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I have a problem. I would like to calculate after how many minutes / hours the water in a $50$ cm diameter pot, $50$ cm high, evaporates completely.

The temperature is constant, $40^o$C the pressure is $4.5 \times 10^3$ Pa

There is a vacuum pump that sucks in the air (therefore also the steam) and allows the pressure to be constant.

Could you tell me how long it takes to evaporate completely?

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  • $\begingroup$ There must also be some contraption to kerp the water at a uniform temperature of 40C, or it.may freeze. $\endgroup$
    – my2cts
    Commented Jul 14, 2021 at 12:16
  • $\begingroup$ Of course ! :) :D $\endgroup$
    – Borja
    Commented Jul 14, 2021 at 12:20
  • $\begingroup$ Have you got the pressure value right? $\endgroup$
    – John Hunter
    Commented Jul 14, 2021 at 13:29
  • $\begingroup$ So you should extend your description with a contraption that keeps the water homogenously at 40C while you are pumping off vapour. This does not seem trivial to me. $\endgroup$
    – my2cts
    Commented Jul 14, 2021 at 21:57

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If you were somehow able to maintain that temperature and pressure, it would be basically instantaneous: the boiling temperature of water at 4500 Pa is 30.9 C. The boiling temperature at the bottom of the pot, due to hydrostatic pressure, would initially be higher than 40 C, so the explosion of superheated water might kind of propagate from surface to bottom, but it would all proceed quite violently.

In any real experimental setup, you would find that as fast as you added heat to the pot, if you keep the pressure always at 4500 Pa, you would not be able to bring the water temperature to 40 C. All the added energy would go into the latent heat of vaporization, not temperature increase: the water would bubble and boil, but would maintain a temperature of around 30.9 C.

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  • $\begingroup$ More info: The 4500 Pa pressure is equivalent to Earth's atmospheric pressure at an altitude of 65000 ft, about 19.7 km. $\endgroup$
    – Bill N
    Commented Jul 14, 2021 at 13:33
  • $\begingroup$ Interesting, but how many minutes? $\endgroup$
    – Borja
    Commented Jul 14, 2021 at 14:35
  • $\begingroup$ Again assuming you can somehow achieve and maintain the stated temperature and pressure, much much less than a minute. $\endgroup$
    – Ben51
    Commented Jul 14, 2021 at 14:36
  • $\begingroup$ Please, can you show me phormula to calculate it ? Is very interesting and important for me $\endgroup$
    – Borja
    Commented Jul 14, 2021 at 15:07
  • $\begingroup$ engineeringtoolbox.com/… You can use the calculator at this link to find the boiling temperature of water for a particular pressure. $\endgroup$
    – Ben51
    Commented Jul 14, 2021 at 17:08

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