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Some math help, please.

daniel

Well-Known Member
May 7, 2009
5,548
5,312
Kihei, HI
Yeah, but will that actually generate the required 1.2 gigawatts for the flux capacitor?

It would please me greatly if this thread did not diverge into sci-fi. That would be a wonderful topic for a different thread.

Sure, but then your miles per electron changes dramatically, depending if you charge with 120V AC, 240V AC, or 400V DC. That's because the battery charger steps up the voltage, thereby reducing the amps. The lower the input voltage, the higher the input current has to be. So your car would have twice the mileage per electron, if you charged on 240V, compared to 120V.

So IMO the battery approach is the only one giving out a consistent miles per electron rating.

You missed the part where I explicitly acknowledged that charging at a different voltage would change the number of electrons, but that this is not about energy; it's about counting the number of electrons that come out of the wall in my particular installation so that I can give a silly and meaningless answer to a dumb question.
 
It would please me greatly if this thread did not diverge into sci-fi. That would be a wonderful topic for a different thread.



You missed the part where I explicitly acknowledged that charging at a different voltage would change the number of electrons, but that this is not about energy; it's about counting the number of electrons that come out of the wall in my particular installation so that I can give a silly and meaningless answer to a dumb question.

Sure, but I like mine better, especially since it's 1 billionth of an angstrom.
 
It would please me greatly if this thread did not diverge into sci-fi. That would be a wonderful topic for a different thread.



You missed the part where I explicitly acknowledged that charging at a different voltage would change the number of electrons, but that this is not about energy; it's about counting the number of electrons that come out of the wall in my particular installation so that I can give a silly and meaningless answer to a dumb question.

Well the answer is really that you are getting infinite miles per electron since you aren't using them up/destroying them. All you're doing is changing their electrical potential energy. You're not even getting the electrons flowing through your EVSE since it's AC. They are just wiggling back and forth a tiny distance (amount dependent upon Amperage, wire gauge, and wire material (copper vs aluminum etc)).
 

daniel

Well-Known Member
May 7, 2009
5,548
5,312
Kihei, HI
Sure, but I like mine better, especially since it's 1 billionth of an angstrom.

Fair enough.

Well the answer is really that you are getting infinite miles per electron since you aren't using them up/destroying them. All you're doing is changing their electrical potential energy. You're not even getting the electrons flowing through your EVSE since it's AC. They are just wiggling back and forth a tiny distance (amount dependent upon Amperage, wire gauge, and wire material (copper vs aluminum etc)).

Picky, picky!
 

mongo

Well-Known Member
May 3, 2017
16,653
62,733
Michigan
You guys are great at math, but not so good at physics. What you should really be calculating is the distance per electron-Volt.

While you are not doing so good at reading comprehension :p. From the first post:
Again, I am well aware that this is really meaningless for several reasons. The number of electrons is only meaningful if the voltage is also stated. And I know that electrons are not stored in the car. Electrons flow through the battery, causing chemicals to change to a higher chemical potential energy. But I'm being silly and I think this is a fun game.
 
While you are not doing so good at reading comprehension :p. From the first post:
My bad on not reading the first post carefully.

In the spirit of this excellent discussion, what do you guys think the mileage would be in miles per gallon of electrons?

Yea, but you have a charger in between, so the voltage and ampere at the battery is different. So I have another approach.

We look at the electrons leaving the battery to the motor (and back). I assumed a nominal voltage of 350V of the pack for this:

If we assume you use 250 wh per mile (4 miles per kWh), you use 5,617 * 10^24 eV per mile. Since the pack has a nominal voltage of 350V (in my example you can plug in a different number), you have 1.6 * 10^22 electrons per mile, which is 6.23 * 10^-23 miles per electron.

Which is almost exactly one billionth of an angstrom per mile! 1.00 * 10^-9 Å per electron is also something that's pretty easy to remember. The Roadster has 375 V nominal voltage, which isn't as cool of a number, but maybe you could drive a bit less efficient to get to 3.7 miles per kWh, then you would still have the billionth of an angstrom per electron.

So we have 6.23 * 10^-23 miles per electron and Avogadro's number is 6.02 * 10^23 mol^-1. So we get 3.75 miles per mol of electrons. Now if only someone could come up with the concentration of electrons in the battery pack ...
 

mblakele

FSD Beta (99)
Mar 7, 2016
1,831
6,424
SF Bay Area
How many electrons are in a gallon of electrons??? o_O

That gave me an idea. Wouldn't Elon want us to start from first principles? E=mc^2

The grid will only get greener, right? Eventually we'll all be charging from 100% efficient mass-energy conversion — if we live long enough. We're looking for mpg, so let's feed a gallon of gas into our mass-energy converter.

It's been a while since I've tried this kind of math, but I gave it a shot.
  1. assume 250 Wh/mi
  2. that's 9x10^5 J/mi
  3. divide by c^2 in m/s: 1x10^-11 kg/mi
  4. specific gravity of gasoline is 0.739, treat that as kg/L: 7.39x10^10 mi/L
  5. in USA units, 2.8x10^11 mi/gal
280 billion mpg? That seems like it might be a little high. But then again mass has a lot of energy tied up inside it. Anyone care to check my work? How many decimal places did I slip?
 

daniel

Well-Known Member
May 7, 2009
5,548
5,312
Kihei, HI
That gave me an idea. Wouldn't Elon want us to start from first principles? E=mc^2

The grid will only get greener, right? Eventually we'll all be charging from 100% efficient mass-energy conversion — if we live long enough. We're looking for mpg, so let's feed a gallon of gas into our mass-energy converter.

It's been a while since I've tried this kind of math, but I gave it a shot.
  1. assume 250 Wh/mi
  2. that's 9x10^5 J/mi
  3. divide by c^2 in m/s: 1x10^-11 kg/mi
  4. specific gravity of gasoline is 0.739, treat that as kg/L: 7.39x10^10 mi/L
  5. in USA units, 2.8x10^11 mi/gal
280 billion mpg? That seems like it might be a little high. But then again mass has a lot of energy tied up inside it. Anyone care to check my work? How many decimal places did I slip?

You are assuming we can completely annihilate the matter into energy. Consider: A hydrogen bomb can obliterate the biggest city on Earth, and it transforms only a teeny tiny itsey bitsey amount of its mass into energy. The difference between the mass of two atoms of heavy hydrogen and one mass of helium is all that's annihilated. If you converted a gallon of matter entirely into energy, 280 billion mpg is probably way too low.

Though I have been getting about 320 Wh/Mi, not 250.

What's a good standard pressure to measure the at? Probably once you reach the state of a degenerate gas. Past that I believe they disappear into neutrons? I should ask my son.....

Electrons will never become neutrons. Neutrons are made of quarks and electrons are a different kind of stuff altogether. Bosons and fermions. I also suspect that a bucket of free electrons would behave very differently than a gas. They would require some sort of special containment. Note that containing a plasma is the hurdle that after decades of research still confounds attempts at a fusion reactor.

I suspect that "a gallon of electrons" will turn out to be a meaningless concept. The electrostatic pressure of even a very small number of them would be immense.

I do like the idea of the number of electrons that it takes to move the car the diameter of an electron. But does an electron actually have a diameter? Do we know enough about its fundamentals? We know its charge and its weight. But its size?
 

ℬête Noire

Active Member
Jan 30, 2018
3,105
2,703
TX
Electrons will never become neutrons. Neutrons are made of quarks and electrons are a different kind of stuff altogether. Bosons and fermions.
They are all of the same stuff, energy. That's the truth told by e=Mc^2. In a neutron star protons and electrons merge/disappear and in their place are only neutrons.
I also suspect that a bucket of free electrons would behave very differently than a gas. They would require some sort of special containment. Note that containing a plasma is the hurdle that after decades of research still confounds attempts at a fusion reactor.
Your thinking is on the right track with "successful fusion reactor". Turns out stars have what is needed for that. Gravity. Electrons reach maximum compression there, in white dwarfs, that's what I was referring to.
I suspect that "a gallon of electrons" will turn out to be a meaningless concept.
Such resignation has no place in this thread, good sir! :D

The electrostatic pressure of even a very small number of them would be immense.

It is!!!!! Mind bogglingly so, and even more-so to overcome it to make the electron go away.
I do like the idea of the number of electrons that it takes to move the car the diameter of an electron. But does an electron actually have a diameter? Do we know enough about its fundamentals? We know its charge and its weight. But its size?
We know some things about it.
1) Its size larger than zero. ((Complicated story which I'm not qualified to tell and I don't remember the short, simple version of the story.))
2) Its size is smaller than...hmmm, I think Linus Pauling first put the upper maximum at 10^-15m. That upper limit has been shrunk since then, though. I'd have to look that up.

We also know it has mass. Because it has energy, but doesn't go anywhere at the speed of light. Again, e=Mc^2.

Also it's a wave too, which is what sets its distance from the nucleus of the atom for a given energy level. So, you know, physics is weird.
 
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