Why water molecules at the surface of water have higher kinetic energy than the bottom ones?

Question

It's written multiple times in my textbook that

Some molecules at the surface of the liquid have kinetic energy more than those in the bottom, so they can escape from the surface.

But what causes them to have more kinetic energy or more speed (as far as I understand more k.e means a higher speed)

My usual guessing to why molecules at the surface only evaporate while the bottom don't is that maybe it has sth to do with the fact that the molecules at the surface only have to overcome the atmospheric pressure and the water molecules bonds under or next to them

But molecules at the bottom have to overcome bonds under, next and above them plus atmospheric and water pressure.

But I can't relate or make this guessing explain why molecules at the surface have more k.e than the bottom ones.

Answer 1

First of all look at the picture below :

The molecule A has attractive forces from molecules all around it. So it has more negative potential energy with other molecules i.e. if each molecule has $5J$ when isolated then A will have very less remaining energy (say $1J$) and this is the vibrational or its kinetic energy.

Now the molecule B has to interact with lesser molecules around it (nearly half) . So it has nearly half negative potential energy with other molecules and so it has greater remaining energy (approximately $3J$) i.e. its kinetic or vibrational energy .

So , A needs $4J$ of energy ( this amount totally depends on the negative potential energies between the molecules) then B will need just $2J$ of energy to come out .

Note : the molecule at the surface also interacts with the molecules of air above it but the interaction numbers are less than the one within the liquid. So the molecules at surface do have greater remaining energy.

Note : as Philip Wood mentioned in the comment , I would like to add that though $(-1)>(-2)$ but I have given the answer with respect to the magnitudes of the energy only. You can think of the negative sign as an indicator of released energy for your convenience.

Hope it helps ☺️.

Answer 2

If this is a system at equilibrium, then either your textbook is wrong or it is being misinterpreted. Temp is uniform throughout a system at equilib.

If not at equilib, and there is net evaporation going on, then surface is cooler (lower kinetic energy) due to preferential evaporation of faster waters.

Answer 3

The water in the container has an average temperature, but there is a statistical distribution around this value.

A given small volume, where the local average is bigger than the global one, is less dense due to thermal expansion.

Buoyancy force displaces that volume upwards.

The opposite happens to fluctuations of the energy distribution to lower temperatures, and the small volumes sinks in this condition.

So there is a gradient of temperature in the container, and elements of volume with higher temperature are more probable at the surface.