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> Is there a theoretical limit on how much energy a rechargeable battery of, say, 1 kg mass can hold?

As with most things, you can find some fairly irrelevant theoretical maximum. It's fairly irrelevant because real life implementations will invariably involve compromises. It can be nice to know the limit, but it's not terribly useful for making an actual device.

For rechargeable batteries, it's not just about how much energy the battery can store, but how fast can you charge and discharge, what's the recharge efficiency like, does it degrade when recharged, can it be deep cycled without adverse effects, how sensitive it is to physical and electrical disturbances, does it have high or low self-discharge and so on.

Different applications have different demands and so there's usually not a single optimal battery technology.



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