A bit funny practical task: frozen dumplings in boiled water, how temperature changes and when will boil again?

Question

This is my question:

1. I take a pot with boiling water (temperature of water is equal to boiling temperature), water was boiled in tea can
2. I take frozen dumplings
3. Now I put dumplings into the pot
4. Only now I put this pot on the stove
5. We know that dumplings would be ready in 7 minutes (so they would start floating up)

My question is - whether in 10 seconds after putting dumplings into the pot, water would be still boiling (taking into account that we put pot on stove again)?

• So, I think that just after putting frozen dumplings into the pot, probably water won't be boiling any more (water temperature would decrease)
• I also assume that water temperature would drop from 100 to maybe 80? Is it logical? Or 80 is incorrect assumption?
• Then when put on the stove, water would start boiling again at some point
• But is 10 seconds enough for water to boil again?
• Does it depend on amount of water/dumplings or not?
• How to calculate (or at least understand approximately) how would water temperature change in 1 sec after we put dumplings into the water? And how it will change when put on the stove back?

I do not need some solution, but just help with correct reasoning, how to think correctly and what are processes that should be taken into account? I am also not given any precise values (like amount of water or dumplings). I want to understand different scenarios if there are possible multiple solutions.

Answer 1

Assuming you have boiling water and standard conditions (T = 20°C, P = 101.3 kPa) and do not add any energy to it, it will stop boiling due to heat loss to the environment. There is no need to add the frozen dumplings to the water. However, due to the addition of the dumplings, the temperature of the water will decrease further.

Your question whether or not the water and dumplings will cook after 10 seconds depends on the amount of heat added to the pot. The water itself has a certain heat capacity as well as the dumplings and the thawing of the dumplings will also play a part in this. You will need to take all these factors into account, among others, to obtain the total necessary heat and devide that by the desired time to obtain the necessary power of the heat source.

The description of steps above does not take into account several factors, for example the conductivity of the pot, the consistancy of the dumplings, so the answer you obtain will always be an approximation.