SeriousEats gives a not-very-scientific representation of what looks like a thermodynamics calculation:
Want to hear something even more interesting? Folks will occasionally say that "using a large volume of water will help the water come back to a boil more quickly."
Back up a minute there, because you know what? This is untrue. In fact, in most real world cases, the exact opposite is the case.
But how is this so? Doesn't adding a fixed amount of pasta to a small pot cause the temperature in that post to drop more than it does in a large pot? Therefore doesn't the large pot come back to a boil more quickly? Let's examine the ideal scenario first.
You have two pots of water. One has 1 quart of water, the other has 1 gallon—four times as much. Both are sitting on top of identical burners and are at a full, 212°F boil. Now add a cup of dry pasta to each one. Because the pasta is at room temperature, it will cause the temperature of the water in each pot to drop, and the water in the quart-sized pot will drop four times more than the one in the gallon-sized pot.
Ah ha!, you say. If the temperature fell four times lower in the small pot, it must take four times longer for it to come back up to a boil!
The problem with this line of reasoning is that it doesn't take into account the fact that it takes four times less energy to raise a quart of water by one degree as it does to raise a gallon of water. Since a burner puts out energy at a constant fixed rate, the small pot, which needs to cover a temperature gap four times as great as the large pot, serendipitously also heats up four times faster. This means that the two pots of water return to a boil at the exact same time!*
- For the record, it's also the same amount of energy and time required to bring a cup of dry pasta from room temperature to 212°F.
In the real world, the "big pots boil faster" camp is even more wrong. See, the larger a pot, the greater its surface area. And the greater the surface area of a hot body, the more rapidly it can lose heat to the outside environment. How does this affect heating?
Let's say your burners put out heat energy at a very respectable 10,000 Btu. Meanwhile, your small pot might be losing heat energy to the air in the kitchen at, say, 1,000 Btu, giving you a net energy input of 9,000 Btu. A large pot, on the other hand, will lose heat more rapidly due to its larger surface area. Let's say, 2,000 Btu. Your burner is still exactly the same, putting out 10,000 Btu, which means that with a large pot, the net energy input is only 8,000 Btu.
Thus, a large pot will actually return to a boil more slowly than a small pot.**
** This doesn't even take into account the heat loss from evaporation, which again compounds the case against large pots.
Will the large pot really return more slowly? This isn't really intuitive, because you'd think that the more water has "more" energy in it already.