We can almost do the experiment in question. We scoop some of the liquid out of the container with a ladle. As far as what molecules got removed, molecules of different speeds had an equal chance of being removed. That which remains is the same temperature as what it was. The only issue is the way we removed them would not be considered escape from the surface. Perhaps if we float a paper towel on the surface and then pull it up after it has soaked up some of the liquid we have actually done the experiment.
Regarding the idea of how evaporative cooling works, I think the idea that faster molecules escape from the surface leaving slower molecules behind works. (I think the explanation given in the Physics Teacher is conceptually correct.) The temperature of the liquid is related to the average kinetic energy of the molecules even when there is potential energy. Because of the potential energy, a fast moving molecule that escapes will have less kinetic energy after it escapes than it did when it was part of the liquid. It was an outlier to start with so whether its kinetic energy after escape is higher or lower than the average kinetic energy of the molecules making up the liquid will vary from case to case. So there is no reason to believe the temperature of the vapor is greater than the temperature of the liquid. Also, the vapor is part of the atmosphere and the temperature of the atmosphere can be higher or lower than the temperature of the liquid. We can use evaporative cooling to keep our body temperature at about 98.6 degrees Fahrenheit whether the atmospheric temperature is 95 degrees F or 100 degrees F. In one case the vapor is cooler than the liquid and in the other case it is hotter.
I interpret the /surroundings/ you wrote about to be everything but the liquid. Interactions of the molecules of the liquid with other molecules of the liquid result in a distribution of the kinetic energies of the molecules making up the liquid. Some of them will have a total energy that is greater than 0. Some of the ones that have a total energy greater than zero will be near the surface. Some of those will have a translational-kinetic-energy-plus-potential energy that is greater than zero. Some of those will have their velocity directed away from the liquid. Those will escape. They don't need energy from the surroundings to escape. If at some earlier time they have insufficient translational kinetic energy to escape, they can get the necessary energy from other molecules in the liquid; they don't have to get it from the surroundings.
-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@mail.phys-l.org] On Behalf Of Robert Cohen
Sent: Saturday, January 20, 2018 5:29 PM
To: Phys-L@Phys-L.org
Subject: [Phys-L] Figuring Physics solution Jan 2018
I am curious as to whether anyone can confirm the explanation given in the Jan 2018 "Figuring Physics" solution provided in the Physics Teacher:
Basically, the question is whether cooling would occur if molecules of every speed in a liquid had an equal chance of escape from the surface. The answer given in the column is no, with a rationale that the cooling occurs because the faster ones are the ones that are leaving and the slower ones are left behind.
The reason I ask is because I used to use somewhat similar logic but stopped, and now I'm not so sure.
I stopped for two reasons. First, the "slow molecules left behind" implies that the remaining liquid becomes cooler than the vapor that is produced. Second, I feel it obscures the fact that the process of leaving (which is a sort of bond breaking) requires an extraction of energy from the surroundings, regardless of whether the molecules involved were initially going faster or slower.
Robert Cohen Department of Physics East Stroudsburg University
570.422.3428 http://quantum.esu.edu/~bbq East Stroudsburg, PA 18301