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Consider I have two type of cooking kettles, which the shape is just like a pure tube with the volume is 1000 cc (1 liter) with the radius and the height as below (volume=pi*r^2*h):

  1. The first kettle: cross-section radius=5.6419cm and the height=10cm.

  2. The second kettle: cross-section radius=3.9894cm and the height=20cm.

Those two kettles filled up with the same kind water from a same source. Consider that I have a small stove that that its flame will be enough to boil the water inside those kettles. Also consider that those kettles has enough additional height so the water will not get spilled when it start boiled. Then my questions are:

  1. Which one will be get boiled faster (shorter time)?
  2. When they are get boiled, which one is healthier (due to it distribute the heat uniformly to that water inside the kettle)?

Edit: Water will be filled up from top. Say that there is a small cap to fill water into it. There is no other hole. Flame on the stove are put the same distance for both the kettles, close enough so the flame will be effective to heat the water.

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  • $\begingroup$ Were the containers filled from the left side or the right? How far above the flame are they mounted? $\endgroup$
    – Solar Mike
    Jan 28 '19 at 4:53
  • $\begingroup$ I have added another info. Water is filled up from above. $\endgroup$ Jan 28 '19 at 5:09
  • $\begingroup$ Is this homework? Nobody has kettles that are tube-shaped; further nobody has kettles lacking a cover! $\endgroup$ Jan 28 '19 at 20:12
  • $\begingroup$ No, this is not a homework. I saw many boiling kettle that boiled water so quickly especially when the amount of the water quite few, but not even hot enough to make coffee. But when I boil water in a small kettle but taller with the same amount of water and consider the water are same, the water seems hot enough to make coffe. The question about which one is distributes heat more uniform between the first and the second one came from my curiosity. Absolutely, there is different betwen the them. $\endgroup$ Jan 29 '19 at 0:30
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The difference between the two containers may be miniscule, but a reference located in the Physics StackExchange presents the statement that evaporation depends on the surface area, local humidity and air pressure. The latter two factors will be presumed to be identical for your question.

Evaporation cools the water, requiring more heat to maintain the water temperature. Allowing that you have sufficient heat to boil the water, this factor can be considered unimportant regarding time-to-boil.

The surface area of the larger diameter container will present faster evaporation than that of the smaller one. Evaporation does not require boiling temperature, which means it will begin larger volume of evaporation sooner than the smaller container.

Your second question may not have a solution, as there will be convection of the water within both containers and heat distribution for either would be about the same and would likely be uniform throughout.

The smaller diameter container should boil sooner than the larger one.

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  • $\begingroup$ but the larger area may help better heat conduction from the flame to the container... $\endgroup$
    – Solar Mike
    Jan 28 '19 at 11:42
  • $\begingroup$ In my opinion, the second one (the smaller radius but taller) is better uniformly heated due to the heat is going up and the heat is transfered from the flame to the kettle then to the lower surface of the water, then that heat will heat the upper layer of the water until it released to the air. But, however, it only my opinion that I am looking for the answer for you all. $\endgroup$ Jan 28 '19 at 13:31
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Backpacker here. I have some practical experience getting the most out of a bottle of fuel. This really is a matter for experiment. But wide pans do better than tall ones in general. If you have enough of a source to actually boil the water, then maximizing heat transfer into the water is your first concern. So check the temp of the air as it rises around the edge of the pan. You want it protected from drafts and just above the boiling point. Even a fairly small flame will favor the wider pan. it would have to be something tiny like a candle to favor the taller one. Also, I'm assuming a lid is available. Doing this without a lid is basically silly. Lids come with pots, and have done for quite a long time.

However, the real point of the question may be to challenge you to think of all the factors that could effect the result.

  1. lid or no lid
  2. material and thickness of pans. Note: you have to heat the pan up too.
  3. fuel type and combustion gas temps.
  4. hob design
  5. fuel rate.
  6. rate of heat loss from lid or possibly sides.
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  • $\begingroup$ But my experience, with the same amount of water and the same flame size, boiling water in a wider base container's surface but shorther and in a smaller base surface but taller, the first is got boiled faster but seems not hot enough. Not even suitable to make coffee, compared to the second one. But about which one is distributes the heat more uniform, that my question. This related to proof that all the water in a container is really boiled, not only partly. That's why I said "healthier". $\endgroup$ Jan 29 '19 at 1:00
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You have left out several things:

Is the flame as wide as the larger diameter kettle? Are there covers?

If the flame is as wide as the larger, then you will lose a lot of its heat when using the smaller kettle, because it'll just create a hot air convection path outside the kettle.

And so on.

Do you need boiling everywhere ("rolling boil") or just at the bottom?

What do you mean by "healthy" ? Just bringing to onset of boiling will suffice if you are worried about things that die instantly at 90 - 100 \degree C , but not if you need to kill things (which exist in nature) that require a few minutes in that temperature range.

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  • $\begingroup$ About the flame: the "size" of the flame should be same for both. From there we may measure. If we put the flame as wide as the first (the bigger) surface, then the flame will heat the water from side surface for the small one. Vice versa, if the flame we set as wide as the second wide (the smaller cross-section), the the flame will not even reach all the surface of the first one (the shorter). There will be consequence for both. Thence came question. $\endgroup$ Jan 29 '19 at 0:37
  • $\begingroup$ About "healthier": even whater get boliled, I worry that the heat were not uniformly distributed. Mean, not all the water in a one container actually boiled. I have experience about it when I boiled water in a large cross-section surface container with few water, water got boiled but not even hot enought to make coffe. Vice versa, the smaller container seems hotter from the first one. Of course I cook the same of water with the same stove and the flame. $\endgroup$ Jan 29 '19 at 0:42

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