6) Carburization is a heat-treatment process in which iron or steel absorbs carbon liberated when the metal is heated in the presence of a carbon-bearing material. In this case, a cylindrical steel roller that is 10 mm in diameter is to be carburized at 900 C in a concentrated carbon gas. This roller is made of steel that already contains 0.2% carbon, and the aim of the process is to increase that percentage to 0.5% carbon at a depth of 0.4 mm into the surface. Estimate the time required to accomplish this. Use the following data: Density of the steel = 7850 kg/m' Density of the carbon gas = 100 kg/m' Diffusivity of carbon in steel = 2.0 x 10'll m'/s