voltage
I = DC current
R = Ohmic resistance
t = time
Z = electrochemical equivalent of hydrogen
HHV = higher heating value of hydrogen
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2) Let us decrease n times voltage V, that is,
V x I x t = (I x I x R x t) + (Z x I x t x (HHV)) (1) <=>
<=> (V/n) x (I/n) x t < ((I/n) x (I/n) x R x t) + (Z x (I/n) x t x (HHV)) (2)
where
n > 1
R = const.; for how to keep R constant please refer for example to our post of July 04, 2020, 01:38:09.
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3) Now let us increase n times voltage V, that is,
V x I x t = (I x I x R x t) + (Z x I x t x (HHV)) (1) <=>
<=> (nV) x (nI) x t > ((nI) x (nI) x R x t) + (Z x (nI) x t x (HHV)) (3)
where
n > 1
R = const.; for how to keep R constant please refer for example to our post of July 04, 2020, 01:38:09.
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4) In one word, it is evident that:
a) equality (1) shows that efficiency is equal to 1;
b) inequality (2) shows that efficiency is bigger than 1;
c) inequality (3) shows that efficiency is smaller than 1.
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5) Therefore by regulating the value of V we can regulate and control the value of efficiency. In other words, efficiency can be either (a) bigger than 1 or (b) equal to 1 or (c) smaller than 1. And this depends on the value of V.
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6) let us remind again that in order to be more precise we have to use V - v instead of V and I - i instead of I, respectively. (For v and i please refer to our previous post of October 18, 2020, 05:28:00.) But if V (and V/n too!) is much bigger than v (and I (and I/n too!) much bigger than i, respectively), then v and i can be neglected and therefore (1), (2) and (3) are perfectly correct.
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7) In one word, we proved theoretically again that the law of conservation of energy is not always valid for any standard DC water-splitting electrolysis process.
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The above theoretical considerations seem to be correct, don't they? What is your opinion? Please share it, if possible.
Looking forward to your answer.
George1

[George1]

Deep silence again? What happens here? How much time will it take for a simple obvious truth to win public recognition? 

[Thaelin]

This is in jest of course but I do have a over unity heater in my apt right now. It mines ETC and keeps my apt at or above 83 degrees. At this moment it is returning a profit of $122 per month.  I do no work for it other than watch. Nice heater huh?
thay

[Floor]

@George1

I don't think that you, your self, actually belive this is over unity.

Other wise, I think you would have shown us some  experimental proof.

Please build an over unity water heater, and show us the measurements and methods.

[kolbacict]

Unfortunately, they don't answer me  often too. so me have been to check the various assumptions yourself.