Re: How does surface area affect boiling time of water?

To a good approximation, pan size should not affect the boiling time at all. The reason is that the time to boil an egg is basically just the time for it to heat up to the right temperature, which is the time for enough heat to be conducted inward from the hot water, through the shell, to the center of the egg. The time for this to happen depends on the temperature of the water touching the shell, and to some extent on the size of the egg. (It takes more heat to warm up a larger egg.)

However, one of the most important facts about cooking is that water in an open pan near sea level will not boil below the normal boiling point of 100 degrees C (ie, 212 degrees F), and it is also impossible to heat it above 100 C. If you add heat faster (turn up the fire, use a larger pan, etc.) it just boils faster, without getting any hotter. This is one of the main reasons we cook things in water so often, because, since the temperature cannot go above 100 C (unless all the water boils away), it tends to prevent them from burning.

So the temperature of the water outside the shell is pretty much guaranteed to be 100 C if the water is boiling, no matter what you do. That means the size of the egg is about all that matters, so long as you put the egg into water that is already boiling.

(You could actually cook an egg somewhat below 100 C, but it takes longer and depends on the exact temperature of the water, which we usually do not measure or know. This makes it much harder to control the results. If you put the egg into cold water and heat it up slowly, heat will be leaking into the egg as the water warms up, so it might overcook and be hard-boiled before the water even boils at all. It is very difficult to say exactly how long it should take to boil an egg if you do it this way, unless you always use the same pan, the same stove, and turn the heat to the same level.)