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1.5 Table 5.1 Tabulation of Error Function Values erf (3) erf(:) 0 0 0.55 0.5633 1.3 0.025 0.0282 0.60 0.6039 1.4 0.05 0.0564 0.65 0.6420 0.10 0.1125 0.70 0.6778 1.6 0.15 0.1680 0.75 0.7112 1.7 0.20 0.2227 0.80 0.7421 0.25 0.2763 0.85 0.7707 1.9 0.30 0.3286 0.90 0.7970 0.35 0.3794 0.95 0.8209 2.2 0.40 0.4284 1.0 0.8427 2.4 0.45 0.4755 1.1 0.8802 2.6 0.50 0.5205 1.2 0.9103 2.8 1.8 erf (3) 0.9340 0.9523 0.9661 0.9763 0.9838 0.9891 0.9928 0.9953 0.9981 0.9993 0.9998 0.9999 2.0 Consider a steel alloy that initially has a uniform carbon concentration of 0.25 wt% and is to be treated at 950 C. If the concentration of carbo at surface is suddenly brought to and maintained at 1.2 wt%, how long will it take to achieve a carbon content of 0.8 wt% at a position 0.5 mm below the surface. The diffusion coefficient for carbon in iron at this temperature is 1.6 x 10-11 m2/s; assume the steel piece is semi-infinite. (25 points)