A simple electric heater, which has efficiency greater than 1

[ME]

Actually you claim that the above three are not in accordance with standard mathematics?

I implied that it is not in accordance with practical application.
You need some energy to generate some hydrogen...
It may be generated fast, it may be generated slow. You may have used high currents or a lower one.
In the end, you have some amount of hydrogen.
That amount just has potential in relation to the lower aquadic state

Separating hydrogen from oxygen is like separating a ball from the ground.
You may do it fast or slow. You may kick it upwards, or tow it upward.
However, in the end that ball has some fixed Gravitational potential in relation to the ground, no matter the method or speed it got up there.

Thus, duration and the exact current you used to generate that amount of hydrogen is of no consequence for the amount of potential it finally has. Perhaps only for the amount of hydrogen that came out of electrolysis, but that's the actual efficiency-factor.
So that's my clarification for why I wrote what I wrote.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Now for something completely different.
You suggest that you performed an operation according to a pure "mathematical standard"?
Well in that case there's something else to remark.

For some unknown reason you multiply some "efficiency" 'n' with some of the parameters... why?
The standard mathematical way, without knowing that "why", is that the left-side of the equal-sign should receive the same treatment as the right of the equal-side... because.... it's a mathematical equation.

So let's have a mathematical look at the left-side, and simply assume the practical validity of that whole expression.
On the left you divide the voltage by 'n', and the current by 'n'.
Thus "V x I x t" becomes "(V/n) x (I/n) x t"
In effect you divide by n².
On the right side you only do it partially for the factor where you rewrote with Ohm's-law: "I x R x t / n²"
But the added "Z x I x t x (HHV)"-part only gets divided by 'n'. It misses another division by 'n'.
We can cross-out "(I/n)xt" on all factors thus:
- either your 'Z" needs to be divided by 'n' - indicating a lesser production of hydrogen,...
... or your 'HHV' needs to be divided by 'n' - indicating a lesser heating value, ...
... or both 'Z' as 'HHV' needs to be divided by the √n - indicating a lesser value for both.

[George1]

To ME.
--------------------------------
Good answer! Pleasure to discuss the topic with you.
I am answering immediately your question.
--------------------------------
1) If R=const, if Ohm's law is correct and if we decrease V n times, then this automatically leads to decreasing of I n times too. That's how is generated this n².
---------------------------------
2) Z=const. by definition and it can be neither decreased nor increased.
---------------------------------
3) You would understand easier my last post if you have read carefully and thoroughly my post of Sun Oct 18, 2020, 3:13 pm. (Please read carefully and entirely my posts, if possible. Otherwise I have to repeat one and same things several times.) For your convenience I am giving below the text of the post of Sun Oct 18, 2020, 3:13 pm. The post's text is surrounded/limited up and down by double dashed lines.
====================
Ok, let us assume for a moment that Tarsier79 is right, that is, let us assume 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
Therefore we can write down the inequalities
V x I x t > I x I x R x t (2) <=> V > I x R (3) <=> V/R > I (4).
-----------------------
The last inequality (4) unambiguously shows that Ohm's law is not valid for liquid resistors.
----------------------
The above considerations are not very precise however. In order to be precise enough we have to introduce the quantities v an i. In other words, we must write down the equality
(V - v) x (I - i) x t = ((I - i) x (I - i) x R x t)+(Z x (I - i) x t x (HHV)) (5)
where
V = DC source voltage
I = DC current
R = Ohmic resistance
t = time
Z = electrochemical equivalent of hydrogen
HHV = higher heating value of hydrogen
v = minimum voltage necessary for the water-splitting electrolysis to begin
i = the related small decreasing of current I, caused by the presence of v.
And from here we can write down the inequalities
(V - v) x (I - i) x t > (I - i) x (I - i) x R x t (6) <=>
<=> V - v > (I -i) x R (7) <=> (V - v)/R > I - i (8).
-----------------------------------------
The last inequality (8) shows again that Ohm's law is not valid for liquid resistors.
------------------------------------------
It is evident that if V is much bigger than v (and I much bigger than i, respectively), then v and i can be neglected and in this case inequality (8) can be replaced with inequality (4).
In one word, if equalities (1) and (5) are valid, then inequalities (4) and (8) are valid too. But this means that Ohm's law is not valid for liquid resistors.
----------------------------------------
Ohm's law is the most basic and most fundamental axiom of electric engineering. No Ohm's law -- no electric engineering.
==============================
Now everything seems to be clear, doesn't it?
Looking forward to your answer.

[Tarsier79]

Your basic math is flawed, and now you are expanding on it, all while claiming ohm's law is incorrect.

Everyone in the room is now dumber.... And may God have mercy on your soul.

[George1]

To Tarsier79.
-----------------------------------
1) You didn't take your medicine this morning. Please take it.
2) And do not involve God here. I am sure that you are not a Christian. It is evident for everyone here that you are an arrogant and aggressive atheist.

[Tarsier79]

It is from "Billy Madison", but highly relevant in this case.

Ok, let us assume for a moment that Tarsier79 is right, that is, let us assume 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)

For a start, I am right.

Secondly, the only way this equation works is if Z or HHV = 0.

That is because V x I x t = I x I x R x t + 0.

Perhaps when you pass core maths and move out of your mothers basement you might understand.

[ME]

I'm trying to find a reply that makes you gain the most insights while sipping my coffee.
You can add the little "v" and little "i", but that's of no consequence from a mathematical point of view...
I have to point out that to me the validity of this seems very far from electronics-relatity.
For me it's been a while, and it looks like Tarsier is still better equiped in handling this.
I also like to entertain my own curiosity.

Let me put that aside for a bit and let's look at the formulae again from a pure literal standpoint.
From a pure literal standpoint the three are totally different equations.
Not only are they different, but they are also mathematically wrong when we analyse it with "standard mathematics".

We start with the equations again and replace "(V-v)" with "&#916;V" and "(I-i)" with "&#916;I".
It makes it easier to read, and you can make little "v" and little "i" as big or small as you want.
Eq.1a. &#916;V x &#916;I x t = (&#916;I x &#916;I x R x t) + (Z x &#916;I x t x (HHV))
Eq.2a. &#916;V/n x &#916;I/n x t < (&#916;I/n x &#916;I/n) x R x t) + (Z x &#916;I/n x t x (HHV))
Eq.3a. n&#916;V x n&#916;I x t > (n&#916;I x n&#916;I x R x t) + (Z x n&#916;I x t x (HHV))

Let's analyze these by making the left-side of all three equal to eachother for easy comparison between these three.
Eq.1b. We use this one as the template
Eq.2b. We multiply by n²
Eq.3b. We divide by n²
- mathematically we are allowed to do this.

Now the equations are transformed to:
Eq.1c. &#916;V x &#916;I x t = (&#916;I x &#916;I x R x t) + (Z x &#916;I x t x (HHV))
Eq.2c. &#916;V x &#916;I x t < (&#916;I x &#916;I x R x t) + (Z x &#916;I x t x (HHV)) x n
Eq.3c. &#916;V x &#916;I x t > (&#916;I x &#916;I x R x t) + (Z x &#916;I x t x (HHV)) / n

Despite a common left side and an almost similar look at the right-side, we can easily see that these are actually all different equations!
We simplify & reduce the equations even further by dividing all factors by "&#916;I x t".
We get the following:

Eq.1d. &#916;V = &#916;I x R + Z x (HHV)
Eq.2d. &#916;V < &#916;I x R + Z x (HHV) x n
Eq.3d. &#916;V > &#916;I x R + Z x (HHV) / n

We can simplify & reduce the Equation again by converting things back with Ohm's law (V = I x R).
Does this work with delta-V too? Let's see: &#916;I x R = (I-i) x R = I x R - i * R = V - v
Also, there is no indication that the "V" on the left indicates anything else, so sure: "&#916;V = &#916;I x R"

Eq.1e. &#916;V = &#916;V + Z x (HHV)
Eq.2e. &#916;V < &#916;V + Z x (HHV) x n
Eq.3e. &#916;V > &#916;V + Z x (HHV) / n

Please note now, that we could deduce from the inequality signs that this "n" should actually be "<1"
This contradicts with your statement that "n>1", see this post: https://www.besslerwheel.com/forum/view ... 929#177929
Lucky you, this also indicates that the conclusion I made in my previous post will be reversed.
Before we get all tangled up in this "n", --because we still don't know why you arbitrarily multiply And divide by it--, let's continue and see where it leads:

Now according to "standard mathematics" we may simplify & reduce one last time by subtracting "&#916;V" from both sides:

Eq.1f. 0 = Z x (HHV)
Eq.2f. 0 < Z x (HHV) x n
Eq.3f. 0 > Z x (HHV) / n

For equation 1 to work, we can deduce that either/or Z=0, and/or (HHV)=0.
It implies that this factor "n" will actually have no meaning at all in those inequalities.
Therefore, Eq.2 and Eq.3 are mathematically false.

Note, mathematically making "n<0" may only seem to help Eq.2 but that invalidates the other two..

--
And I look at the following comments and notice that Tarsier comes to the same conclusion... now what?

[George1]

Let me explain again simple obviuos things. You are not reading carefully and thoroughly my posts and that's why you are distorting (either deliberately or not) my words.
-------------------------------------
1) V x I x t = (I x I x R x t) + (Z x I x t x (HHV)) (1). This is the law of conservation of energy. Do you accept the validity of this item 1? YES OR NO?
--------------------------------------
2) V = I x R (2). This is the Ohm's law. Do you accept the validity of this item 2? YES OR NO?
--------------------------------------
3) If equality (1) is correct, then the inequalty V x I x t > (I x I x R x t) (3) must be correct too. Do you accept the validity of this item 3? YES OR NO?
-------------------------------------
4) If we divide both sides of inequality (3) by (I x t), then we will get the inequality V > I x R (4). The latter is a severe violation of the Ohm's law and that is why it cannot be true. Do you accept the validity of this item 4? YES OR NO?
------------------------------------
5) Inequality (4) is directly related to (directly follows from) equality (1) and as inequality (4) cannot be true, then equality (1) cannot be true either. Do you accept the validity of this item 5? YES OR NO?
------------------------------------
You have to answer the question "YES OR NO?" five times.
------------------------------------
I am really shocked that I have to explain the basic axioms of electric engineering to people who pretend to be qualified. Tragedy!

[ME]

Well George, thanks for your projection but it appears you didn't understand my earlier reply at all.
It's purely what comes out of your own math.

1. No
2. Yes, it's defined
3. No, because of (2)
4. Yes, so you agree with my answer (3)
5. Yes, so you agree with my answer (1) and you are contradicting yourself;

You may be shocked, but you could also try to keep projections in check and explain those things you think are obvious. Just as I talked you through the math.

[Tarsier79]

Hi ME

From what I have read, you are perfectly qualified to answer George. He is trying to explain something with math. You are very adept at math. I enjoy it, but am not as competent as I would like to be. You know the old saying: "Use it or lose it".

[Tarsier79]

Arrogant, incompetent and delusional george

It seems your spectrum disorder disallows you to separate meanings from consecutive sentences. My hypothesis is based on your use of separated and numbered points, even though you seem to be unable to correctly relate between them. Let me try:

1. What you are trying to prove is not possible using the math you are trying to use.

2. Your mathematical model does not represent it's supposed real world application

3. Your mathematical dexterity is not as comprehensive as you would like to believe.

4. Your scientific method is flawed.

5. Your knowledge of the subject is limited.

6. You are unable to grasp any logical argument.

7. You are unable to comprehend how one idea or point relates to another.

[Tarsier79]

I have 2 dogs and a cat. One of my dogs has a chronic mental disorder. It is completely untrainable, unable to understand action and consequence (like shitting on the floor, having its nose rubbed in it, a tap on the nose and being put outside on the grass). It has the attention span of approx 1.5 seconds and is constantly on edge, believing everyone and everything are out to get it. Any sudden noise or movement could make it wet itself in fear. It is so unsociable, we have to lock it in a room whenever anyone comes over. It growls at and tries to attack any dog (or person) we walk past, even though they are 5 times its size, until they look like they are going to retaliate. It goes into alarm mode and starts barking at me if I walk into the house wearing sunglasses or a hat.

Kinda reminds me of someone.

[George1]

V x I x t = (I x I x R x t) + (Z x I x t x (HHV)) (1) <=> V x I x t > I x I x R x t (2) <=> V > I x R (3).
-----------------------------------------------------------------------------------------------------------------------
If some member of this forum rejects the validity of the above simple chain of simple mathematical expressions, then he/she has really a serious mental problem. He/she must urgently and immediately see his/her doctor.

[ME]

Later that day:

M: "Doctor, how can I possibly validate those mathematical expressions? Do I have a serious mental illness? Please doctor, what can I do?"

D: "Well, before we jump to conclusions what we need is an assessment first young man."

M: "Whatever you say Doc (what a weird sentence)"

D: "So can you give me an example of a simple mathematical expression?

M: "Sure, we can take Ohm's law"

D: "Isn't that Ee equals Pee times tee?"

M: "No that's Joules's law"

D: "Oh, what's the difference, and what do they have in common?"

M: "Well first, Watt's Law states that Power equals the amount of charge per second to overcome a voltage potential difference, or P=U·Q/t."
M: "Ohm's Law states that this amount of charge per second equals that potential difference over some resistance, or I=U/R."

D: "Uh, ok.. en Joules?"

M: "We can combine these with Joule's Law"

D: "eeh, and what's that then?"

M: "Well, the amount of heat produced, or work, equals the amount of generated power for some duration, W = P·t"
M: "We can expand this by substitution with Watt's law and state that W = U·I·t, Of course everyone knows that Q/t is the Amperage in units Coulombs per second"
M: "We can expand that even further and substitute with Ohm's law W = I·R·I·t"

D: "That sounds amazing. That reminds me indeed about math classes"
D: "So Watt's your problem.. ghe ghe, that pun totally intended"

M: "Well, somehow we need to add a factor to that expression to make it complete"

D: "So that expression was not complete before?

M: "Well yes. That just came out of substitution"
M: "According to some guy on the internet we need to add some factor or otherwise that would surely indicate some mental illness"

D: "And you believe that"

M: "eehm, I reject that validity... but I have to check don't I?"

D: "Firstly, no mathematical expression is anywhere closely related to a mental illness. Only how you might act on it."
D: "Secondly, that mathematical stuff you did seems just fine to me even when I'm able to check"
D: "Thirdly, who is that who's telling you about mental illnesses? Could you send him over"

M: "Oh I'll try. And when you speak to him, could you please give him these answers"

D: "Which are"

M: "No, Yes, No, Yes, Yes"

D: "ehm, NO! Good bye."

[George1]

To ME.
---------------------------------
Hi ME,
Hi dear colleague,
You are obviously a nice man of good sense of humor! And an expert in addition! My congratulations and my respect! It's a real pleasure to correspond with you!
----------------------------------
I would like only to ask you to have a look again at the simple chain of the three simple mathematical expressions
V x I x t = (I x I x R x t) + (Z x I x t x (HHV)) (1) <=>
<=> V x I x t > I x I x R x t (2) <=>
<=> V > I x R (3).
Everything seems to be mathematically correct, doesn't it?
Looking forward to your answer.
Respectfully yours,
George

[Tarsier79]

Arrogant george.

I don't know why you refuse to see the problem. It has been explained to you simply, mathematically and logically. The only explanation that makes sense: you are trolling. Either that or your mental capacity is chronically inhibited.

Which one is it? I hope it is the second, because surely no-one can be that bigger dick.