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With lid, assuming you're boiling cold water. You have to get the water up to temperature first, so evaporative cooling and vapour pressure aren't an issue (at least initially), keeping the heated vapour in, and transferring heat to the liquid water are a bigger factor. If you're boiling hot water, and just trying to get bubbles, it might be faster to leave the lid off.
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re: Gio
You know, I've done some thinking about this old maxim, and I've concluded that our modern interpretation is wrong. In the old days (and today), when you boiled porridge or something similar in a pot, the one thing you didn't want was for the pot to boil over, possibly putting out the fire - so you paid close attention to the pot in order to prevent that from happening (by stirring, moving the pot off the flame briefly - or lowering the burner, today).
Hence the helpful hint: a watched pot never boils <over>. This makes sense to me in a way that the other interpretation never did - after all, as jfood has noted, it's very easy to prove the statement in that sense is simply false.
YMMV, of course. :)
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There are several things that come into play. First of all, the lid traps the higher 'humidity' which reduces evaporative cooling. It tends to contain and reflect heat. Lastly there is a micro increase of pressure that also helps reduce evaporative cooling. There is some interesting physics involved with boiling liquids.
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re: Harters
Here's a guess. Because if it's a heavy lid the pressure inside the pot will rise slightly causing the boiling point of the water to increase. Note that the water may reach 100°C (at sea level) faster but it won't *boil*. Now when you lift the lid off you have released that pressure and the water may boil furiously (like super heating water in the microwave) causing a burn.
Me personally, always with the lid on but I'm careful when removing it. I also don't salt my water until it is at a rolling boil. Not anything to do with how fast it will boil; I don't like a big pile of undissolved salt sitting on the bottom of my pot and possibly reacting with the metal.
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Heat rises. Since a lid will slow this action some, a pot with lid will boil slightly sooner, although is shouldn't be a large effect on a standard sized pot on a standard range top. The larger the volume of water and the smaller the burner, more effect since the time to boil and time to transfer heat to the room would be longer.
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