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Chemistry

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"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 165.0 ppm and is initially uniform through the thickness of the steel. The atmosphere of the carburizing furnace maintains a carbon concentration of 7715.0 ppm at the surface of the steel. Calculate the time required to carburize steel so that the concentration of carbon at a depth of 61.5 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"

I keep getting 2.127 hours, but apparently it's wrong. I've checked and checked and I can't find what's wrong. Accuse me for cheating or whatever; I've done it with other data and I do get the right answer.

  • Chemistry - ,

    **We are here to help each other on this forum. Hope the info below helps'!


    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* 7715.0 - 7715.0 )/ ( 165.0 - 7715.0 )= erf(ξ)

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

    Step 3:

    t= d^2/4*D*ξ^2

    d=61.5 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)

  • Chemistry - ,

    Yawnnnn. What a kind-hearted person you are Odesa I am touched by your way of cheating and helping each other. LOL.

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