# Cup of warm water suspended in a pot of water held at a steady boil

The question asked by a website is as such:

A cup of warm water is suspended in a large pot of water held at a steady boil. Will the water in the cup ever boil? Assume that the pot never runs out of water.

No. When the cup of water is placed in the boiling water, the cup is cooler than the surrounding water and heat will flow into it. Eventually, the water in the cup will increase to $$100 ^{\,\circ}$$ C — if any more energy goes into the cup, then the cup will begin boiling. But at this point, the boiling water in the pot and the $$100 ^{\,\circ}$$ C water in the cup are at the same temperature. Since there is no temperature difference, there will be no more heat flow into the cup, so it will never boil.

According to the explanation (emboldened sentence), the water in the cup does reach a 100 degrees. Doesn't that mean that the water in the cup does indeed boil, because the boiling point of water happens to be a 100 degrees Celsius? Additionally, I don't really get the difference (temp or state wise) between the cup-water & the water in the pot, because the heat source is the same and it ought to always flow into the cup to reach thermal equilibrium?

• We do have steam and water both at 100ºC. Jul 2 at 13:49
• This looks like a perfect candidate for doing the actual experiment yourself. This just requires household equipment and should be easy to do. Jul 2 at 14:27
• @silverrahul, I agree. The stated answer looks like an assumption based on theoretical considerations, those theoretical considerations are based on an assumed physical and mathematical model, and all mathematical models are simplifications of real world phenomena. I wouldn't be surprised if the water in the cup did boil, and I may decide to do this experiment myself to find out. Jul 2 at 16:11
• @DavidWhite I actually did try this. And i can confirm that the water in the cup did not boil WHEN the water outside started to boil. But i cannot state if the water in the cup would NEVER boil. I ran out of patience and did not want to waste fuel waiting to see if the water in the cup does boil after some time or not. Jul 2 at 18:25

Just reaching the boiling temperature is not enough for boiling. Boiling happens when the the vapour pressure becomes equal to atmospheric pressure. When the temperature of $$100ºC$$ is reached then too we need more heat to vaporise it. The term is Latent Heat.