The outer surface o f a steel gear is to be hardened by increasing its carbon content. The carbon is to be supplied from an external carbon rich atmosphere, which maintained at an elevated temperature. A diffusion heat treatment at 1030°C (1303 K) for 12 min increases the carbon concentration to 0.85 wt% at a position 1.2 mm below the surface. Estimate the diffusion time required at 875°C (1148 K) to achieve this same concentration at the same location.

Assume that the surface carbon content is the same for both treatments, which is maintained constant. Use appropriate diffusion tables for C diffusion in α-Fe.