Weight difference between a charge and discharged battery

[soothsayer]

Thanks for the link, Wannabe. I'm actually pretty dismayed that I never learned this in college.

When was GR used in this thread?

 

[WannabeNewton]

GR was mentioned more than once in the thread but never in a correct manner (we don't need it anyways).

 

[Nugatory]

So if we have two identical boxes, and we fill one of them with light, even though the light has no rest mass, the energy from the light will contribute to the rest mass of the box? I mean I get that it would increase the weight, like, on a scale...

Yes, that is exactly what happens. And if you were to open a hole in the box and let out some of the light inside the box, the mass of the box+contents will decrease, just as it would if you opened a hole and let some of the gas inside the box out. Conversely, if more light to were enter through the hole than left, or more gas, the mass of the box would increase.

How does the box know it is filled with light, and how does that change its inherent properties? Is it because the light is being absorbed by the box? What if we have two identical boxes and poke a hole in one to let light in?

Suppose I put a lead shot in the box... How does the box know that it contains a lead shot so has a greater mass?

Here's a thought experiment. The box, when empty, has a rest mass of 1 kilogram. It contains one gram (rest mass) of matter and one gram (rest mass) of antimatter, so its total rest mass is 1.002 kg as long as the matter and antimatter are separated. But eventually the matter and antimatter will come into contact with each other, annihilate, and turn into (an amazing amount of amazingly energetic) photons that have zero rest mass. If the box is strong enough to contain the resulting explosion so that we on the outside stilll see the same closed system, does the mass of the box plus its contents change?

No. The total rest mass is still 1.002 kilograms.

Backing up from here, the easiest way of thinking about this is to say that energy has mass, given by $E=mc^2$. The trick and pitfall is that kinetic energy depends on speed, hence is frame-dependent. Thus, if you're going to use this equation, you can either:
1) Choose a frame in which the speed is zero so there's no kinetic energy and you are dealing with rest mass. This makes the math especially simple, and feels right for this thread where we're talking about a battery sitting on a table in front of us - no movement, no kinetic energy to mess with. The kinetic energy in the system is captured in the $(pc)^2$ term of $E^2=(m_{0}c^2)^2+(pc)^2$, conveniently zero in this frame.
2) Go with the concept of relativistic mass given by $m_r=\frac{m_0}{\sqrt{1-v^2}}$ and use $m_r$ in $E=mc^2$ so that it includes the non-zero kinetic energy, so is not frame-independent.
3) Use $E^2=(m_{0}c^2)^2+(pc)^2$ (and note that if $v$ and hence $p$ is zero this option reduces to #1 above). As in #1, we're only dealing with rest mass and rest energy here; the frame-dependent kinetic energy is captured in the $(pc)^2$ term.

 

[leothorn]

There is absolutely no need to mention GR (it's not even being used correctly in this thread anyways); this is over-complicating things. Read the following and then reread Nugatory's and Drakkith's posts: http://en.wikipedia.org/wiki/Mass_i...individual_rest_masses_of_parts_of_the_system

Do the conclusions of then discussion hold if the concept of mass in special relativity does not hold ? ( A contention held at the end of the article linked above ?


I was thinking on the following lines..

When the battery system is at higher energy that is the constituent particles are at higher state of activation, they hit the confines of the battery at a much faster rate than when the battery is at lower energy. The combined affect of higher average impulse over time should affect the weight of the battery.

Is this thought process wrong. Could this argument be repaired to make it right ( if its incorrect).
Thanks to all those who replied

 

[Nugatory]

When the battery system is at higher energy that is the constituent particles are at higher state of activation, they hit the confines of the battery at a much faster rate than when the battery is at lower energy. The combined affect of higher average impulse over time should affect the weight of the battery.

The energy of the battery isn't stored in faster-moving versus slower-moving particles. It's stored in high-energy chemical bonds, and the energy is released by chemical reactions in which those bonds are replaced by lower-energy bonds. As long as the battery is not overheating (something that battery designers try to avoid), the constituent particles of the battery are bouncing around at the same speed whether the battery is charged or discharged.

 

[BruceW]

Do the conclusions of then discussion hold if the concept of mass in special relativity does not hold ? ( A contention held at the end of the article linked above ?

It was just saying that some people think the definition of 'relativistic mass' is not very useful. They are not saying it is wrong.

When the battery system is at higher energy that is the constituent particles are at higher state of activation, they hit the confines of the battery at a much faster rate than when the battery is at lower energy. The combined affect of higher average impulse over time should affect the weight of the battery.

As Nugatory said, the molecules won't necessarily be moving around faster. Remember that the molecules have more than just kinetic energy. They also have 'chemical energy', which is energy stored in the electromagnetic field. And it is this chemical energy that changes, to provide the energy to the circuit.

Now, if you want to talk about what happens when we place the battery in a gravitational field, then put it on a scale... Well, the mass of the molecules is greater in the high-energy state. So it makes sense that the battery will then push down more on the scales when its molecules are in the high-energy state.

I guess the last 'connection' to make is that the mass of the molecules of an object effect the mass of the object. But this is classical physics. There is no relativistic argument required here.

edit: more explanation: I can see why (for fluids), it is not obvious why the mass of the molecules should affect how much the battery pushes down on the scales. But if you think of the pressure created by these molecules, the pressure will be greater when the molecules are more massive.

 

[Jonnyb302]

Yes there would be a weight difference. The charged battery would weigh* more. All energy** gravitates.

*here the working definition of weight, is what you measure on a scale

**gravitational energy is a concept only useful in certain limits, and does not apply here.

 

[soothsayer]

Thanks, Nugatory! I think this is making more sense to me, now.

So am I getting this right? Light does not have a rest mass itself, but it can increase the rest mass of systems it is contained in?

 

[BruceW]

a single photon cannot have rest mass. A collection of more than one photon can.

 

[Naty1]

There is a key aspect of batteries that seems to have been overlooked:

The easiest way to think about what is happening in the battery to start with Drakkith's comments. In addition what needs to be explicitly mentioned is that no battery is an ideal power source: all batteries have internal resistance. That is where chemical energy lost during discharge is converted to heat energy, or mass equivalent losses if you prefer.

So when chemical reactions take place in the battery, chemical potential energy* is dissipated and this partially appears within the battery as heat [i²R losses where R is the internal resistance of the battery]. Most power is delivered to the external circuitry. So Nugatory's quick power loss calculation [post #11 I think] has the right idea regarding energy/mass-equivalent loss, but some of that loss IS within the battery.

edit: * As Bruce noted: ..." 'chemical energy'... is energy stored in the electromagnetic field" of the battery components. Charging and discharging changes the chemical composition of the battery plates.

[For example some 20% of the power delivered by a wet cell lead acid battery [like a car battery] is dissipated via its own internal resistance losses, and conversely when charging, some 20% of the charge power is lost in internal heating. So you cannot charge them too fast or they will overheat [boil off electrolyte] ...not above about 20% of their rated amp hours. In contrast, an AGM [absorbed glass mat] battery, for example, has very low internal resistance, so heating is not much of an issue: they can be charged at 100% of their rated amp hour capacity and in charging and discharging only a few percent of power is lost to internal heating..about 2% or 3% as I recall. ] So an AGM battery offers significantly higher efficiency [at significantly higher cost].]

Light does not have a rest mass itself, but it can increase the rest mass of systems it is contained in?

yes.
The photon has the equivalent of 'mass' via it's energy content E = hf. So when an atom absorbs a photon, typically an orbital electron might be bumped to a higher energy level. So now the atom has stored some additional energy and via E = mc² it has a tad more equivalent mass...but that is stored as energy.

photon energy relationships described here:

http://en.wikipedia.org/wiki/Photon_energy#Physical_properties