For some applications, it is necessary to harden the surface of a steel (or iron-carbon alloy) above that of its interior. One way this may be accomplished is by increasing the surface concentration of carbon in a process termed carburizing: the steel piece is exposed, at an elevated temperature, to an atmosphere rich in hydrocarbon gas, such as methane (CH4). Consider 1025 Steel which will be treated at 950°C. If the concentration of carbon at the surface is suddenly brought to and maintained at 1.20 wt%, how long will it take to achieve a carbon content of 0.80 wt% at a position 0.5 mm below the surface? The diffusion coefficient for carbon in iron at this temperature is 1.6X101 m²/s; assume the 5781-erfi the steel is semi-infinite.