Determine the carburizing time necessary to achieve a carbon concentration of 0.30 wt% at a position 4 mm into an iron–carbon alloy that initially contains 0.10 wt% c. the surface concentration is to be maintained at 0.90 wt% c, and the treatment is to be conducted at 1,100°c (1,373 k). the iron is γ-fe with preexponential d0 = 2.3 10-5 m2 /s and activation energy qd = 148,000 j/mol.