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## Tesla weight change when 100kWh battery is full

I know there are those who are wondering, so I did the calculation. If the 100kWh battery of your Tesla is topped off, the added weight is 4 x 10-9 kg compared with a completely empty battery.

Seen from another direction, once Elon decides to go nuclear, the fuel weight will be negligible.

Someone please check my work :-)

J.G.

SCCRENDO | 15 février 2019

To those of us less physics savvy could you you show how you got to that number.

jimglas | 15 février 2019

How much does 1.21 gigawatt weigh?

ryandetzel | 15 février 2019

The "fuel" weight is negligible now. :-)

science-isbetter | 15 février 2019

Commenting on @goldwein and responding to SCCRENDO.

First the physics. e=mc^2 (m * c squared). So the mass of a certain amount of energy is the energy divided by c^2 (the speed of light squared).

The first step is to convert 100 kilowatt hours to a more convenient measure of energy. I chose joules. 100KWh = 360,000,000 joules.

Now I run into trouble. Goldwein asks what is the increase in weight. Can't answer that (as I suspect Goldwein knows) because weight is a unit of force and Einstein's equation gives mass. But we can answer in terms of mass without confusing the issue or being pedantic with the difference between mass and weight.

Doing the math we get an increase of 4 x 10 ^(-9) kg or 4 x 10^(-6) grams. Goldwein and I agree...a kind of peer review which is how science should be done.

As to jimglass, the only way I know to determine how much 1.2 gigawatt weighs is to use the Tesla app when the battery is at 121 miles. Unfortunately, that gives a terrible unit conversion problem (miles and meters) one that may inadvertently trigger the Tesla emissions easter egg.

science-isbetter | 15 février 2019

Commenting on @goldwein and responding to SCCRENDO.

First the physics. e=m * c squared. So the mass of a certain amount of energy is the energy divided by c squared (the speed of light squared).

The first step is to convert 100 kilowatt hours to a more convenient measure of energy. I chose joules. 100KWh = 360,000,000 joules.

Now I run into trouble. Goldwein asks what is the increase in weight. Can't answer that (as I suspect Goldwein knows) because weight is a unit of force and Einstein's equation gives mass. But we can answer in terms of mass without confusing the issue or being pedantic with the difference between mass and weight.

Doing the math we get an increase of 4 x 10 (-9) kg or 4 x 10(-6) grams. Goldwein and I agree...a kind of peer review which is how science should be done.

Sorry for the sloppy notation. Tesla's spam checker won't let me use the proper symbols.

As to jimglass, the only way I know to determine how much 1.2 gigawatt weighs is to use the Tesla app when the battery is at 121 miles. Unfortunately, that gives a terrible unit conversion problem (miles and meters) one that may inadvertently trigger the Tesla emissions easter egg.

NKYTA | 15 février 2019

Worth posting twice, with notation change. :-)

blue adept | 15 février 2019

How much does electricity/energy weigh?

What a novel question!

rxlawdude | 15 février 2019

But what's a henway?

Dramsey | 16 février 2019

"Someone please check my work :-)"

Well, OK. Your math may be correct-- I didn't actually check-- but your work is wrong in the sense that you're not converting energy to matter when you charge your Tesla, so there's no weight gain, however minute.

Oversimplifying a bit, the classic "e=mc^2" applies to matter-energy _conversion_. Hydrogen fusion is a good example: take two atoms of "heavy hydrogen", aka deuterium, each of which has a nucleus comprised of a proton and a neutron, and mash 'em together REALLY HARD. You get a helium-3 nucleus (two protons and one neutron), which has less mass than the two deuterium nuclei. The missing mass is expressed as kinetic energy.

Another example would be matter-antimatter annihilation, where the energy is released as photons.

As for creating matter from energy, I know places like CERN have created particles from photons via pair production, but this is exotic high-energy physics.

But when you charge your Tesla battery, you're pumping energy into _chemical_ reactions (reactions involved the electrons of atoms) rather than _nuclear_ reactions, which involve the nuclei of atoms. No matter is being created.

Saying charging your Tesla makes it heavier because you're putting energy into the system is like saying your cake gets heavier in the over because it's getting hotter, or that a rock's mass increases when you carry it to the top of a tall building, putting gravitational energy into it.

Blue Adept asks how much electricity weighs. This is easy to answer: the mass of an electron is 9.10938356 × 10-31 kilograms (thanks Google!) But that's no good for figuring out how much 100kWh weighs because there isn't a fixed number of electrons in any kW measurement. Remember, when you're charging your car, you're not pumping electrons into it. It's the _flow_ of electrons you're taking about when you speak of (electric) kW; and you can get any number of kilowatts by moving a small number of electrons for a long time, or a large number of electrons for a shorter time. It's the whole volts * amps thing.

Damn I was bored this morning. Back to Hackintoshing.

Yodrak. | 16 février 2019

"your work is wrong in the sense that you're not converting energy to matter when you charge your Tesla, so there's no weight gain, however minute."

Correct.

science-isbetter | 16 février 2019

This is an interesting topic as so many issues in relativity are tricky and counter-intuitive. So let's discuss this in peace, no name calling, and let's use the forum to learn and to teach. Let's avoid the nonsense that goes on on these forums when people discuss climate change. Facts matter, this is not politics.

I'm pretty convinced that the mass of the battery increases when charged. Dramsey is correct there is no increase in electrons so that's not the cause of the mass increase. Respectfully, statements that atomic energy is somehow different in terms of the fundamental constructs of physics such as conservation of mass-energy, conservation of momentum and so on, is wrong. Even Newton's F=ma is not in doubt.

Let's do a thought experiment. Take an atom of uranium, wait for it to split and measure the combined masses of the fission products. They weigh less than the original uranium. The difference? The kinetic energy of the fission products (usually things like barium, iodine and moving neutrons). No photons are needed in this gedanken experiment. In short the kinetic energy (energy of motion measured by one half mv squared) plus the masses of the fission products equals the mass of the original uranium atom.

When you charge a battery you change its chemical composition. When it discharges the mass of the chemicals in the battery is less than when you started and that mass difference is equal to the kinetic energy (divided by c squared) imparted to the Tesla.

Yodrak: You seem quite certain and brief in saying there is no weight gain. I'm curious as to why. Is there something wrong with the analysis above.

By the way, for those who want a deeper discussion, including forms of potential energy at https://physics.stackexchange.com/questions/274329/does-potential-energy....

syclone | 16 février 2019

This question has been asked and answered on The Model 3 Forum. Basically - no measurable change.

Dramsey | 16 février 2019

"When you charge a battery you change its chemical composition. When it discharges the mass of the chemicals in the battery is less than when you started and that mass difference is equal to the kinetic energy (divided by c squared) imparted to the Tesla."

I'm sorry, that's simply not correct. If you can provide a citation saying otherwise, please do so.

Yodrak. | 16 février 2019

"Is there something wrong with the analysis above."

Yes. There is no conversion of energy to mass or mass to energy in charging and discharging a battery.

SCCRENDO | 16 février 2019

Enjoying the discussion and learning guys. Continue please but get your facts straight for our benefit.
@science-is-better. You are incorrect I saying that there’s no science on the climate change forums. Only among the deniers

syclone | 17 février 2019

To put this in the simplest of terms: Charging a battery is the equivalent of using energy to hoist an object . Now the object can supply energy by going down. It's mass or weight doesn't change. The same thing occurs in a battery. You are just moving atomic particles from an area of low potential to an area of high potential, expending energy doing so.

goldwein | 17 février 2019

Love the discussion - thanks for all the amazing comments.
1. It is "mass" and not "weight"
2, It is potential mass

FWIW, my spouse corrected me on both counts before I got to read the comments. I am in big trouble at home LOL

Mike83 | 17 février 2019

From 2008 an interesting calculation of a Roadster battery:

https://www.tesla.com/blog/weighty-matters-involving-electrons

blue adept | 17 février 2019

An electron's "mass" is negligible, so inconsequential in fact that it is not even counted in an atom's mass.

rxlawdude | 18 février 2019

In weighing this thread, I decided to go to mass.

But then, I'm not Catholic. Now I'm just looking for the energy to go.

PrescottRichard | 18 février 2019

Woah, RX, are you taking some RX? Deep.

Isn’t charging separating electrons from molecules, not adding them?

CSFTN | 18 février 2019

Related question, particularly to blue adepts answer.

When once charges a battery, one does not convert energy to mass, so (I agree) Einstein's equation has no applicability. However, when one charges a battery, does one add electrons, or do the electrons already present get moved to higher energy orbitals, or does the chemistry change such that the added energy is in nuclear bonds?

science-isbetter | 18 février 2019

@SCCRENDO glad you're enjoying. That's why some take the time to educate and to ask if we'd like to learn. I didn't mean that there's no science on the climate change threads. Just nonsense from time to time. Not everyone and I certainly did not mean to offend. I didn't mean your posts.

@blue adept. The increase in mass is not from adding any electrons. Anyway, the mass of an electron is 10^(-31) kg. Not particularly relevant in this discussion.

@RXlaw. A Higgs Boson goes into church and after being ejected says, "too bad for you, you can't have mass without me."

@Goldwein. Thanks for coming back in. I don't want to get you in more trouble with your wife. I don't think there is such a thing as "potential mass." If you accelerate the charged it will take more force. But you can get out of trouble with your wife (maybe :} ) if you weigh the car on earth. It will weigh more. Mass has weight in a gravitational field.

@Yodrak. Your statement is called a "conclusory statement." No further comment here.

@Mike83. Interesting discussion on the weight of electrons. But no electrons are added. They are simply moved from the anode to the cathode while charging.

Finally, for this go around, @ Dramsey. I think you are challenging the statement that the chemical composition of the battery changes and you would like a citation for that. It depends on the type of Li ion battery used (there are several) but a representative example is the anode half-reaction for the Lithium Cobalt battery CoO(2) + Li(plus) yielding LiCoO(2). Sorry for the notation problems. Also because of limited notation capability, I've left out the flow of electrons. In short Cobalt Oxide plus a Lithium ion gives up an electron at the cathode to yield Lithium Cobalt Oxide. Many don't like Wikipedia, but you can look at the electrochemistry section of Lithium Ion batteries if you want at least an easy to understand citation.

science-isbetter | 18 février 2019

@CSFTN your post appeared while I was preparing my response. As to your questions, chemistry doesn't involve nuclear bonds. It's easy to think that Einstein and all that he proved has to do with nuclear energy. But that's just the most demonstrable proof of it because of the large amounts of energy.

In the case we're discussing here, orbitals aren't ultimately involved. Consider two atoms of hydrogen plus one atom of oxygen. Both in their lowest energy (ground) state. Add them together and you get one molecule of water plus a lot of heat (energy). The atoms might go into an excited state during the reaction...but it still yields water in what is called the "ground state." And, as I'm sure you're aware, it takes energy to split water back into its component atoms (electrolysis).

I'm afraid though that I stand by my statement that the battery is (very, very minutely) heavier after charging.

science-isbetter | 18 février 2019

@PrescottRichard. "Isn’t charging separating electrons from molecules, not adding them?"

In a battery, when a battery is charged, electrons are added to the molecules at the cathode and removed from the molecules at the anode. The net electrical charge of the battery stays neutral.

Dramsey | 18 février 2019

@science-isbetter,

"I think you are challenging the statement that the chemical composition of the battery changes and you would like a citation for that."

No. Changing the chemical composition of a battery is what charging is all about. I'm challenging this:

"When it discharges the mass of the chemicals in the battery is less than when you started and that mass difference is equal to the kinetic energy (divided by c squared) imparted to the Tesla."

Which, again, is not correct. Chemical batteries are not mass-energy conversion devices.

Dramsey | 18 février 2019

After poking around online, I have found a number of discussions that support @science-isbetter's OP. Here's one example:

But there are many others. The basic argument is the one the OP has been making: a charged battery has more energy that a discharged battery, therefor it technically has more mass, and that the extra mass can be calculated working from e-mc^2. Some of the arguments supporting this proposition are quite creative.

(I've been unable to find-- "unable" == "can't find in 10 minutes on Google"-- any _authoritative_ opinions on the subject, in the sense of "I'm a battery expert / professional physicist". My perhaps jaded interpretation is that this is for the same reason I don't find authoritative supporting opinions on free energy devices, but that's just me being snarky.)

Anyhoo, the problem with this approach is that it assumes energy has mass. It doesn't; matter has mass. Take light: photons, depending on their frequency, have widely varying amounts of energy: a blue-light photon has a lot more energy than an infrared photon. A high-energy gamma burst photon has _billions_ of times the energy of a visible light photon.

And yet all photons are zero mass.

science-isbetter | 19 février 2019

@Dramsey. Thanks for the link. There are a few *opinions* there as you implied. Nothing too rigorous. I appreciate that you've done some Internet searches. If you google "Do photons have mass" you are probably pointed to this link http://www.desy.de/user/projects/Physics/Relativity/SR/light_mass.html

That page starts as you finish your post "And yet all photons have zero mass." The article goes on to say that the answer could be "yes." Let me go further, the answer *is* yes.

There is an easier to understand article at http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html. One of the authors, Philips Gibbs, is the same on both articles.

Now, this is going to muddy the discussion but the second article is clear to point out that a photon has zero *rest* mass. But it does go on to say that a photon has mass as a consequence of its momentum and energy. The classical laws f=ma, momentum = mass*velocity and even Einstein's famous equation haven't change. A photon has no rest mass but there is no such thing as a photon at rest. (Imagine a photon at rest!) All of a photon's energy comes from the frequency of the light it represents times Planck's constant. You are absolutely correct to say that a gamma burst photon has billions of times that energy of a visible light photon (maybe even more).

Einstein's famous mass/energy equivalency is not at odds with any of this. The mass of a proton, say, is equal to its rest mass plus the mass attributed to its motion relative to an observer.

Updating your last sentence
And yet all photons are zero rest mass
Photons have mass

Off topic, I think, from whether a battery gets heavier when its charged. That has little, if anything, to do with photons. And, I repeat it here because there were so many opinions posted here to the contrary, the increase in mass of a charged battery has nothing to do with adding electrons.

Dramsey | 19 février 2019

"Off topic, I think, from whether a battery gets heavier when its charged. That has little, if anything, to do with photons."

True, but the basic idea still applies. Your original assertion:

"So the mass of a certain amount of energy is the energy divided by c^2 (the speed of light squared)."

...is that energy has mass. I was trying to point out that if this were in fact the case, adding energy to any system would increase its mass: from heating something in an oven to carrying a physical object out of a gravity well. Photons are an example of massless particles that can nonetheless have extremely high energies; if energy were massy, one would expect this to be pretty easy to prove experimentally with photos of varying frequencies.

I can't find any online cites that definitely say that energy has mass. I think you may be misinterpreting the mass-energy equivalence Einstein spoke of. But I am not a physicist; just a retired programmer. Surely we have some physicists here...

syclone | 21 février 2019

A Photon walks into a hotel to check in. The desk clerk says, "Can I take you luggage?" The Photon says, "No thanks, I'm traveling light".

rxlawdude | 21 février 2019

But any way you slice it, the difference between an empty 100kWh battery and a full one is less than a henway.

Tesla2018 | 21 février 2019

If you fill your tires with nitrogen it will offset the weight difference. If Elon had filled his roadster tires with helium he could have saved the expense of having to use a rocket.

blue adept | 25 février 2019

I'm surprised no one has figured this out yet...

It's a really simple answer, all things considered.

blue adept | 25 février 2019

@science-isbetter

Yes, I know, hence my comment about how inconsequentially negligible an electron's mass is.

That was my effort to point others in a different, hopefully correct, direction.

blue adept | 27 février 2019

@rxlawdude

>>> "But what's a henway?"

About 4 to 6 pounds (said while raising eyebrows and wiggling a cigar)...

Which is still more than the negligible weight gained by a Tesla when fully charged.

blue adept | 27 février 2019

No one? Really...?!

TabascoGuy | 27 février 2019

Crickets Groucho. You got a chuckle from me but rxlawdude's been dangling that carrot for a while now...

blue adept | 27 février 2019

@TabascoGuy

Yeah, I didn't want to leave 'em hanging

Ah well then, I guess that the only thing left to do is answer @goldwein's question...

First off, everyone is using the wrong equation(s) for determining the temporary increase in weight of a Tesla battery after charging...You guys are trying to calculate mass/weight when what you should be focused on is FORCE and CHARGE.

Einstein's special-relativity equation is not the one that is used to determine the perceived increase, Gauss's flux theorem (for determining charge) and the Lorentz force equation (for determining the charge's force conversion) are.

Out of respect for @SCCRENDO and the other non-Physics savvy amongst us I'll keep this as simple as possible...

Charging a battery increases its electromagnetivity due to the increase of kinetic energy in the electrons through excitation from the charging.

This in turn causes increased interaction with the gravitational force of the Earth (due to the charge's generated force) which results in an inconsequential increase in weight as a result which dissipates over time from the gradual discharge of the battery from use.

Don't even get me started on electric flux or permittivity or permeability.

akasroy30 | 27 février 2019

Looks like a good thread. Thanks for sharing. I even didn't know about this.

Ross1 | 28 février 2019

Energy does not change to mass, it is only interpreted as mass

SCCRENDO | 28 février 2019

I guess what I am understanding is that energy is stored in charging. And according to E=mC2 mass is created or added. But is is transient to the SOC, negligible and inconsequential. Is my thinking correct???

jimglas | 28 février 2019

I don't think any mass is created, electrons are just moved to a higher energy

Urban_3 | 28 février 2019

this should have been in a don'topenuntil01Apr2019 wrapper

blue adept | 4 mars 2019

@Ross1

The induced ENERGY is changed to FORCE which is perceived as an increase in GRAVIMETRIC weight and/or an increase in its (the battery) attraction to the Earth.

Hmm, this might actually be a simpler way of explaining it..."?"

blue adept | 4 mars 2019

Simpler still, I suppose, would be:

F=E^2m

blue adept | 4 mars 2019

BTW, this is the thread I was referring to in silb3r's thread.

blue adept | 4 mars 2019

EDIT:

Excuse me, I meant mrporter6's thread, NOT silb3r's...My bad.

psusi | 5 mars 2019

science-isbetter is right. E=mc^2, period. It is not something that only applies to nuclear reactions. Mass and energy are literally the same thing. Most of the mass of neutrons and protons comes from energy. If you add up the mass of the quarks that make them up, it is almost nothing. It's the binding energy holding them together where most of the mass is. Veritasium did a good video about this on youtube. This is also why you can have a big laser in space and get some propulsion out of it, even though the photons leaving have no mass; they have energy, and energy is mass. When you fuse hydrogen into helium, you aren't "loosing mass". It isn't like some small part of the protons break off and become energy. You loose mass because the binding energy of the helium nucleus is lower than the binding energy of two hydrogen nuclei, and that energy is equal to mass.

SCCRENDO | 5 mars 2019

I guess the main point is that electrons have negligible mass.

science-isbetter | 5 mars 2019

I think psusi is adding quite a bit to this discussion because they are helping clarify why some are having trouble with this topic. When we say "mass increases" we do not mean that we are adding extra particles. We are not creating "matter" in the sense that we are filling a vacuum with something that wasn't there before. There are lots of ways to think of mass. Since Newton we think of mass as resistance to change in movement. More mass, the harder it is to accelerate (including changing direction). Less mass, as psusi puts it, does not mean we are chipping off a proton/neutron or an electron here or there. And, as Einstein showed mass is also a measure of gravitational attraction. The fact that resistance to acceleration mass is the same as gravitational mass is really quite remarkable. Hence General Relativity.