How is distilled water for batteries produced?

Answer 1

It is distilled.

Distillation is a process of boiling then cooling a fluid in a contained environment such that the gas produced is collected and condensed to flow out into another container.

It is typically comprised of several components: a heater, a source beaker, a vapor-capturing lid, an iced steam channel leading off and downward from the vapor capturing lid, and the collection beaker under the outlet of the iced steam channel.

Beaker on heater, topped by vapor lid, steam flows through lid, into iced channel, condenses into water and flows out the outlet into the collection beaker.

While it's not a 100% clean, it gets out all solid materials in the fluid and all solutes that are not of similar or lower boiling point of the fluid being collected. Since the fluid is converted to steam, it loses the capacity to carry solids in suspension, leaving them behind. Similarly, dissolved material with a higher boiling point is left behind because it is not converted to a gas at the temperature it is subjected to. If the boiling temperature is similar, for instance, ethanol and methanol (one makes you drunk, the other makes you blind and/or dead), the process isn't very efficient, meaning a lot of cross contamination - you get both parts in the collection beaker. And if the boiling temperature is lower, it will all boil by the time the desired fluid starts boiling, meaning it will all be transferred to the collection beaker.

There are ways to overcome these problems, but it's difficult; certainly not something one can accomplish easily without dedicated equipment. Thus, making your own Alcoholic Beverages is a really bad idea.