A bar of steel 10 cm x 10 cm x 100 cm has an initial carbon content of 7.6 x 10^-3 gm/cm^3. At t=0, the surface of the bar is exposed to a carburizing gas for which the equilibrium composition is 1.52 x 10^-2 gm/cm^3. Assume the surface composition is the equilibrium value and that the diffusion coefficient is 2.5 x 10^-7 cm^2/sec. Discuss the validity of the use of the "semi-infinite" case for considering the penetration of carbon in this situation. At what point does this simplified treatment break down?