Question

Nitrogen is sometimes diffused into the surface of a steel component in a process called case hardening. Consider a sheet of steel (1.416x10A0) mm thick which has nitrogen atmospheres on both sides at a temperature of 1200°C. The system is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is (6.735x10A-11) m2/s. The diffusion flux is found to be (2.52x10A-7) kg/m2-s. It is also known that the concentration of nitrogen at the high-pressure surface is (6.0470x10 O) kg/m3. How far into the sheet (measured in m from this high-pressure side) will the concentration be (4.467x10 0) Hint: Steady-state leads to a linear concentration profile Use scientific notation with 3 significant figures (X.YZ x 10^n). Note that Avenue automatically enters x10, so you only need to enter X.YZ and n Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: X10 Answer

Answer 1

J = -D C_A - C_B/x_A - x_B If we take C_A to be the point at which the concentration of nitrogen 6.047 kg/m^3, then it becomes necessary to solve for x_B, as x_B = x_A + D [C_A - C_B/J] Assume x_A is zero at the surface, in which case x_B = 0 + (6.735 times 10^-11 m^2/s) [6.047 kg/m^3 - 4.467 kg/m^3/2.52 times 10^-7 kg/m^2 g] x_B = 4.22 times 10^-4 m x_B = 0.422 mm