Can you boil this water?

Water at 100 degrees Celsius needs more heat to boil. That is, water will boil at room conditions if and only if heat is added to it after its temperature is 100 degrees Celsius. This is the energy required for liquid water to convert into steam at 100 degrees. This energy is called the latent heat of vaporization, as it is "hidden". This is also the reason why the temperature of water remains constant throughout boiling. The heat is used to turn water into steam and not to raise its temperature.

We know that the heat flow between two bodies will stop once they are at the same temperature. So what happens here is that the water outside the cup and in the cup both get to 100 degrees Celsius. The water outside the cup receives more heat from the heater and starts boiling(keep in mind that the temperature is always 100 degrees throughout boiling). But as the cup and its surroundings are in equilibrium (same temperature), there is no heat being transferred into the cup. This means that the water in the cup is at 100 degrees, but it doesn't get more energy to turn into steam, and hence it does not boil.

Edit:

Guess what? I tried doing this experiment at home and it came out with favorable observations, even after 10 mins of continuous boiling, the water in the floating cup did not boil! Here is the pic(tried adjusting brightness and contrast to bring out difference):

Also, I uploaded a video of this on youtube, here's the link.

This is a well known cooking technique. In my country it's called Baño María. The water inside the cup doesn't boil because it doesn't reach the necessary amount of energy. Of course, if the water outside of the cup was saltier than the water inside, then the cup would boil.

answer is no... it acts like a water bath... the cup water reaches 100 centigrade and transfer of heat is stopped as the outside temperature of boiling water is also 100. further phase change of cup water to steam needs latent heat which cant happen as heat transfer is stopped. provided the whole system is under std atmospheric pressure. close example is household milk cooker

From an engineering point of view:

Heat is needed to increase temperature and change the phase of water in the cup.

Heat transfer can only happen if there is temperature difference.

The reason the water in the pot can boil is because there is temperature difference between the water and the heat source. Since there is also temperature difference between the water in pot and cup, heat transfer into cup happens to increase the temperature of the water in cup to its saturation temperature. However since the water in the pot is always boiling, its temperature is constant so when the water in the cup reached the saturation temperature as saturated liquid, there is no temperature difference between water in cup and pot so no heat can be transferred into cup to change its phase to gas.

I think what some are missing here is that the only water that is actually "boiling," or changing state to vapor, is the water in contact with the pot at the heat source, the bottom. Although it appears the entire pot is boiling, depending on your definition of boiling, it is not. The only reason the water is boiling is it is at 100 degrees and then receives more energy to push it to vapor. The suspended cup being no where near the heat source and not receiving any further energy will not boil.

This is a "double boiler", I've used it for cooking/baking with chocolate. The practical purpose is that the cup (and it's contents) never get hotter than boiling water, so the chocolate will not burn.

I've also seen this in my thermodynamics courses. The liquid water in the pot will never get hotter than boiling, so the liquid in the cup can reach equilibrium with the liquid in the pot, but not get any hotter.

It is possible that vapor bubbles (> boiling temp) will contact the cup, transferring some energy, facilitating the transition from liquid to vapor inside the cup. However, this would require a very hot source in the pot to produce enough vapor bubbles to heat the cup above boiling.

My answer to " Will the water in the cup ever boil?" is: Probably not; it depends on the temperature/heat transfer from the heater to the liquid in the pot.

To change phase from a liquid to a gas, water must first reach it's boiling point and then additional energy must be added for it to change to a gas. That is. liquid water at 100C has significantly less heat than steam at 100C. Since the pot of water is at boiling temperature any additional heat applied goes toward creating steam, not raising the temperature of the water. Because heat flows due to a temperature difference, the water in the cup will not receive any additional heat once it reaches equilibrium with the water in the pot, therefore it cannot boil.

Boiling is basically phase transfer of the liquid. Heat is absorbed to make the phase transfer. Now the heat required to maintain the boiling keep the water at 100 deg C. And the cup is also maintained at 100 deg C. However it does not receive the extra heat to convert it into steam, i.e. Latent Heat!!!

We all know that water boils at 100°centigrade,it does not get more energy to turn into steam,hence it will not boil

The water will remain at a temp of 100 degrees but will never heat the Styrofoam enough to cause the water inside to boil. At the heat of vaporization, liquid water can not get any hotter, thus undergoing a phase change to gas, the cup's specific heat capacity will prevent the water from ever boiling inside of it.