0
$\begingroup$

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 $C_{0}=0.22$?

$\endgroup$
0
$\begingroup$

No.

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.

Besides, concentration cannot be linearly added. (Does adding a 1M solution to a 2M solution give 3M?)

$\endgroup$
  • $\begingroup$ Thank you for your answer and for the analogy, but does this not mean that we are assuming that the initial carbon content is 0, and not 0.22? I am confused because the problem use the word "increase". $\endgroup$ – Akitirija Oct 5 '14 at 14:55
  • $\begingroup$ Nope. Its initial carbon content throughout the entire steel is 0.22wt%. You are not trying to increase it by 0.30wt% but increase it to 0.30wt%. $\endgroup$ – t.c Oct 5 '14 at 15:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.