# FeaturedI Are charged batteries heavier?

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1. Feb 27, 2018

### rootone

Since you can add energy to a battery then extract it later, considering mass energy equivalence, it should be more massive, no?
Somehow that doesn't make sense though.

Last edited: Feb 27, 2018
2. Feb 27, 2018

### phyzguy

It is more massive. Let's calculate how much. The battery on my laptop stores about 50 W-h = 180,000 Joules. Δm = ΔE/c^2 ~= 2 picograms. Hard to measure!

3. Feb 27, 2018

### rootone

Thanks and yes it would be hard to measure but not impossible.
I expect somebody will be able to confirm that this has been checked out.

4. Feb 27, 2018

### phyzguy

Of course mass-energy equivalence has been checked in many different ways. Here's one for example. But I don't think there is any scale accurate enough to measure the mass difference between a charged and uncharged battery.

5. Feb 27, 2018

### rootone

I heard also about the planes flying in different directions as well, although I think that is GR rather than SR.
Back to batteries though, if they become more massive when charged, even by an immeasurably small amount, where is the extra mass?
Do electrons get more massive?

6. Feb 27, 2018

### Staff: Mentor

Are you thinking of Hafele-Keating? https://en.wikipedia.org/wiki/Hafele–Keating_experiment
The battery as a whole is more massive; you can't assign the extra mass to any one part of it. The mass of the charged battery is greater than the sum of the masses of its constituent parts.

7. Feb 27, 2018

### rootone

1 Yes that is the experiment I heard of.

2 Aggregated mass of constituents is something I need to think about,.

8. Feb 27, 2018

### Staff: Mentor

The molecules in a charged battery are different than the molecules in an uncharged battery. The ones in the charged battery are more massive than the ones in he uncharged battery. You cannot assign the mass to any part of the molecules, just the molecules as a whole.

9. Feb 27, 2018

### rootone

How?

10. Feb 27, 2018

### Staff: Mentor

By being in a configuration with more potential energy.

11. Feb 27, 2018

### rootone

OK I get the idea.
But what exactly is configuration?
Something to do with Higgs field?

I am puzzled, but hey that's why I am here,

12. Feb 27, 2018

### Staff: Mentor

No. For a chemical reaction it is just electromagnetic. The Higgs is not relevant.

Configuration means the various distances between nuclei and electron orbitals etc. That is what gives chemicals their energy.

13. Feb 28, 2018

### Staff: Mentor

Slightly off-topic comment: this is something that irks me about many sci-fi stories. Some devices, such as weapons, have an incredibly big energy supply, but are still lightweight. Not possible, $E=mc^2$ rules!

14. Feb 28, 2018

### CWatters

Not sure if it's possible to weigh something like a smartphone battery to within 2 pico grams? I know you can weigh much smaller things more accurately but i don't think the method used for that can be applied to something big like a battery.

According to Wikipedia the international standard kilogrammes gains around about 1 micro gram a month by absorbing contaminants from the air despite being under two nested bell jars. That works out at about about 33 Pico grams a day.

15. Feb 28, 2018

### mjc123

An exception would be the lithium-air battery, which uses oxygen from the atmosphere to oxidise lithium in the discharge reaction:
2Li + O2 → Li2O2
As the oxygen comes from the atmosphere on discharge and is released to it on charge, it is not part of the battery, which therefore weighs more in the discharged state than the charged state.

16. Feb 28, 2018

### CWatters

I did wonder is some sort of balance could be created using an ink jet cartridge....

Ink jet cartridges create pico litre droplets of ink so I was thinking that perhaps you could use one to squirt ink onto a counter weight until it was in balance with a discharged battery. Then charge the battery using a wireless charger and count how many additional drops are required to bring it back into balance again.

Then I realised that the tiny drops produced by an ink jet printer would be three orders of magnitude too big! (pico Liters >> pico grams)

17. Feb 28, 2018

### Andy Resnick

Minor quibble (since I'm an experimentalist): I think you mean 'precise', not 'accurate'. This measurement, for example, requires about 14.5 significant figures (to reliably measure 1 pg changes in a 100g battery). I don't know any existing balance that can do this (maybe the Watt balance). The standard kilgoram calibration campaign quotes about 11 digits (1 ug/kg) using one of these:

https://www.mt.com/dam/P5/labtec/08...tion/03_Datasheet/DS_Vacuum_M_one_M_10_EN.pdf

18. Feb 28, 2018

### 256bits

For absolute mass measurement.
Using a Cavendish torsion balance, the period of oscillation should be comparable to the square root of the difference in mass, or rather 10-6 seconds, and that 'should be' fairly easy to measure with a current time clock.
Just wondering.

19. Feb 28, 2018

### Khashishi

Check out https://en.wikipedia.org/wiki/Binding_energy

The binding energy can sometimes be interpreted as a reduction of field energy. For example, an electron and a proton are bound as a hydrogen atom. The electric field has energy $\frac{1}{2}\epsilon E^2$. When the electron and proton are close together, the E fields overlap and mostly cancel out, reducing the field energy. By rearranging the atoms in matter, you can change the energy even though the number of atoms is equal.

20. Feb 28, 2018

### Andy Resnick

Why go through the effort? The uncertainty/statistical spread of a discharged battery's mass is likely many times larger than a pg.

Edit- I just realized, how did you get 10-6 seconds fractional difference for the oscillation period?

Last edited: Feb 28, 2018