A sheet of steel 2.5-mm thick has nitrogen atmospheres on both sides at 900"C and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is 1.85 x 10^-10 m^2/s, and the diffusion flux is found to be 1.0 x 10^-7 kg/m^2 s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 2 kg/m^3. How far into the sheet from this high-pressure side will the concentration be 0.5 kg/m3? Assume a linear concentration profile.

x = 2.78x10⁻³ m

Explanation:

According to Fick's law of diffusion:

Where:

J: is the diffusion flux = 1.0x10⁻⁷ kg/(s*m²)    

D: is the diffusion coefficient = 1.85x10⁻¹⁰ m²/s              

: is the nitrogen concentration in the surface of steel = 2 kg/m³

: is the nitrogen concentration in the point x = 0.5 kg/m³

s: is the position at the steel's surface = 0

x: is the position into the sheet where the concentration is Cₓ

So, x is:

Therefore, the nitrogen concentration will be 0.5 kg/m³ at 2.78x10⁻³ m in the steel sheet.

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