The outer surface of an iron alloy is to be hardened by increasing its carbon content. The carbon is to be supplied from an external carbon-rich atmosphere, which is maintained at an elevated temperature. A diffusion heat treatment at 871°C for 12 min increases the carbon concentration to 0.85 wt% at a position 1.8 mm below the surface. Estimate the diffusion time required at 650°C to achieve this same concentration also at a 1.8 mm position. Assume that the surface carbon content is the same for both heat treatments, which is maintained constant. The pre exponential and activation energy values for the diffusion of carbon in the iron are 6.5 × 10-8 m2/s and 77.6 kJ/mol, respectively.