Mathematical Analysis of Boiling Two Eggs vs. One Egg

[_anant]

source:british physics olympiad 1993
it is said that it takes as long to boil one egg as it takes to boil two eggs. comment on the statement indicating the conditions under which it is valid?
can someone give me the mathematical analysis of the problem?

 

[light_bulb]

two separate pots?

 

[lpfr]

This is a reasoning physics problem, not a mathematical one. It does not ask for a single equation. You just have to ask a housewife if you have never boiled an egg yourself.

To be boiled, an egg needs to stay in hot water during a time depending on the wanted result (soft-boiled, hard-boiled) and in the temperature of the water. Usually, housewives and other people, use boiling water which uses to boil near 100°C when you are not in very high mountains. Then the temperature is almost the same... but for the fact that when you put a cold egg in hot water the temperature lowers and it takes some time to return to the boiling point. This is why light_bulb said "two separate pots". The other solution is to have a big pot full of so much boiling water that one o two eggs do not stop ebullition.

 

[_anant]

This is a reasoning physics problem, not a mathematical one. It does not ask for a single equation. You just have to ask a housewife if you have never boiled an egg yourself.

To be boiled, an egg needs to stay in hot water during a time depending on the wanted result (soft-boiled, hard-boiled) and in the temperature of the water. Usually, housewives and other people, use boiling water which uses to boil near 100°C when you are not in very high mountains. Then the temperature is almost the same... but for the fact that when you put a cold egg in hot water the temperature lowers and it takes some time to return to the boiling point. This is why light_bulb said "two separate pots". The other solution is to have a big pot full of so much boiling water that one o two eggs do not stop ebullition.

we should not talk about trivial matters like one or two pots or pressure dependencies.Let us take a single pot let us boil eggs there.Then some analysis in entropy of the egg has to be done as the proteins in the yolk become uncoiled.LET us take into account the specific heat capacities of the egg and water too and then let us formulate the cases.After making logical guesses we can provide the equations.This is the way i think this should be attempted as this is a genuine olympiad level question.{it is worth marks, of course!}

 

[haiha]

source:british physics olympiad 1993
it is said that it takes as long to boil one egg as it takes to boil two eggs. comment on the statement indicating the conditions under which it is valid?
can someone give me the mathematical analysis of the problem?

I think there's something connecting with the temperature conductivity of the egg'white especially when it is cooked. In fact the heat to cook an egg is very small, it take quite a time because the heat transfers to the yolk very slowly. So if you put one egg or two eggs into the pot when the water is hot or even when it is cold and you raise the temperature fast it take the same time for the heat to get into the yolk and cook it.

 

[denverdoc]

Agree with all that's been said. To formalize what has been said, i would suggest that when the reservoir of heat available to the egg is very much larger than that of the egg itself, and/or the heat added to the water (the source is equal to or greater than the sink, so that the temperature gradient is maintained irrespective of the number of eggs present. Just to be on the safe side I would say a lid should be used to minimize the presence of any non-uniform heating among eggs depending on their proximity to the surface or sides.

 

[Werg22]

In order for an egg to cook it has to attain a certain temperature. If we add another egg, it's as if we have an egg with twice the mass of one. This means that for this one big egg to cook, it has to absorb twice the heat that one egg needs (because mass and heat are directly related when it comes to raising temperature). Since the rate at which heat is transferred is almost constant at these relatively low temperatures, the more heat water has to transfer, the longer it takes. Consequently, it would take longer for 2 eggs to cook. The only possible way would be to change the temperature of the water adequately. This is how I see it, from a physics view point and from a food tv viewpoint

 

[_anant]

In order for an egg to cook it has to attain a certain temperature. If we add another egg, it's as if we have an egg with twice the mass of one. This means that for this one big egg to cook, it has to absorb twice the heat that one egg needs (because mass and heat are directly related when it comes to raising temperature). Since the rate at which heat is transferred is almost constant at these relatively low temperatures, the more heat water has to transfer, the longer it takes. Consequently, it would take longer for 2 eggs to cook. The only possible way would be to change the temperature of the water adequately. This is how I see it, from a physics view point and from a food tv viewpoint

did you take into account water's exceptionally large heat capacity?

 

[Werg22]

did you take into account water's exceptionally large heat capacity?

Be it water, oil or milk it doesn't change the fact that substance, if it is under constant conditions, transfer energy at fixed rate. This means that if it has to transfer twice as much energy as before, it will take twice the time. Since energy is directly proportional to mass, this means that time is itself proportional to mass. So it will take something around twice the time (I say "around" because in reality we have to use an integral with several variables to get the answer).

 

[denverdoc]

Be it water, oil or milk it doesn't change the fact that substance, if it is under constant conditions, transfer energy at fixed rate. This means that if it has to transfer twice as much energy as before, it will take twice the time. Since energy is directly proportional to mass, this means that time is itself proportional to mass. So it will take something around twice the time (I say "around" because in reality we have to use an integral with several variables to get the answer).

Think carefully about this. I always like to think in terms of absurd extremes to help intuition along, as few of are blessed with a physically intuitive mind.

Along those lines, take the pacific ocean which 4 billion years from now is a superheated cauldron of boiling water due to the sun's expansion, will it take twice as long to boil two eggs as one? So your statement is right but assumes a very limited supply of energy. Either we can supply this energy externally to keep up with any draw by the egg, or have such a huge reservoir of energy that an egg is a drop in a bucket.
J

 

[light_bulb]

so it's still two pots

 

[light_bulb]

kdelta+tdelta*2/E=kdelta+tdelta*1/E

yes i pulled that out of my bleep