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I was thinking and had this discussion with my sister about this. I said that if I had the same stove and same pot and whatever that boiling 1 cup of water in an empty pot would take the same amount of time as boiling water in a pot that already has boiling water. Theoretically of course minimal heat loss and minimal specific heat of the pot.

Since both stoves (identical) are heating up the same amount of water to the same temperature, It should take the same amount of time.

And bonus question if it wasn’t theoretical would the pot with the starting water be faster or slower? I hope my question made sense! Thank you!

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  • $\begingroup$ I don't understand how the bonus question is different from the main question! The question is: how does the amount of time it takes to boil a pot of water change if there is already boiling water in the pot, right? $\endgroup$ Commented Jul 21, 2023 at 20:56

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I would agree that the cup of water on its own and the cup of water added to an already boiling stove need the same amount of energy to come to a full boil. But it would be very difficult to say it took the same time because of various issues. Here are where I think you would have the most difficulty with making this a real experiment in your kitchen:

  • The boiling pot is already hot and has specific equilibrium temperatures (cooler next to the water, hotter next to the stove). Probably you would have to boil water in the pot to prep it, then pour the water out and put in the cold cup. Trying to do this with a cold pan or a pan heated with no water seems like it would be horribly innacurate.
  • The water in the pot is not at a single temperature. As the water approaches boiling, some of the water in contact with the pot will be hotter and could form bubbles before the rest of the water is at temp. The more water you have, the more difficult it is to find when you've reached boiling point throughout.
  • You mention heat loss. The full pot will be losing more energy through the sides than the single cup volume. It might be minimal, but that would mean it should take just a bit longer for the full pot to come back to a boil.

It's possible that doing this in a microwave (with a boiling stick to prevent bumping) would be more reproducible than using a large metal pot on a stove.

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