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Homework Help: Diffusion across surface with constant temperature

  1. Feb 9, 2016 #1
    1. The problem statement, all variables and given/known data
    A Ti Rod is to be put into a furnace to try and increase the carbon content of the rod. Initially, the carbon content of the rod is 0.2%wt. The carbon content of the furnace is 1.0%wt. What would the temperature have to be in order to get a final carbon content in the Ti rod to be 0.5%, using a depth of 44 mm over 48 hours.

    Given: erf(k)=z value table, R = 8.314 J/mol*k, Di = 3.2x10^-3 cm2/s, Q = 83.862 KJ
    2. Relevant equations
    1: J=-D dC/dx
    2: (C(x,t) - Ci)/(Cs - Ci) = 1 - erf(x/2√(DT))
    3: D = Di*e^(-Q/RT)

    3. The attempt at a solution
    My thought process to solve this was to use equation 2 to solve for a value of D. I set Cx= 0.5, Ci=0.2, and Cs=1.0. Then I rearranged the equation so erf(x/2√(Dt)) was on its own side and looked at the erf value table to match my erf value with the table's to find out what x/(2√(Dt)) has to equal. It wasn't given so I had to interpolate, which I ended up with 0.627.

    Once found I could then plug in 0.04cm for x and 1.728*10^5 seconds for t to solve for D. I think it was around 5.92*10^-9 cm2/s.

    Rearranging equation 3 to solve for T, I get T = Q/R * (1 /( ln Di - ln D) which I got 763 Kelvin.

    The one thing I am really unsure of is if I can leave the carbon content in %wt and if my order of evaluation is correct. Thanks.
  2. jcsd
  3. Feb 14, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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