E = mc^2 In Basic Energy Transformations?

[cloudsweeper]

I had always believed that when you charge a battery, stretch a spring, or raise a mass you are merely changing energy from one form to another.

In nuclear reactions however, E = mc^2 comes into play as mass is actually converted into energy and vice-versa.

I recently read that all energy transformations - not just nuclear ones - incur a change in mass, so that a battery's mass increases by a tiny amount after being charged.  I have difficulty reconciling this with ingrained conceptions.  

Surely the extra, stored, chemical energy acquired has been provided by electrical energy causing changes in chemical bonding only, so why would there also be a slight increase in mass?

Do I need to alter my understanding of these matters?

Or is it a case of not everything in print being correct?

 

 

[andrew s]

The strong and weak nuclear forces and the electromagnetic force are all best explained by quantum field theories. To that extent the change in mass when a heavy nucleus splits into two lighter ones with a net energy release is no different from when a molecule splits into two smaller ones during an exothermic reaction. The initial binding energy of the nucleons or atoms shows up as an increase in mass in both cases.

I am not sure about how this plays out for gravity ( I would need to research it more) but I am sure the equivalence of mass and energy is preserved.

Regards Andrew 

[Riemann]

It is not true that mass is converted into energy in a nuclear reaction.    Mass is always just a manifestation of energy as given by E=mc^2 .   The total energy is always conserved (does not change) and likewise for mass.

What does happen is that the mass of the matter a nuclear reactor slowly declines and energy is released from the reactor (as photons and kinetic energy originally, this being transformed in heat and usually electrical energy).   The energy that is released has mass.    The mass of the matter plus the mass of the energy released equals the mass of the original matter (or to put it another way the intrinsic energy of the matter plus the energy released does not change)

Dealing with your battery example, any increase in energy in object or system A that takes energy from object or system B will results in an increase in the mass of A and a decrease in the mass in B.    For normal everyday energy exchanges the change in mass is so tiny that you not notice.   So for instance charging a battery with 20 Wh of electrical energy will give rise to a mass increase of only 8*10^-13 kg (assuming I have done the mental arithmetic correctly).   You can see this by working through E=mc^2 with c as 3x10^8 m/s.    What we normally perceive as a very small amount of mass is equivalent to what we normally perceive as a very large amount of energy.

Hope that helps a little.

Peter

[cloudsweeper]

Thanks Andrew and Peter.

Yes, m and E are equivalent, and taken as whole are conserved.

It looks as if my established view needs to be amended.  I like the battery example, also the point about similarities between nuclear and molecular binding.

So a wound spring has a microtad more mass than before. Inertia and amount of 'stuff' are equivalent, so does the increase only manifest itself as energy?

I like all this analysis. It passes time until we do more observing!

Cheers, 

Doug.