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.

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 (-5x10-4 m4/kg)

where x =.001 m

Therefore x = 0.001 m