A sphere 30mm in diameter initially at 800K is quenched in large bath having a constant temperature of 320K with a convection heat transfer coefficient of 75W/m^2. K. The thermo-physical properties of the sphere material are rho = 400kg/m^3, c = 1600 J/kg. K, and k = 1.7W/m K. a) Sketch the temperature gradient in the sphere over time with temperature (y-axis) and radius (x-axis) showing several lines to represent the initial time, an intermediate time, and the temperature at after a long time has elapsed. Note the boundary conditions you assumed in the center of the sphere and the edge of the sphere and show them on your sketch b) Calculate the Biot number and determine the best solution path using a characteristic length of gamma _o. c) Calculate the time required for the surface of the sphere to reach 415K [seconds]. d) At the time found, determine the heat flux [W/m^2] from the surface of the sphere.