Are charged batteries heavier?

[DaveC426913]

It does, but the particle in question is the whole atom or molecule, not the electron. An excited atom is more massive than an atom in the ground state. In the transition the energy is lost to photons and/or KE.

I've struggled with this on and off over time.

(I know this is a digression, since now I'm invoking nuclear reactions, but humor me for a moment.)

When a nucleus f̶i̶s̶s̶e̶s̶ undergoes fission, and loses mass, that mass is carried away by a particle moving very fast. If I have read correctly, the momentum of that particle (which incorporates its KE) will account for the mass missing from the end product. True?

Does this mean that the energy that the mass was converted from is KE? No mysterious other energy emitted?If so, is the same momentum at work in a molecular reaction? i.e, is the change in the KE of the various particles factored into the equation?

(I'd better go back and read my books. This stuff is slipping out of my head. Actually ,maybe I'd better pick up some new books.)

 

[bland]

When a nucleus f̶i̶s̶s̶e̶s̶ undergoes fission, and loses mass, that mass is carried away by a particle moving very fast. If I have read correctly, the momentum of that particle (which incorporates its KE) will account for the mass missing from the end product. True?

I believe this is what Lise Meitner understood when she helped her previous subordinates back in Germany understand what was happening. She calculated that the missing mass had indeed become the kinetic energy of the split atom pieces.

 

[jartsa]

I've struggled with this on and off over time.

(I know this is a digression, since now I'm invoking nuclear reactions, but humor me for a moment.)

When a nucleus f̶i̶s̶s̶e̶s̶ undergoes fission, and loses mass, that mass is carried away by a particle moving very fast. If I have read correctly, the momentum of that particle (which incorporates its KE) will account for the mass missing from the end product. True?

Does this mean that the energy that the mass was converted from is KE? No mysterious other energy emitted?If so, is the same momentum at work in a molecular reaction? i.e, is the change in the KE of the various particles factored into the equation?

(I'd better go back and read my books. This stuff is slipping out of my head. Actually ,maybe I'd better pick up some new books.)

Nature's conservation laws say that a box filled with matter and anti-matter and weighing 1 kg can become a box filled with radiation and weighing 1 kg.

The law of conservation of mass demands that the total mass of the box does not change.

In that annihilation process matter became radiation. Those two things, matter and radiation, have the same mass, if we assume that the mass of the container stays the same.

("Radiation" can be replaced e.g. by charged batteries. "Matter and anti-matter" can be replaced e.g. by nuclear plant)

Quantum mechanics: "If cat's transformation to a dog does not violate conservation laws, then the transformation happens with some probability"

 

[Tom Kunich]

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!

Has anyone ever told you what a spoil sport you are?

 

[phyzguy]

Has anyone ever told you what a spoil sport you are?

Oh well. Reality has a way of intruding on some of the best ideas.

 

[SongDog]

@CWatters, you might want to re-read that Wikipedia entry more closely.

 

[anorlunda]

Several posters in this thread talked about the relationship between mass and energy. If the OP had chosen a gas-filled bottle instead of a battery, the complex talk about molecules in this thread could have been avoided.

For example, a scale would measure the kinetic energy of the molecules in a bottle of gas to be part of invariant mass of the bottle, and thus also its rest mass.

So if a the gas in the bottle is warmed, it weights more. No atomic/molectular effects are necessary.

I think the easier way to think about it is that energy gravitates. But it can be very tricky. KE is frame dependent. So if all the particles in the bottle move the same direction, their KE is zero in some rest frame, and there is no invariant mass. But if they move in many directions, there is an invariant KE and an invariant mass associated with the KE.

From the same wiki article:

Note that for reasons above, such a rest frame does not exist for single photons, or rays of light moving in one direction. When two or more photons move in different directions, however, a center of mass frame (or "rest frame" if the system is bound) exists. Thus, the mass of a system of several photons moving in different directions is positive, which means that an invariant mass exists for this system even though it does not exist for each photon.

 

[PAllen]

Several posters in this thread talked about the relationship between mass and energy. If the OP had chosen a gas-filled bottle instead of a battery, the complex talk about molecules in this thread could have been avoided.
So if a the gas in the bottle is warmed, it weights more. No atomic/molectular effects are necessary.

I think the easier way to think about it is that energy gravitates. But it can be very tricky. KE is frame dependent. So if all the particles in the bottle move the same direction, their KE is zero in some rest frame, and there is no invariant mass. But if they move in many directions, there is an invariant KE and an invariant mass associated with the KE.

From the same wiki article:

And on this score, there is experimental evidence:

https://arxiv.org/abs/gr-qc/9909014

Part of this paper reanalyzes existing experiments to establish that kinetic energy has weight.

 

[Redbelly98]

When you connect a battery to a charger, some material from the connectors can transfer from the charger's connector leads to the battery terminals. Or material from the battery terminals can get transferred to the connectors. Then when the battery is connected to a device and discharged, the same thing can happen.

As a result, a charged battery has about a 50% chance of being more massive than a discharged one. :-)

 

[mfb]

For absolute mass measurement.
But what about mass difference.
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.

The period of oscillation is proportional to the square root of the total mass. You don't have anything that is directly sensitive to a mass difference of the same object at different times. There is no known way to repeat the Cavendish experiment with a 10^-14 accuracy. If there would, we wouldn't have such a large uncertainty for the gravitational constant.

The best relative gravimeters reach a ~10^-12 sensitivity. Heating something can change the mass by ~10^-12 - but not if you want to keep it superconducting, as required by the gravimeters. We are maybe 1-2 orders of magnitude away from measuring a mass change from a temperature change. The mass change of a battery is even smaller.

 

[Stephenk53]

This reminds me of the discussion on Chief delphi about whether or not adding code to a robot increases mass

 

[rkolter]

Since you can add energy to a battery then extract it later, considering mass energy equivalence, it should be more massive, no?

Yes.

Energy and mass can be converted into each other and are equivalent. But, the conversion factor is the square of the speed of light. Hydrogen bombs convert mass to energy - a little mass makes a lot of energy. Charging a (sealed) battery converts a little bit of energy to mass - and a little bit of energy makes a miniscule amount of mass.

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!

To put phyzguy's value into perspective, from 2010 to 2017 there have been, give or take, about 1.5 billion laptops sold. Pretend all those batteries could hold the same charge... if you measured the mass of all the batteries sold with laptops from 2010 to 2017 uncharged, and then charged them all, and measured the mass precisely again, you would find the 1.5 billion batteries gained about 3 grams of mass total.

 

[PAllen]

Picking up a battery to put it on a scale will transfer many orders of magnitude more mass from your fingerprints than the increase due to charging it.

 

[jerromyjon]

What if instead of weighing batteries, you could prove one was lighter and by roughly how much...

 

[jerromyjon]

Hydrogen bombs convert mass to energy - a little mass makes a lot of energy.

and a little bit of energy makes a miniscule amount of mass.

Way to put it into perspective.

 

[mfb]

What if instead of weighing batteries, you could prove one was lighter and by roughly how much...

Measuring masses and mass differences is commonly known as weighing...

To avoid material changes, you could discharge the battery via a resistor. Measure the full battery plus resistor, wait until it is discharged and cooled down and measure again.

 

[Derek P]

So, to bring this back to the OP's question:
the inflow of electricity, in the form of electrons, causes molecules to change shape, and some of the electrons' orbital energy is converted back to mass ... by way of muons?

Or am I word salading here?

Word salad with mayonnaise :) Muons and electrons are different fundamental particles. Unless your battery has a built-in particle accelerator, it's not going to change the particles themselves. Electrons remain electrons.

The energy of interest is indeed the orbital energy but it is not simply kinetic, it includes (and arguably it is) the energy of the electromagnetic field that holds the molecules together. And a field that has energy must have mass. E=mc^2.