Recent theoretical and experimental studies of evaporation have suggested that on average, molecules in the higher-energy tail of the Boltzmann distribution are more readily transferred into the vapor during evaporation. To test these conclusions, the evaporative cooling rates of a droplet train of liquid water injected into vacuum have been studied via Raman thermometry. The resulting cooling rates are fit to an evaporative cooling model based on Knudsen's maximum rate of evaporation, in which we explicitly account for surface cooling. We have determined that the value of the evaporation coefficient (gamma(e)) of liquid water is 0.62 +/- 0.09, confirming that a rate-limiting barrier impedes the evaporation rate. Such insight will facilitate the formulation of a microscopic mechanism for the evaporation of liquid water.