In heat treating to harden steel ban bearings (c = 500 J/kg ∙ K p = 7800 kg/m3, k = 50 W/m ∙ K), it is desirable to increase the surface temperature for a short time without significantly warming the interior of the ball. This type of heating can be accomplished by sudden immersion of the ban in a molten salt bath with T∞ = 1300 K and h = 5000 W/m2 ∙ K. Assume that any location within the ball whose temperature exceeds 1000 K will be hardened. Estimate the time required to harden the outer miI1imeter of a ban of diameter 20 mm, if its initial temperature is 300 K.