Halliday, Resnick & Walker — The Kinetic Theory of Gases: Problem 11

11 Water standing in the open at $10.0^\circ\text{C}$ evaporates because of the escape of some of the surface molecules. The heat of vaporization ($539\text{ cal/g}$) is approximately equal to $\epsilon n$, where $\epsilon$ is the average energy of the escaping molecules and $n$ is the number of molecules per gram. (a) Find $\epsilon$. (b) What is the ratio of $\epsilon$ to the average kinetic energy of $\text{H}_2\text{O}$ molecules, assuming the latter is related to temperature in the same way as it is for gases?