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 193.5 ppm and is initially uniform through the thickness of the steel. The atmosphere of the carburizing furnace maintains a carbon concentration of 7865.0 ppm at the surface of the steel. Calculate the time required to carburize steel so that the concentration of carbon at a depth of 59.0 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
Don't think its a correct answer!
Corect Answer,
Use:
concentration of carbon at a depth
___________________________________
4*(3.091*10^-7)*0,26277
777.78
No right!
Corect Answer,
Use:
concentration of carbon at a depth//[
4*(3.091*10^-7)*0,26277]
Had 3.24888828e-07 but place 777.78 and had wrong answer. What when wrong?
DO NOT ANSWER THIS QUESTION, IT IS A MIDTERM QUESTION FOR AN ONLINE CLASS
What is 4
What is this formula and why the comma between 0.26277
What is the formula?
T(sec)= d^2 / 4*D*error^2
Finally, what's the correct answer?
Could someone fill the data above into the formula, so we can get an idea how to search the answer? Thank you
Agree to Yamy
Step 1:
(0.5*7865 - 7865)/ (193.5 - 7865)= erf(ξ)
Step 2:
erf(ξ < 0.6), use the approximation erf ξ = ξ
Step 3:
t= d^2/4*D*ξ^2
d=59.0 x 10-2 cm
D=3.091 x 10-7 cm2/s
Step 4:
t in sec -> hours
Step 1:
(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
0.78850182838 hours and had it wrong.
Got the answer 297.622419061 hours.Thank you all for the advise, check through, and help, great way to make sure all of us don't use up our submissions. Again thank you bra, qwerty and yamy.
This is a question from the second midterm of 3.091x by edx. Stop cheating, it's silly and pointless.
Thank you for the info, great help
But what is ξ??
how to find erf? error function ξ? and what is use of erf(1) and erf(2)??
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)
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 223.0 ppm and is initially uniform through the thickness of the steel. The atmosphere of the carburizing furnace maintains a carbon concentration of 6125.0 ppm at the surface of the steel. Calculate the time required to carburize steel so that the concentration of carbon at a depth of 84.5 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.
DATA: Error Function Values
erf(ξ 0.6), use the approximation erf ξ = ξ
erf(1.0) = 0.84
erf(2.0) = 0.998