Figuring out Dry Tarn - Maxwell-Boltzmann

 

I think I have thought of a solution to my question about Dry Tarn. The Maxwell-Boltzmann distribution for a constant temperature is above. Particles with high speed will have enough kinetic energy to escape from the tarn by evaporation. But that means the internal energy falls and the temperature goes down. My realisation is that there is plenty of time for thermal energy to cross the system boundary from the surroundings and bring the tarn water back up to the same temperature. This means that if there is some evaporation at a given temperature because some particles have enough energy to escape, that will always continue to be the case because of the heat from the surroundings. I should add that the evaporative cooling will mean the tarn water is at a lower temperature than the surroundings so thermal energy will flow from the surroundings into the tarn until equilibrium is reached.