Question

The depth of the carburized layer after high temperature carburization for 1 hr at 600oC is 2 micrometers in steel. If the same process is done but for 2 hrs at 700 oC the depth of the carburized layer is 6 micrometers. a) What is the activation energy for diffusion of the carbon? b) What is the depth of the carburized layer in micrometers after carburization at 650C for 1 hr?

Please show your work, I am completely lost. Thanks

Answer 1

To do this, you need to use the following Expression:

D = Do e(-Ea/RT)

Where D is the diffusion coefficient of the carbon in cm²/s and Ea (Usually labeled as Q) is activation energy in eV.

With the first data, we can obtain the diffusion coefficients at both temperatures:

D₁ (600°C) = (2x10^-4 cm)² / 3600 s * 2 = 0.56x10^-11 cm²/s

D₂ (700°C) = (6x10^-4 cm)² / 7200 s * 2 = 2.5x10^-11 cm²/s

Now,According to the above expressions:

D₁ = Do e(-Ea/RT1)

D₂ = Do e(-Ea/RT2)

Dividing both expressions:

D₁/D₂ = e(-Ea/RT1 + Ea/RT2) Taking logaristm

ln(D₁/D₂) = Ea/R (1/T2 - 1/T1)

Now substituing the above values, we solve for Ea: (R = 8.62x10^-5 eV/K)

ln(0.56x10^-11/2.5x10^-11) = Ea/8.62x10^-5 (1/973 - 1/873)

-1.496 = Ea/8.62x10^-5 (-1.18x10^-4)

Ea = 1.0928 eV

For the second part all you have to do is calculate D, with the temperature given and the activation energy calculated before, and then, convert it to meters and the micrometers.

Hope this helps