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Consider a simple experiment, such as boiling water in a pot in your kitchen, is it possible to estimate the time needed for the water to boil based on elementary properties of water ?

In the physics and chemistry literatures we find many computational and theoretical works attempting to predict the boiling temperature of water, from elementary properties, such as the molecular bonding strength or angles. But what about the boiling time ?

The basic parameters for the boiling time should the heating power, the heat conductivity of the pot, the heat capacity of water, and possibly other properties that characterize the transfer of energy from the environment to the water. My question is about the time needed from the moment where the water temperature is close to boiling point, to the moment where water has left its initial liquid state.

It is mentioned in many lectures and textbooks that nucleation is a limiting step in the formation of a new phase, in particular for the boiling of water. But I was never able to find a critical comparison of such statements. So I would appreciate any references or indications. Which kind of computations do you expect to be necessary ? What kind of empirical parameters enter in the calculation ? Was this done in a reference?

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  • $\begingroup$ I probably don't know the answer yet, but i find it interesting. To confirm that i understand it right, do you mean like the time between the moment when a pot of water reaches 99.9 degrees Celcius at atmospheric pressure, and the moment when all the water has just been boiled away and just a dry pot is left? $\endgroup$
    – aystack
    Jul 28, 2023 at 12:56
  • $\begingroup$ Yes, exactly. Qualitatively, the time-dependence of temperature of water in this experiment would roughly show three windows : First a linear increase due to heating of the liquid. Here the rate should be controlled by thermal conductivity and heat capacity properties. Then temperature is flat at 100 degrees, this is the "boiling" window. Then temperature increases linearly again due to heating of the gas, while all the liquid phase boiled away. $\endgroup$ Jul 29, 2023 at 12:47

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One needs some information about the heating device - it is somewhat complicated one heating on fire, even with a gas stove, and somewhat easier with an electric one. The simplest estimate is the one for an electric pot - one has to look at the package (or the pot itself) to check its power, $P$, measured in Watts. The energy produced by the pot is then $U=Pt$, where $t$ is the time. This energy has to be equal to the energy required to heat water to the boiling temperature (typically $373K$, but can be lower at higher altitudes) and to convert it to gas, just as they teach in basic physics and chemistry: $$ Pt=C(T_{boiling}-T_{room})m + \lambda m, $$ where $m$ is the mass of water that we are trying to boil. The mechanism of boiling - how the bubbles form etc. would really lead to only small adjustments.

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    $\begingroup$ Let us take the pot on the electric plate. I agree of course that the basic parameters are the heating power, the heat conductivity of the pot, the heat capacity of water, and possibly other properties that characterize the transfer of energy from the environment to the water. But my question was more about the time needed from the moment where the water temperature is close to boiling point, to the moment where water has left its initial liquid state. I adapt my question. $\endgroup$ Jul 28, 2023 at 8:28
  • $\begingroup$ @YoussefMabrouk then the question becomes about the dynamics of a phase transition, which makes it a lit more complex (though also very interesting). $\endgroup$
    – Roger V.
    Jul 28, 2023 at 8:39

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