My nephew showed me an exercise from his school-textbook about boiling eggs. Here is the exercise (translated from german):
- To make one hard-boiled egg in a pot of water one has to put it for 8 minutes into boiling water. How long does it if you put 10 eggs into the boiling water instead of one to make hard-boiled eggs?
- Using an electric egg cooker (something like this: https://www.buyegggenie.com/) one needs 7 minutes to make 3 hard-boiled eggs. How long does it take to make 6 or 10 hard-boiled eggs?
The chapter in the textbook is about simple calculations with proportionalities ("Dreisatz" in german). For my nephew it was not problem to solve the exercises if one assumes that the cooking time and the number of eggs are proportional. But for him and also for me it is not clear why and when one can assume proportionalty and how to justify it physically.
My intuition (which is probably wrong in this case) says that in both cases we don't have a proportionality moreover that the cooking time is independent of the number of eggs.
To the second part of the problem: I don't own a electic egg cooker. From googling around I have found that it works with water steam (whereas in the first case the eggs are in the water). And that one needs less water in the electric egg cooker to boil more eggs. It is not clear to me how to interprete the second problem. One could assume that one uses always the same amount of water in the electric egg cooker or that one fit's the amount of water to the number of eggs (which will result in different cooking time - number of eggs relationships, perhaps one proportional and one constant...)
So it would be great if someone could clarify this physically. I.e. how does the cooking time depends on the number of eggs and why and under which assumptions in each case.
How does the situation change if one puts the eggs not in the already cooking water but into cold water at the beginning.
Are there methods of making hard-boiled eggs such that the cooking time is proportional to the number of eggs and are there methods such that the cooking time is (roughly) independent of the number of eggs? How to justify it physically?