Problem 4 (30 points): Metallic spherical objects [with thermal conductivity 25 W/m.K, heat capacity 600 J/kg.K, density 8000 kg/m), which have been uniformly heated to a temperature of 850C, are hardened by quenching (suddenly cooling) them in an oil bath that is maintained at 40C. Each sphere's diameter is 20mm, and the convection heat transfer coefficient associated with the oil bath is 1000 W/m .K. 1. If quenching is to occur until the surface temperature of each sphere reaches 100C, how long must the spheres be kept in the oil? And what is the center temperature at that time? 2. If 10,000 spheres are to be quenched at the same time, what is the rate at which energy must be removed from the oil bath in order to maintain the oil temperature at 40C