You can find a number of sites online that describe how to start a fire with a 9V battery and some steel wool. Apparently, in some circumstances, a paperclip dropped in the same drawer as a 9V can do the same trick … though that's probably not what folks are expecting to have happen in their junk drawer.
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NH Fire Marshal Warns About ‘Junk Drawer’ Items After Amherst Blaze – CBS Boston
A fire at an Amherst, New Hampshire home is being blamed on a battery, paper clips, post-it notes, and other items stashed in a junk drawer.
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When I was younger, I had some button cells in my pocket and, I think, a paperclip. Some time later in the day I felt a searing pain against my leg. Thankfully they just got very hot and my "junk" was OK but lesson learned and never forgotten! Even those tiny little batteries pack a punch when they're shorted out. Needless to say, I never store a mobile phone battery in anything other than a phone or a plastic bag. I'd hate to think what they could do.
Yes. Two 9 volts can touch lead-to-lead and create a short, too. It only takes a few seconds for them to get almost too hot to handle. I don't know if they ever get hot enough to start a fire.
Lithiums (like cell batteries) are even worse. They can supply amazing amounts of current for surprising durations. Those dramatic "cell-phone fire-ball" stories are pretty accurate descriptions of what can happen. Out of the phone, the contacts are often fairly exposed, as well.