A sheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200C and is permitted to achieve a steady-state diffusion conditio

Question

A sheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200C and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is 6  10-11 m2/s, and the diffusion flux is found to be 1.2  10-7 kg/m2 -s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3. How far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3? Assume a linear concentration profile.

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Helga 5 years 2021-07-23T22:52:20+00:00 1 Answers 441 views 0

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  1. thongdat2
    0
    2021-07-23T22:54:18+00:00
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    Answer:

    The answer is 0.001 m

    Explanation:

    Solution

    Recall that,

    A sheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at = 1200°C

    The diffusion coefficient for nitrogen in steel at this temperature is =6 * 10-11 m2/s

    The diffusion flux is = 1.2 *10^-7 kg/m2s

    Concentration of nitrogen in the steel at the high-pressure surface is= 4 kg/m3.

    The high-pressure side will the concentration is estimated to be = 2.0 kg/m3

    Now,

    The flux = -D dC/dx

    1.2 x 10-7 kg/m2s = – 6 x 10-11 m2/s dC/dx

    ∫ˣ₀ dx = -5x^10-4 ∫²₄ dC

    so,

    x = (2-4) kg/m3 (-5×10-4 m4/kg)

    where x = .001 m

    Therefore x = 0.001 m

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