Problem $6(2$ pts$).$ Suppose the droplet is water. A quick trip to Wikipedia reveals that the latent heat of water in $\frac{J}{g}$ can be calculated using the following:

$L(T)=2500\mathrm{.}8-2\mathrm{.}36T+0\mathrm{.}0016T^2-6e-5T^3$

T must be in Celcius.

This is a polynomial fit to tabulated values of $L$ vs $T$ given by Rogers and Yau in a famous monograph called A Short Course in Cloud Physics. The thermodynamic properties of water and the solubility of trace gases in water are highly interesting in atmospheric science and, incidentally, in aqueous process control for, e$.$g$.,$ photochemical treatment of drinking water. The acceptable margin of error for water properties over a wide range of conditions is small when $W_{H2O}$ and $x_{H2O}$ are close to unity. Recall that $w$ and $x$ are mass and mole fractions.

$($a$)$ What is the latent heat of water at $25$ Celcius?

$($b$)$ Assume liquid water has a mass density of $1gc{m}^{-3}.$ This is often referred to as "unit density," meaning the density is $1\mathrm{.}00("$unity$")$ the unit is assumed to be $gc{m}^{-3}.$ What is the rate of energy consumption associated with the evaporation rate of water in this description, at this temperature?

$($c$)$ Note that the example given does not necessarily accurately reflect the evaporation rate of real water droplets, nor is the evaporation rate constant. What added complexity is missing? Please format as a bulleted list of three to five other considerations.