Question

# After a 34-hour heat treatment at 1080°C (and subsequent cooling to room temperature), the concentration of...

After a 34-hour heat treatment at 1080°C (and subsequent cooling to room temperature), the concentration of A is 3.4 wt% at the 13.6-mm position within metal B. If another heat treatment is conducted on an identical diffusion couple, this time at 890°C for 34 hours, at what position will the composition be 3.4 wt% A? The preexponential and activation energy values for the diffusion of A in B are 3.4 × 10-5 m2/s and 156 kJ/mol, respectively.

After a 34-hour heat treatment at 1080°C (and subsequent cooling to room temperature), the concentration of A is 3.4 wt% at the 13.6-mm position within metal B. If another heat treatment is conducted on an identical diffusion couple, this time at 890°C for 34 hours, at what position will the composition be 3.4 wt% A? The pre-exponential and activation energy values for the diffusion of A in B are 3.4 × 10-5 m2/s and 156 kJ/mol, respectively.

1080+273=1353 K

890+273= 1163 K

13.6 mm

3.4 %

NA= D(ΔC)/z= NA= 3.4x10-5 m2/s (3.4kgA-0)/13.6x10-3m

DA= 3.4x10-5m2/s x e-(156000J/mol) /(8.314 J/mol K * 1353K)

DA=3.4x10-5m2/s x 9.48x10-7= 3.226 x10-11 m2/s

DA= 3.4x10-5m2/s x e-(156000J/mol) /(8.314 J/mol K * 1163K)

DA=3.4x10-5m2/s x 9.84x10-8= 3.347 x10-12 m2/s

NA=3.226 x10-11 m2/s x (3,4-0)kgA / 13.6 x 10-3 m

NA= 3.047x10-8 kg/ms

zA=3.347 x10-12 m2/s x (3,4-0)kgA / 3.047x10-8 kg/ms

zA=3.74 x10-4 m

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