Evaporation in a mist of little drops is sometimes used to cool hot, dry air. Let Consider the Temperature in a spherical drop of liquid that is evaporating slowly enough that its temperature profile is "quasi-steady." In other words, the radius of the drop is changing so gradually that the temperature profile can be measured from the steady form of the thermal energy equation (Laplace's equation).
a. Demonstrate that, under these pseudo-steady conditions, the temperature in the drop must be a constant.
b. If the rate of evaporation per unit area of drop surface is qm, the heat transfer coefficient among the drop and surrounding air is h, and the latent heat of vaporization is λ, measure the temperature inside the drop relative to the ambient temperature T∞.
c. Give a criterion for when you believe pseudo-steady conditions apply, with a brief clarification of your reasoning.