By your logic of E=MC^2 photons would therefore have no energy since 0*X^2 = 0
If we imagine a battery as two containers where one is on top of the other. They are connected by a pipe with an electrical generator in the pipe which will create electricity as water flows from the top container to the bottom container. The discharging of the battery occurs when the water flows down but to charge this battery you either switch the containers or pump the water back up. There is no net gain or loss in mass. I don’t see why it has to be any different in any other type of battery.
The number of particles doesnt change, but mass is more than the sum total of all the particles. Even in your water example, relativistic effects dictate that water at the top of the hill has more mass.
The water doesn’t have more mass, but the system of earth and water does.
The complete equation is:
E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + p[sup]2[/sup]c[sup]2[/sup]
The photon has momentum and thus energy.
Mass doesn’t increase with velocity. You’re thinking of relativistic mass which is an outmoded concept. if such a thing existed a single quantum particle traveling at close to c would collapse the sun to a black hole.
This is what happens when a chemist attempts to explain things outside of chemistry. Thank you for the clarification.
By the same token, you could count up all the protons and neutrons before and after a nuclear explosion, and you’d have the same number of each. But I think everyone accepts that that’s an example of E = mc[sup]2[/sup].
I am having trouble grasping this concept. So I have a battery charger plugged into the wall. As it forces chemical changes to the battery, the mass increases. What kind of mass? Whole atoms? Electrons? Maybe quarks, baryons, and mesons? Do lead acid Nicads, and lithium ion batteries all form the same kind of matter? When the electricity flows out of it, it loses mass?
Say my power comes from a huge hydroelectric dam. The generator is steadily putting out massive amounts of energy as it has for years. What is happening to its mass?
I think you need to study Einstein’s relativistic equation that relates mass energy and momentum. (c = 1)
m[sup]2[/sup] = E[sup]2[/sup] - p[sup]2[/sup]
Do you see anything that relates to stuff (as you seem to define it)?
Also, don’t think of mass and energy as things; They’re not things they’re properties of a system.
So if you wind a clock, its mass increases?
Yup, potential energy stored in a spring works the same way.
So again, what type of particles?
No, not type of particles.
Nope, that’s capacitors. In both batteries and capacitors, the imbalance in number of electrons on the two plates determines the battery voltage. During battery charge/discharge, chemicals are moved from place to place, but the voltage and the electron distribution on the plates remains about the same.
Batteries are charge pumps, and the path of current is through the battery. If there’s one ampere in the connecting wire, then there must be one ampere in the electrolyte between the plates. In other words, the battery completes the closed circuit, and the electrolyte is a good conductor which electrically connects the plates together.
They’re talking about lost photons and ideal theoretical descriptions of the indetectably small mass which potential energy always has. If you squeeze your fist, you become heavier. Too small to measure! Warm objects are always heavier than cold objects. Is this important to the OP’s question?
Do batteries become detectably heavier when charged? Significantly heavier?
No.
From a practical standpoint, the mass of a battery doesn’t change, since the charge/discharge process is simply converting fuel into waste products and back again. Any change due to General Relativity is far below the measurement noise. If we’re not worrying about the weight of fingerprints from you touching the battery, then GR is irrelevant too.
Well, is it dirtier than when it was first installed? Or wetter? The accumulated damp filth made it slightly heavier. 
It depends on what this “Dr. Karl” was talking about. If the OP can point us to the episode (and time marker) that he was listening to, we can address the claim directly. But, short of that, I can’t imagine what else the claim would have been if not the relativistic effect mentioned above.
The energy isn’t coming from the generator at the dam. The dam is just converting potential energy in the water into electrical energy. The water has less potential energy after it’s traveled through the generator at the dam. Technically it’s lost a tiny bit of mass when after traveling through the generator, but it’ll get that back when it’s heated by sunlight, evaporated, and then falls back to earth as rain and returns to the reservoir behind the dam. Ultimately the energy is coming from the Sun, which is constantly converting mass into energy through fusion.
I find little there to back batteries gaining mass when charged. I also note Wiwi asking for citations. You may post anything you want to wiki, but without citations, it means nothing.
The point of the link was to introduce you to the ideas (1) that energy content and mass are intimately related and (2) that you needn’t introduce new particles into a closed system (like a battery) to increase its mass (something you seemed to be thinking). And as wiki pages go, that one is very well cited. How about citation #1 as a starting place?