A steel sphere with a diameter of 7.6 cm is to be hardened by first heating it to a uniform temperature of 870?C and then quenching it in a large bath of water at a temperature of 38?C. The following data applysurface heat transfer coefficient h = 590 W/(m2 K)thermal conductivity of steel = 43 W/(m K)specific heat of steel = 628 J/(kg K)density of steel = 7840 kg/m3Calculate: (a) time elapsed in cooling the surface of the sphere to 204?C and (b) time elapsed in cooling the center of the sphere to 204?C.GIVENA steel sphere is quenched in a large water bathDiameter (D) = 7.6 cm = 0.076 mInitial uniform temperature (To) = 870?CWater temperature (T??) = 38?CSurface heat transfer coefficient (h) = 590 W/(m2 K)Thermal conductivity of steel (k) = 43 W/(m K)Specific heat of steel (c) = 628 J/(kg K)Density of steel (ρ) = 7840 kg/m3ASSUMPTIONSConstant water bath temperature, thermal properties, and transfercoefficient

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Steel D-7.6 cm+ Water T.= 38°C