My textbook asks the question why a liquid cools down when partial evaporation occurs just below the surface at a temperature below the boiling point.

The answer is of course that only those molecules who "randomly" possess high kinetic energy are able to shoot out of the liquid, thus leaving behind molecules with (on average) less kinetic energy.

But then I was left wondering whether the molecule that leaves the liquid itself used some of its energy to break the bonds with adjacent molecules, in a manner similar to the "heat of fusion"? I.e. does the molecule that leaves the liquid lose some of its energy as well?

  • $\begingroup$ I don't know why someone downvoted this question; it seems to be a good question. This link [faculty.spokanefalls.edu/InetShare/AutoWebs/georget/… explains that, indeed, a water molecule must "leave some energy behind" in breaking hydrogen bonds with its neighbors as it escapes the surface of the liquid. $\endgroup$
    – S. McGrew
    Aug 5 '18 at 14:23
  • $\begingroup$ @S.McGrew Good point. You may need to remove the square brackets from the link - did not work as is for me. Regarding the energy of vapor molecules, it seems reasonable that they should lose some energy when breaking off the surface, but still, on average, have energy higher than the average energy of liquid molecules - to cause evaporation cooling. $\endgroup$
    – V.F.
    Aug 5 '18 at 14:49
  • $\begingroup$ Here is the link without brackets: faculty.spokanefalls.edu/InetShare/AutoWebs/georget/… $\endgroup$
    – S. McGrew
    Aug 5 '18 at 15:03
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    $\begingroup$ Actually, the molecule - after escaping the surface of the liquid- can have lower energy than the average molecule in the liquid. $\endgroup$
    – S. McGrew
    Aug 5 '18 at 15:09
  • $\begingroup$ Thank you for your comments! And as energy is never lost, but rather transformed: where does that energy lost by the leaving molecule go? $\endgroup$
    – Pregunto
    Aug 5 '18 at 15:15

The Kinetic Theory deals with Ideal Gases, where by definition no intermolecular forces of attraction exist, i.e., there are no enthalpies of fusion, evaporation, etc. Because of this all collisions are elastic, meaning all energy is purely kinetic: The leaving particle is the fastest particle. So we can rightly assume in pressurised Ideal Gas containers that when we release pressure, the highest energy particles are the ones which are leaving.

And now the answer. Like all elegant theories, they naturally get used out of context, oftentimes to very interesting effect. Water wapor is about the least Ideal Gas anyone can think up. For such a simple molecule, it has one of the strongest intermolecular force of attraction known to us: the hydrogen bond. So we must take care to identify where the applicability of the Kinetic Theory ends, and where we need more sophisticated concepts to explain the observations.

When one water molecule leaves the liquid phase it is implied that significant kinetic energy has been consumed for the pre-requisite hydrogen bond breaking. The implication is clear: the liquid body must now have a lower kinetic energy (and therefore temperature). If we were still constrained to thinking about this in the frame of the Kinetic Theory, we would be forced to assume that the leaving water molecule (now a gas) has a higher kinetic energy. This is not true, as we cannot ignore the bond energy just mentioned. The energy premium expended by the liquid body to break the H-bond now exists in the gas molecule as potential energy (to be released eagerly as kinetic energy for bond forming later should the opportunity arise). One can also say it is now in a higher energy state, just not kinetic in nature. So in fact, the leaving water molecule can either be of a higher, lower or equal kinetic energy as the liquid body it just left. Although, practically speaking, in order for there to be sustained evaporation, the water vapor should not be of a lower temperature than the water (otherwise it would just recondense).

TLDR Water is one of those molecules which can contain/release very high levels of potential energy in the form of H-bonds, so it can be very misleading to look at it from the Kinetic Theory perspective which only considers kinetic energy and not potential (bond) energy.


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