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Suppose we have a closed container not isolated from the external environment so that heat exchanges can occur on the lateral wall (mainly for convection). The water inside is pressurized by a gas (nitrogen for example) starting from a pressure that is not exceeding 20 bar.

As water is drained from the tank I'm expecting that pressure will decrease as a result of the expansion and so will temperature that will lead to the onset of heat exchanges between liquid and gas and internal lateral walls. At this point a question comes: If a thermal control is inserted in the tank so that liquid temperature stays always in the range of 10 - 30 degree Celsius, boiling will occur only if vapor pressure of liquid will equate the pressure exerted by nitrogen on the liquid free surface. Can evaporation take place before reaching this condition? In this case, it is possible to consider that phase equilibrium is present?

I'm saying this since I can expect that some water molecules will have enough energy to escape liquid but will eventually come back due to volume constraint (even in the case of small quantities of vapor).

The same can be said also when boiling happens in such a way that its onset is always accompanied by condensation?

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  • $\begingroup$ For plain text formatting by StackExchange markdown, see as inspiration SE meta - formatting // SE meta - tables // Advanced formatting $\endgroup$
    – Poutnik
    Oct 4, 2023 at 14:28
  • $\begingroup$ If there is an inert gas as nitrogen, the liquid would never boil if there is enough time for evaporation of liquid vapor. Because external pressure would be always bigger than vapor pressure. $\endgroup$
    – Poutnik
    Oct 4, 2023 at 17:06
  • $\begingroup$ Thanks @Poutnik. Suppose that pressure of nitrogen will lower up to equate vapor pressure of water (around 0.03 bar for a temperature of 25 degree Celsius). Boiling will occur in these conditions? $\endgroup$
    – Enrico
    Oct 4, 2023 at 20:00
  • $\begingroup$ Imagine a pressure cooker that contains water and air, that is sealed and slowly heated, within safe margins. The the p = p_vapor + 1 atm (of air). Pressure is always higher than vapor pressure. Boiling is possible only temporary and locally, if water is heated fast enough so gas phase is not about saturated. $\endgroup$
    – Poutnik
    Oct 4, 2023 at 20:24
  • $\begingroup$ Ok thanks, so if heat exchanges are controlled we could assume phase equilibrium in the tank. An equal amount of water will evaporate while the exact amount will condense. $\endgroup$
    – Enrico
    Oct 4, 2023 at 20:36

1 Answer 1

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Boiling can only occur if the equilibrium vapor pressure of water at the liquid phase temperature exceed the the gas phase pressure. But, of course, evaporation can occur at the upper liquid surface if the equilibrium vapor pressure at the liquid phase temperature exceeds the partial pressure of water vapor in the gas phase.

You are controlling the temperature within the tank, so that it stays about constant. In that case, the partial pressure of the water vapor in the gas phase will about match the equilibrium vapor pressure of the liquid. Since the volume of the gas phase is increasing, some of the liquid water will have to evaporate to maintain vapor-liquid equilibrium.

A more interesting question would be what would happen if no heat was added to maintain the temperature.

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  • $\begingroup$ Thanks so much @Chet Miller, so I'm expecting that as liquid is drained outside the tank a small amount of water will evaporate for compensate the additional volume so that water vapor will become saturated. At that point, since no more vapor is allowed, there will be a mass exchange due to condensation towards the bulk liquid. As you said, boiling can only occur if vapor pressure is sufficiently higher than external pressure. At this point, can I consider properties unchanged during evaporation? Equal amount of mass and heat will be transferred during the processes until boiling occurs. $\endgroup$
    – Enrico
    Oct 4, 2023 at 15:01
  • $\begingroup$ I don't understand these question at all. $\endgroup$ Oct 4, 2023 at 15:12
  • $\begingroup$ Sorry @Chet Miller, it's mainly because I'm trying to understand the physics behind the process. We both agree that equilibrium exists since water is evaporating as liquid is drained. My question was mainly regarding what happens when vapor pressure of liquid equates pressure above its surface but as you said boiling will occur in that condition. $\endgroup$
    – Enrico
    Oct 4, 2023 at 15:30
  • $\begingroup$ You can model it and see how it plays out. Would you be able to handle that. $\endgroup$ Oct 4, 2023 at 16:01
  • $\begingroup$ Yep, I will work on it these days $\endgroup$
    – Enrico
    Oct 4, 2023 at 19:58

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