A plate of 1020 steel (0.2 wt%C) is placed in a carburizing furnace at 900 \[Degree]C. The atmosphere forms a surface layer that is approximately 1.2 wt%C. The diffusion coefficient for C in 1020 steel follows the Arrhenius relationship, D=Subscript[D, 0]exp(-Q/(R T))where the activation energy, Q=80 kJ/mol, and the diffusion coefficient, Subscript[D, 0]=6.2 10^-7 m^2/sec. (a) Plot the concentration profile from the surface of the plate to a depth of 5 mm at times of 30 minutes, 2 hours, and 5 hours. These three curves should be plotted together on the same plot. (b) How long does it take for the carbon content to reach 0.8 wt% at a depth of 1 mm?