You wish to increase the carbon content of a slab of steel by exposing it to a carburizing atmosphere at elevated temperature. The carbon concentration in the steel before carburization is 200.5 ppm and is initially uniform through the thickness of the steel. The atmosphere of the carburizing furnace maintains a carbon concentration of 9110.0 ppm at the surface of the steel. Calculate the time required to carburize steel so that the concentration of carbon at a depth of 88.5 x 10-2 cm is one half the value of the carbon concentration at the surface. The diffusion coefficient of carbon in steel is 3.091 x 10-7 cm2/s at the carburizing temperature. Express your answer in hours.

Question

DATA: Error Function Values
erf(ξ < 0.6), use the approximation erf ξ = ξ
erf(1.0) = 0.84
erf(2.0) = 0.998

Answer 1

CHEAT!

Answer 2

This is a question from the second midterm of 3.091x by edx. Stop cheating, it's silly and pointless.

Answer 3

Step 1:

(0.5*9110.0 - 9110.0)/ (200.5 - 9110.0)= erf(ξ)

Step 2:
erf(ξ < 0.6), use the approximation erf ξ = ξ

Step 3:

t= d^2/4*D*ξ^2

d=88.5 x 10-2 cm
D=3.091 x 10-7 cm2/s

Step 4:
t in sec -> hours
Conversion seconds to hours is total/(60x60)

Answer 4

Thanks mate!!!