Achieve a concentration of 0.5%wt of carbon at a depth of 0.2 mm below the surface of the slab of a metal. The initial concentration of carbon in the metal is 0.1wt%. We first do an experiment by applying a concentration of 5%wt of carbon at the surface of a similar slab and maintaining the system at 900 K for an hour. We find that this is just adequate to produce the required concentration at a depth of 0.1 mm. We now take the original slab and apply a concentration of 5wt% of carbon at the surface, at a temperature of 1200 K. The diffusion coefficient of this metal increases by a factor of 2 when the temperature is raised to 1200 K from 900 K. How long must it be maintained at this temperature to achieve the required concentration? (10) Hint: You do not need the error function tables.