# Is there a limit to the energy density of a battery?

Better battery technology is very important today: improving the energy stored per volume or mass. This led me to wonder whether there is a theoretical limit. (I'm not expecting that we are at all close to it. Real life just inspired the question.)

One extreme battery would have a reservoir of anti-matter which it could combine with ordinary matter in a controlled fashion. Could anything beat that for stored energy per mass?

• You might be better off limiting the question to chemical-reaction batteries. leave nuclear reactions (let alone black holes) to a separate question. Feb 19 at 15:05
• Actually, I was more interested in the non-chemical possibilities. Feb 19 at 16:11
• The big issue in battery technology (and engines using fuels) is how much equipment you need to manage or control the release of energy. There are readily available fuels (like hydrogen) which would be good if you didn't have to store them safely. I imagine that antimatter is at the extreme end of that scale. If you need a 100-tonne device to contain a mg of anti matter that might outweigh the apparent advantages. Feb 22 at 13:55
• @matt_black Indeed, this is not an engineering question, I don't expect to build a super battery. I just wanted to know the theoretical limit. For example, we know the theoretical limit of a heat engine even if we cannot build one that achieves it. Feb 22 at 14:24

For a battery powered by electrochemistry, there will be a natural limit on its energy density of the following form:

Batteries work by capturing and diverting the electron transfers occurring in chemical reactions that happen in solution (commonly). This means that a chunk of, say, zinc metal in a zinc-copper battery has a certain number of charge units (of electrons) which it releases at a certain voltage. the charge transfer is current and current times voltage is power; divide by the density of zinc and now you have some number which represents the maximum theoretical electrochemical power density of zinc metal on a per-kilogram basis.

To fully exploit that power density requires the invention of a battery consisting almost entirely of replaceable chunks of zinc metal and an electrochemical reaction with no resistive losses- neither of which are possible today.

If you put a maximum amount of energy in a volume you get a black hole. Note a black hole can be used as a battery because the energy will be released as hawking radiation which can be used to do work. The limit to the maximally dense battery then is the Schwarzschild limit $$r=2GM/c^2$$ and $$E=Mc^2$$ so $$r=2GE/c^4$$.

• And rechargeable as well, a nice idea. I'll order my black hole powered Tesla now. The anti-matter powered ones are last year's models. Having to drive to CERN to refuel was a nuisance. Feb 19 at 11:50
• Other then this though your antimatter idea is ideal efficiency per mass. It represents the case of 100% rest mass becoming energy. The only way to improve this would be to give the antimatter kinetic energy as well. Feb 19 at 11:58
• That was my guess but I thought that others may know more. For a battery to be used on Earth, my anti-matter battery has the advantage of carrying only half the mass. I can suck in the matter that I need. My spacecraft battery will need a normal matter reservoir. Feb 19 at 12:18
• hmmm... then you get involved in the "max power output vs. battery density" problem. Also a serious problem with long-term storage, since you can't "turn off" the Hawking radiation. Feb 19 at 15:07
• @CarlWitthoft I expect that RTGs have thst problem. You could use more conventional batteries to smooth the demand. Feb 19 at 16:36