# Question #d2fe3

Jun 21, 2015

In most cases, increasing temperatureScience Kids will produce a dramatic increase in the rate of evaporation, but there are factors that moderate the effect, so the observed increase may be less than predicted.

#### Explanation:

The major factor for increasing the rate of evaporation is increasing the probability that a molecule will have enough energy to escape the surface if the liquid. To estimate this, we can set the activation energy for evaporation equal to the enthalpy of vaporization. For water, $\Delta {H}_{v a p} = 40.65 \frac{k J}{m o l}$. Therefore, the maximum increase in evaporation rate for increasing $T$ from $298 K$ to $308 K$ can be estimated by

$\frac{{k}_{2}}{{k}_{1}} = \exp \left(\frac{\Delta H}{R} \left(\frac{1}{T} _ 1 - \frac{1}{T} _ 2\right)\right) = 1.70$

which predicts a 70% increase for a rise in $T$ of only 10 degrees!

However, in order to realize this increase, the vapor must be effectively transported away from the surface, by diffusion, convection or advection (e.g., wind). Also, evaporation requires considerable energy, so the actual surface temperature may be lower than the overall ambient temperature.

Therefore, the observed increase may be considerably less than the theoretical maximum increase calculated here.