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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.enter image description here

The provided answer & explanation:

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?

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  • $\begingroup$ We do have steam and water both at 100ºC. $\endgroup$
    – Goarkz
    Jul 2 at 13:49
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    $\begingroup$ This looks like a perfect candidate for doing the actual experiment yourself. This just requires household equipment and should be easy to do. $\endgroup$ Jul 2 at 14:27
  • $\begingroup$ @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. $\endgroup$ Jul 2 at 16:11
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    $\begingroup$ @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. $\endgroup$ Jul 2 at 18:25
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The illustration here is enlightening. The vapor bubbles form at the bottom of the pot, where the temperature of the heat source exceeds 100°C, as is required in practice for boiling*. As they float to the top of the water, they condense somewhat, indicating that the water is at 100°C or cooler. This water is thus not capable of making the water in the cup boil.

*A summary of the linked discussion: the formation of a vapor bubble costs energy beyond the latent heat, as we also need to create a new gas–liquid interface. Surfaces cost energy because the bonds are comparatively unsatisfied relative to the bulk. Consequently, some degree of overheating is always required for boiling, even in the heterogeneous nucleation case.

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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.

As the two systems (cup and pot) reach thermal, the heat flow do not literally stop, but yes, there is no net heat gain in the cup system. So, no extra heat is acquired by cup water, to set the bonds free and to change the state from liquid to vapour.

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I agree with you, the water in the cup is boiling at 100°C, and after reaching the 100°C there is no difference of the two separate waters the inflowing energy will evaporate same of the water outside and inside the cup.

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    $\begingroup$ Both liquid and gaseous phases of water can exist at 100C - the fact that the water is at 100C does not necessarily mean it's turning into vapor (i.e. boiling). The difference between the water in the pot and cup is that the pot is heated by the stove which is more than 100C, while the cup is heated by the water in the pot, which is never more than 100C. Thermal energy only flows when there is a temperature difference, so once the liquid water in the cup and pot both reach 100C, there is no heat exchange between them. Water in the cup stays at 100C, but does not boil. $\endgroup$ Jul 2 at 14:08

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