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Over a flame, small bubbles will start to form on the bottom of the pot, and as the average temperature rises, the bubbles will become larger until they start rise to the top. As it gets even hotter, the amount of boiling becomes more vigorous as well. It is a rather gradual process. In a microwave however, I noticed that the boiling happens all of a sudden. One moment there is no sign of boiling and the next, the water spontaneously boils. The bubbles that form are spontaneous and much larger than the ones formed from the heat of a flame. What is the explanation for this phenomenon?

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Several things: first, a stovetop heats the water only (primarily, anyway) by heating the bottom of the pot. This causes a significant thermal gradient. The water is hottest at the bottom and starts to boil there.

The microwave heats the water more or less uniformly from all sides of the container, with a penetration depth that you can look up -- i.e. how far microwaves penetrate water before being fully absorbed. This means a lot more water reaches the boiling point than just the bottom layer. But that's part of the story. The other is that not only do you need a bunch of energy to vaporize (without changing the temperature), but bubble formation is greatly enhanced either by lots of energy being added, as in the case of water at the bottom of the pot, or by the presence of sharp edges such as scratches in the container walls. Lacking such scratches, the microwaved water gets "superheated" (an actual chemistry term) and suddenly boils when a few molecules turn to vapor and 'encourage' their adjacent molecules to do so.

You may also have noticed that a non-boiling microwaved water will boil like crazy if you drop in some sugar, a tea bag, etc. Those solids provide the surface nonuniformity for bubbles to form (but as you note, smaller ones).

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