Deutsche Version Experiments - The paradoxical egg cooker

During a project of the TU-Darmstadt (initiated and guided by Professor Hoffmann) some students, one of them has been me, have taken a closer look at the physics of a normal egg cooker.

Our laboratory - with thanks to F. Greil

Introduction

The scenario: I'm sure that you know how a normal egg cooker works. The eggs are held by a small construction above a small amount of water which itself is over a boiler plate. The water vaporizes until after some time nothing is left and the eggs are just ready.
But how much water is needed to cook a given amount of eggs? Therefore every cooker has its own special measuring jug that tells you how much water to take. But this is exactly where an egg cooker is "paradox": You will need more water to cook less eggs, why?

The history: We are not pioneers on the science of this area. Our predecessor for "egg-research" is Wolfgang Buerger, professor of mechanics at the University of Karlsruhe. He developed his own theory and wrote a book about it, there has even been an article in "Spektrum der Wissenschaft" about his groundbreaking work.

Our aim: It has been our declared aim to find out how one may describe the physics of an egg cooker and whether reality is described by Buerger's mathematics in a satisfying way.

Execution

Before we could start our actual experiments we had to define some standards that had to ensure that our results are reliable and reproducable. This is our standardized method:

big diagram Having developed those standards we could finally start our measurements. First of all we measured the size and the weight of our (class M) eggs, then we measured the time a given amount of water needed to evaporate for a defined number of eggs.
The diagram shows the evaporated amount of water in gram after a certain time in seconds. You can see here that our measured times can be described quite well with our theoretical model after we changed the boundary conditions to match the first few seconds better. This was necessary as the cooker does not know anything about the eggs should he only have very little water. The water just vaporizes without condensing on the egg's surface. This is why we had to move our graph a bit along the line representing no eggs.

The experiment during our lecture

The standardized egg

Real eggs taste good but they have some disadvantages for experimentation: They are not all the same (size, form, weight) and we do not know the specific values (specific heat, thermal conductivity, etc.) exactly. This is why we build our own "standardized" egg.
After we tested several materials whether they would make a good model of an egg, we chose stainless steel. He is stainless (good for working with water) and could be processed by our workshop quite good. Our new "egg" is now spherical with a diameter of 46mm. We found out that this egg could be described by our formula as well but with a restriction not to look at the first few seconds as our theory would give negative numbers because of the high thermal conductivity of steel, which is, of course, not realistic. In reality the amount of water just stays nearly constant.

Solution of the paradox

After that much practical experience I will sum up our results and try to solve the mystery:
How do the eggs get hot in the cooker? They do not take their energy directly hot water but from the vapor. They take the energy from the vapor which results in a condensation of the water on the surface of the eggs which will drop back to the boiler plate. It can easily be understood that the amount of recycled water is proportional to the cold surfaces thus the amount of eggs. However, the cooker is always creating the same amount of vapor per time interval that carries a constant amount of energy away that only some eggs cannot absorb completely. Because of this the vapor can escape into the surrounding kitchen. If the egg cooker contains many eggs much more energy is absorbed and more water drops back to be vaporized again.
But stop: more eggs also mean that we need more energy to bring them to the same temperature as only a few eggs. This would be contradictory to our theory. But our experiments and calculations show that this effect is not as strong a the "recycling" of the available water.
Looking back now it seems quite natural that more eggs mean less water.

If you want to know it exactly

View of the lecture room After we finished our project "The paradoxical egg cooker" we wrote a lengthy summary including all our calculations, experiments, ideas, values and results. I recommend it for interested readers (note: it is in German). You can download it here as a .pdf file.
About 50 biology students wanted to know about it, too. This is why they met at the university one Saturday to listen to a lecture we prepared on the subject of cooking eggs. Some of the pictures on this page have been made on this occasion.

During the preparation of another lecture which will be given during a special event at the TU-Darmstadt, called "Saturday Morning Physics", a presentation has been created by us. The HTML-version is online available as well.

I would also like to refer to the webpage of another member of our team containing further information. Furthermore, he created a Windows application simulating the thermal development inside a sphere which can be downloaded there.

contact me
Last change of this page: Jun 19, 2007