Chapter 1, Problem 13P

Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area.

$\frac{dV}{dt}=-kA$

where $V=$ volume $\left({\text{mm}}^{\text{3}}\right)$, $t=$ time (min), $k=$ the evaporation rate (mm/min), and $A=$ surface area $\left({\text{mm}}^{\text{2}}\right)$. Use Euler's method to compute the volume of the droplet from $t=0$ to 10 min using a step size of 0.25 min. Assume that $k=0.08$ mm/min and that the droplet initially has a radius of 2.5 mm. Assess the validity of your results by determining the radius of your final computed volume and verifying that it is consistent with the evaporation rate.