# Carburizing Calculation

The problem is stated as follows: The surface of a steel gear made of 1022 steel (0.22 wt% C) is to be gas-carburized at $927$ °C. Calculate the time necessary to increase the carbon content to 0.30 wt% at 0.030 in below the surface of the gear. Assume the carbon content of the surface to be 1.20 wt% and $D_{927^{\circ}C}=1.28 \times 10^{-11}\frac{m^{2}}{s}$

The formula is $\frac{C_{s}-C_{x}}{C_{s}-C_{0}}=ERF(\frac{x}{2\sqrt{Dt}})$

The solution manual is setting $C_{x}=0.30$, but should it not be $C_{x}=0.30+0.22=0.52$, since the initial carbon content in the steel is $C_{0}=0.22$?

In the equation $C_x$ simply means the concentration at depth x. It does not mean the change of concentration. There is no need to add its initial concentration.