Question

A sheet of steel 3-mm thick has nitrogen atomospheres on both sides at 900 C and is permitted to achieve a steady-state di usion condition. The di usion coecient for nitrogen in steel at this temperature is 1:85 10????10 m2=s, and the di usion ux is found to be 1:0 10????7 kg=m2s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 2 kg=m3. How far into the sheet from this high-pressure side will the concentration be 0.5 kg/m3? Assume a linear concentration profile.

Answer 1

`X_B = 1.8 * 10^(-3) m = 1.8 mm`

Step-by-step explanation:

Given data:

Diffusion constant for nitrogen is
`= 1.85* 10^(-10) m^2/s`

Diffusion flux
`= 1.0* 10^(-7) kg/m^2-s`

concentration of nitrogen at high presuure = 2 kg/m^3

location on which nitrogen concentration is 0.5 kg/m^3 ......?

from fick's first law

`J = D (C_A C_B)/(X_A X_B)`

Take C_A as point on which nitrogen concentration is 2 kg/m^3

`x_B = X_A + D(C_A -C_B)/(J)`

Assume X_A is zero at the surface

`X_B = 0 + ( 12* 10^(-11) ) (2-0.5)/(1* 10^(-7))`

`X_B = 1.8 * 10^(-3) m = 1.8 mm`