I read lectures of Richard Feynman and try to solve problems and I have some trouble with a problem on water evaporation.
A glass full of water is left standing on an average outdoor window in California.
- How long do you think it would take to evaporate completely?
- How many molecules $~\text{cm}^{-2} ~\text{s}^{-1}$ would be leaving the water glass at this rate?
- Briefly discuss the connection, if any, between your answer to part 1. above and the average rainfall over the earth
I think calculation the rate of evaporation at first is the easiest way for solving this problem. So I break glass into layers, every layer as thick as one water molecule ($2.8\cdot10^{-8}\,\text{cm}$). I know the number of molecules in one cubic centimeter in the water ($3\cdot10^{22}$). The average diameter of glass is $6.75\,\text{cm}$ and I suppose that it is surface. Next I look at surface layer in 2 dimensional view. So each molecule moves in 4 main directions. I suppose that in $\frac{1}{4}$ of cases, the molecule goes into the air. I take normal humidity of air as 60%. But I don't know the velocity of this molecule that I need for calculating rate of evaporation. This velocity should be related to the temperature (because temperature is only movement of molecules).
Should I use the temperature in Joule?
Can someone help me with algorithm of solution? I want to understand analytical part of this problem. I am not sure that my method is right.