Starting with a pot of cold tap water, I want to cook a hard-boiled egg using the minimum amount of energy. Is it more energy efficient to bring a pot to boil first and then put the egg in it, or to put the egg in the pot of cold water first and let it heat up with the water?
[Physics] the most energy efficient way to boil an egg
thermodynamics
Related Solutions
Assuming the first was also tap water at the same temp and the pot was room temperature, then all that can be said given your question is "less than 20 minutes". It depends on the thermal capacity of the pot.
Put another way, the first time you boil the water you have to do two things:
- Heat the pot to boiling temp
- Heat the water to boiling temp
The second time all you have to do is:
- Heat the water to boiling temp
What really happens when you put the tap water in the hot pot for the second time is that thermal energy from the pot flows into the cooler water and warms it up. This lowers the temperature of the pot and raises the temp of the water until they are roughly equal temperatures (thermal equilibrium). After this balancing the whole system starts out warmer than the first system did and less energy must be put into the system to heat it to the same boiling point. If the first one took 20 minutes then the second one will take less time. The actual amount of time saved depends on how much heat energy was stored in the pot and that depends on the size of the pot, what it's made out of, etc.
In the real world, you are approximately right and the cooking time is pretty much independent of the number of eggs. An egg only cares about the temperature of the water that surrounds it and as long as it is kept near the boiling point at all times, an egg can't possibly "know" how many siblings it has. So its gradual change (and its rate) is universal, independent of the number of eggs.
On the other hand, if this is some textbook example about proportionality, it's one of the would-be real-world applications of proportionality and the underlying assumption is that the cooking time is proportional to the number of eggs. In the real world, this can only be true if the number of eggs affects the actual temperature of the water around them.
A justification of the proportionality is that the egg cooker needs to pump a certain amount of energy $E$ to an egg to turn it into a hard-boiled egg. Because the egg cooker consumes the same amount of energy per unit time, it needs $N$ times longer time to pump the energy $NE$ into the $E$ eggs. In practice, this may be a somewhat reasonable description if the egg cooker is weak enough and it has a hard time to achieve or maintain the boiling point as the eggs are cooling the water down.
The truth in the real world will be somewhere in between: the cooking time may grow with the number of eggs but the growth is much slower than the direct proportionality.
When I am cooking various deeply frozen lunches, the recommended cooking times for half a bag are often something like 80% of the cooking times for the whole bag. The idea is that with more food on the pan, it takes a bit longer for the heat to penetrate from the pan to the interior of the food. The idea with the eggs is similar if the cooking time is supposed to increase with the number of eggs.
Best Answer
Break egg into vacuum vessel, lower pressure until egg boils (sorry don't have a phase diagram for eggs handy)