# Is this the right conclusion for a thought experiment?

In this thought experiment, let’s consider the surrounding to be air that is composed of entirely water vapor (no other species like $\ce{O2}$ and $\ce{N2}$ are present). The surrounding is infinitely large. The system in question is a pan containing a thin layer of liquid water. The liquid water is brought to its boiling point by uniform heating. This pan is open (not covered in any way) and is exposed to the surrounding water vapor.

By definition, boiling occurs when the vapor pressure of the liquid is equal to the external pressure. So in this case, at boiling point, the vapor pressure of the liquid $\ce{H2O}$ is equal to the external pressure of gaseous $\ce{H2O}$. Thus, the system is in a dynamic equilibrium, and the rate of vaporization is equal to the rate of condensation.

This implies that the amount of liquid water will not change over time. In particular, it will not all “boil off” as steam. Is this the right conclusion? It certainly seems a little absurd.

• How fast is the water heated? If it is heated quickly, the vapor pressure of the water in the pan could reach a point above the pressure of the vapor, a nonequilibrium situation. How large is the volume of water compared to the volume of the system? If it is significant, the system could boil for some time before equilibrium is reestablished. It seems that you are asking whether or not boiling is possible in a liquid that is in equilibrium with its vapor. – Brinn Belyea Jan 13 '15 at 4:16
• i think the statement "(no other species like O2 and N2 are present)" will create side problems – RE60K Jan 13 '15 at 8:44
• @brinnb Jon Custer below seems to indicate the rate of heating does not come into play. That's not what I was asking - I believe boiling is possible in a liquid that is in equilibrium with its vapor; this can be easily achieved in a closed container. – JHN Jan 14 '15 at 1:05
• @ADG Could you explain what side problems this will cause? – JHN Jan 14 '15 at 1:06
• Thank you all for your answers and comments - some of the concepts discussed are new to me, so I will need to take some time to learn them before selecting an answer. Thanks again! – JHN Jan 19 '15 at 8:57