Consider a packed bed of spheres, each of diameter 2 mm, at an initial temperature of 87.5°C. Cold water at 5.0°C is poured onto the bed at 0, producing a large convection coefficient about each sphere. Determine the magnitude of the rate, in °C/s, at which an individual sphere near the top surface of the bed is cooled at 0.1, 0.25, and 1 s. The spheres have thermophysical properties similar to Pyrex.