A sphere 30 mm in diameter initially at 800 K is quenched in a large bath having a constant temperature of 320 K with a convection heat transfer coefficient of 75 W/m2.K. The thermophysical properties of the sphere material are = 400 kg/m3 , k = 1.70 W/m. K, Cp = 1600 J/kg. K. a) Show, in a qualitative manner on T-t coordinates the temperatures at the center and at the surface of the sphere as a function of time. b) Calculate the time required for the surface of the sphere to reach 415 K. c) Determine the heat flux (W/m2 ) at the outer surface of the sphere at the time determined in part (b). d) Determine the energy (J) that has been lost by the sphere during the process of cooling to the surface temperature of 415 K. e) If the same sphere is cooled in air at 320 K with a heat transfer coefficient of 20 W/m2.K, calculate the time required for the surface of the sphere to reach 415 K. Compare your result with that of part (b). f) Compute and plot the center and the surface temperature history over the period 0 ≤ t ≤ 150 s. What effect does an increase in the convection coefficient to h = 200 W/m2 .K have on the forgoing temperature histories? For h = 75 and 200 W/m2 .K, compute and plot the surface heat flux as a function of time for 0 ≤ t ≤ 150 s.