The outer surface of a steel gear (BCC Fe) is to be hardened by increasing its carbon content. The carbon is to be supplied from an external carbon-rich atmosphere that is maintained at an elevated temperature. A diffusion heat treatment at 850°C (1123 K) for 10 min increases the carbon concentration to 0.90 wt% at a position 1.0 mm below the surface. Estimate the diffusion time required at 650°C (923 K) to achieve this same concentration also at a 1.0- mm position. Assume that the surface carbon content is the same for both heat treatments, which is maintained constant. Diffusion parameters for the diffusion of C in BCC Fe: D0 = 6.2 x 10-7 m2 /sec QD = 80 kJ/mol.