-Given Values- Concentration of Nitrogen (wt%):-0.36 Position in mm 3.9 Diffusio

Question

-Given Values- Concentration of Nitrogen (wt%):-0.36 Position in mm 3.9 Diffusion Coefficient for Nitrogen in Iron at 700°C Nitrogen in Iron Heat Treatment Time (hours):-19 Carburizing Time (hrs): -10 Steel Alloy Case Depth (mm): 4.7 Steel Alloy New Case Depth (mm) 8.90E+00 Activation Energy kJ/mol: 104 Temperature for Problem 3 (Celsius): -815 -Data for Problem 4 Temperature in C-600 Diffusivity (m-/s) 5.60E-14 Temperature in C:-698 Diffusivity (m-/s) 3.58E-13 5.30E-10 Problem 1: Nitrogen from a gaseous phase is to be diffused into pure iron at 700°C. If the surface concentration is maintained at the level listed above, what will be the concentration (in weight percent) with the given case and heat treatment time? The diffusion coefficient for nitrogen in iron at 700°C is given above. (Round your answer to the ten thousandths place, 0.0000) Your Answer-523 Incorrect. Problem 2: For a steel alloy it has been determined that a carburizing heat treatment for the time, given above, will raise the carbon concentration to 0.42 wt% to the depth given from the surface. Estimate the time necessary to achieve the same concentration at the new position stated above for an identical steel and at the same carburizing temperature (in hours) Your Answer 1749749 Incorrect.

Explanation / Answer

Problem 4: b) Part b is presented first because it is the first step to determine the rest.

From the diffusion equation:

D = Do * exp [-Qd / RT]

a mathematical arrangement is made dividing all the expression for D1 between all the expression for D2 and we have the constants Qd and R, and Do disappears from the equation to be equal in both D:

D1 / D2 = exp [(-Qd / R) * (1 / T2 + 1 / T1)]

Qd is cleared and we have:

Qd = Ln (D1 / D2) * R / (1 / T2 + 1 / T1)

And replacing:

D1 = 5.60x10 ^ -14

D2 = 3.58x10 ^ -13

R = 8.314

T1 = 873 K

T2 = 971 K

we have left: Qd = 133414.73 J / mol

a) We just clear Do from the first equation and evaluate any of the two known points:

Do = D / exp [-Qd / R * T] = 5.39x10 ^ -6

c) Following the proposed relationship of D1 / D2 we can propose a D2 / D3 for a T3 = 1093 K:

D3 = D2 * exp [-Qd / R * (1 / T3 + 1 / T2)] = 2.26 x10 ^ -12.

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