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 243.0 ppm and is initially uniform through the thickness of the steel. The atmosphere of the carburizing furnace maintains a carbon concentration of 9015.0 ppm at the surface of the steel. Calculate the time required to carburize steel so that the concentration of carbon at a depth of 5.0 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.
DATA: Error Function Values
erf(ξ < 0.6), use the approximation erf ξ = ξ
erf(1.0) = 0.84
erf(2.0) = 0.998
I keep doing and doing it but I get it wrong... it has happened to other people with d = 5.0 x 10-2 cm. Why's that?
Example:(remember to substitute with your data)
Step 1:
ξ= (0.5 * carbon concentration at the surface of the steel - carbon concentration at the surface of the steel)/ (carbon concentration in the steel before carburization - carbon concentration at the surface of the steel)
(0.5*7865 - 7865)/ (193.5 - 7865)= 0.512611614417(erf(ξ))
Step 2:
erf(ξ < 0.6), use the approximation erf ξ = ξ
Step 3:
t= d^2/4*D*ξ^2
t=(59.0x10^-2)^2/4(3.091 x 10^-7)(0.512611614417)^2
t=0.3481/3.2488965297e-07
t=1071440.70862
d=59.0 x 10-2 cm
D=3.091 x 10-7 cm2/s
Step 4:
t in sec -> hours
1071440.70862/60x60
297.622419061 hours
Do you any idea to answer this question below, do give some input by providing data and how to with formula.
A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.31 kg m-3. Under these conditions the total surface area of the balloon is 0.11 m2. The diffusion coefficient of He in latex at room temperature is 4.9 x 10-9 m2s-1. Calculate the rate of helium effusion (in g/hr) from the balloon.
I did the same, and I get the answer of 2.127 hours which is wrong... So I don't really know what to do.
In that problem you got to do this
J = -D dc/dx
D = 4.9 x 10-9
dc = 0.31
dx = 3.091 x 10-4
Then, after you get your answer, multiple by the surface area (which in your case is 0.11 m2).
Your answer will be in kg/s. Convert to g/hr, by multiplying by 3600000.