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.
Best Answer
In real life situations like this there tend to be lots of variables, so it's dangerous to make predictions based on (over?) simplified physical models.
Having said this, the article makes a good argument. Newton's law of cooling tells us that the rate of heat loss per unit area from an object is roughly proportional to the temperature difference between the object and it's surroundings. For a large and a small pan, both containing boiling water and both in the same kitchen, the larger pan has the larger surface area and it will lose more heat per second than the small pan.
You ned to distinguish carefully between heat loss and temperature fall. The temperature of the big pan will fall more slowly than the temperature of the small pan because its surface area to volume ratio is smaller. However it will lose heat faster.
The point the article is making is that the burners on your stove supply heat at a constant rate that is independant of the pan size. Because the larger pan loses more heat per second the net heat flow from the burner is lower, and it will take longer to get it back to the boil.
Of course this assumes that the efficiency of heat transfer from the burners to the pan is independant of pan size, but then as I mentioned at the outset in real life there are lots of such variables.