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The story

If there is an easily understandable problem that fascinates me compare to apparently how hard it is to model and solve accurately, and how little it has been studied, the time to cool down my cup of tea taking into account the evaporation of water comes up first in my mind.

I did a simple experiment: cool down water in my cup, once with a lid on top of it and once without. The results are unequivocal. It takes (for my cup) twice as much time to cool it down when the lid is on (and this agrees my theoretical heat balance up to 5%).

I would like then to take into account the evaporation of water as it cools down. But so far I haven't found great literature on the subject when I thought for such a little question there would be a huge mound of it.

What I have found so far

I found this article that gives the rate of evaporation of water at low pressure (up to 900 Pa). What is cool is that they derive the equations to solve the problem but I don't know how to implement them, nor what a tensor is and I would prefer using a correlation-based rate of evaporation as a function of temperature determined with the least square methods to correlate data to an equation model. And even for that, I don't find anything but I may have not searched correctly. It would be great to get data from 20 °C up to almost boiling water.

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  • $\begingroup$ Why not measure weight v. temperature over time for a well-insulated cup/mug filled with (initially) hot water? $\endgroup$
    – Gert
    Feb 5, 2021 at 22:19
  • $\begingroup$ @Gert I would have to buy a precise balance which requires the use of a small cup otherwise the mass of the cup itself may be too much for the range of the balance. I don't have any good apparatus to do such a thing and working in the industry where evaporation is such as thing I find it mind-blowing that such precise experiment has never been done. $\endgroup$
    – ParaH2
    Feb 5, 2021 at 23:03
  • $\begingroup$ See Mass Tranfer Operations by Treybel. $\endgroup$
    – Chet Miller
    Feb 5, 2021 at 23:53
  • $\begingroup$ A $200\pm0.01\mathrm{g}$ is very cheap. Use a small ramekin, plastic preferably. $\endgroup$
    – Gert
    Feb 6, 2021 at 0:00
  • $\begingroup$ Is your goal to calculate temperature of the tea vs. time? If so, is the calculation to be done for one particular cup that is filled to the same level every time? What I'm getting at: if you want a correlation of temperature vs. time, it would be much more straight-forward to directly measure that variable instead of looking for a way to determine evaporation rate vs. time and then using some type of correlation to calculate temperature vs. time. $\endgroup$
    – David White
    Feb 6, 2021 at 0:33

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Here is one source that provides a simple relationship that may be accurate enough for your purposes: https://van.physics.illinois.edu/qa/listing.php?id=1440

The text Transport Phenomena by Bird, Stewart, and Lightfoot has correlations for mass transfer, including evaporation.

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