Why is it possible to boil water in a paper cup without the cup in any way burning? When I was still in grade school, I bought a book on science that included this. But it has been so long, I don’t remember why it can be done.
Why is it possible and what physical laws does it demonstrate?
Thank you in advance to all who reply 
Because paper does not burn in any way at the temperature at which water boils, 100 degrees Celsius. Water keeps the paper at that temperature even if externally heated through the magic of convection. Any water that absorbs enough energy at 100 degrees C to change states will turn into a gas and escape the cup.
My recollectuion is that the heat energy all gets absorbed by the water, thus protecting the cup. It takes quite a bit og heat to first raise the temperature of the water to boiling, then a huge amount to enable the p=hase change to steam.
a more impressive version is to boil water in a playing card, with the edgfes bent up to form a sort of square basin. There’s a lot less water, and it doesn;'t last as lomng.
As Boy Scouts know, the trick is useful if you have to boil water out in the woods and you have no pot. A container of birch bark will not burn as long as water is inside (and the flame doesn’t reach the part that isn’t containing water.)
Og heat burn!
To be precise, paper burns at Fahrenheit 451 degrees, while water boils at Fahrenheit 212 degrees.
And that will permit boiling a few ounces of water in a tissure paper bag that won’t leak or fall apart when wet. Much more impressive than a paper cup.
Of course, Fahrenheit 212 wouldn’t really be the same book.
I agree, though, that you will probably need the moderating effect of the water unless you can really control the temperature of what you’re using.
And a little cup of water will sustain a boil long enough to hard-boil an egg. I’ve done this trick quite a few times.
A couple of notes, though: don’t try it with plastic, which melts at very low temperatures. Also, it looks nicer if you get paper cups that are not coated with wax; the wax melts and runs off, which isn’t very pretty and makes a film on top of the water.
I too have boileed water in a paper cup many times. When I was in camp as a kid my friends and I caught a fair number of crawdads and wanted to cook them but all we had was paper cups (not having planned on this). I told my friends to just use the paper cups to which they told me I was an idiot till I filled one with water and set it right on the coals in the fire. The paper burns down to the water line then voila! Boiling water. Made me hero for a day as we had a very good meal out of those hapless crawdads.
All respect to Bradbury, but there are many kinds of paper and not all of them have the same flashpoint. Copies of *National Geographic *have been known to survive house fires intact.
I guess it should also be noted that you can boil water in just about any container. Even at room temperature. Just pull a partial vacuum above the water… 
Proof that Og loves pictures of topless native women and wants you to enjoy their curvatures.
Which begs the question: could steam above 451°F start a paper fire or would the humidity somehow prevent combustion? How about just regular air at that temperature? Or is temperature aloe not enough and some sort of spark also nessecary?
Steam is water vapor, which might alter the ignition point. Heated dry air will burn paper; I have done that.
As a young Boy Scout, I was shown the flame under a paper cup of water trick. That was before microwave cookery, though. A 2006 Boy Scout will say, “Well, duh, of course you can.” The outer surface of the paper is cooled by the water, and you’ll never get the paper to burn as long as there is water inside.
A lean, five foot ten friend showed me another paper cup trick. He’d take a new vending machine coffee cup, and bet somebody he could stand on it without crushing the cup. He’d set the cup upside down on a flat, level floor, and slowly, carefully ease his weight onto it. Once the sucker was satisfied that he had won the bet, he’d slowly reach down and tap the cup on both sides with his fingers. In a flash, it collapsed. He was just on the verge of structural integrity. I was thirty pounds heavier, and I couldn’t do it. By the way, a used cup wouldn’t work.