# Which sublimates faster

Calculus Level 3

Two identical spheres of dry-ice are left to sublimate in two different chambers.

In chamber 1, which is exposed to air, the rate of sublimation is proportional to the instantaneous surface area of the sphere.

In chamber 2, which is in a microwave oven, the rate of sublimation is proportional to the instantaneous volume of the sphere.

For the sake of simplicity, it is assumed that the sublimation rate is uniform spatially (i.e., the sphere retains its shape at all times),

Which sphere will be the first to evaporate completely?

Note : Here the rate of sublimation means rate of change of volume.

×