The surface of 0.10 wt% carbon steel is to be strengthened by carburizing. The steel is placed in an atmosphere that provides a maximum of 1.2 wt% carbon at the surface of the steel at a high temperature. Carbon then diffuses 0.2 cm into the surface of the steel giving a carbon concentration of 0.45 wt% carbon at that depth. How long will the process of carburizing take if the diffusion coefficient is 2 x 10^-7 cm²/s? Use Table 5-4 for error function values as needed.

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Table 5-4 Error function (erf) values erf (z) 0 0.0282 0.0564 0.1125 0.1680 0.2227 0.2763 0.3286 0.3794 0.4284 0.4755 0.5205 Z 0 0.025 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Z 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.0 1.1 1.2 erf (z) 0.5633 0.6039 0.6420 0.6778 0.7112 0.7421 0.7707 0.7969 0.8209 0.8427 0.8802 0.9103 Z 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.2 2.4 2.6 2.8 erf (z) 0.9340 0.9523 0.9661 0.9763 0.9838 0.9891 0.9928 0.9953 0.9981 0.9993 0.9998 0.9999