Can evaporation take place in this scenario?

[Puma]

This is extemely important to me!

In an isolated system of a very large box half filled with water, a small soaked sponge is placed just above the surface of the water. Will the sponge eventually dry? At first I thought not. But the molecules in the vapour above the water might have a higher temperature than the water itself because they have all managed to reach the escape velocity to evaporate. This indicates that the sponge with a greater surface area to water mass in comparison to the body of the water might also be warmer and eventually dry because of this.

Thanks very much if you can help.

 

[mfb]

But the molecules in the vapour above the water might have a higher temperature than the water itself because they have all managed to reach the escape velocity to evaporate.

They don't - this excess energy is exactly what they need to escape, and don't have any more afterwards. The system will go towards an equilibrium with the same temperature everywhere. The sponge will have some water (capillary forces help here), but won't stay completely soaked. The air will reach 100% humidity.

 

[Puma]

Thanks for the reply.

If the tank was filled with helium would there be a gradation of humidity in the tank from top to bottom due to the high relative mass of the H2O, thus allowing the sponge to dry or partially dry?

 

[mfb]

If your box is several kilometers high to make that effect notable (you don't need helium, just the overall reduction in pressure is sufficient), the amount of water in the sponge will depend on its height, but it will never be completely free of water.