**Iron-Carbon Alloy Carbon Diffusion Analysis**An iron-carbon alloy initially containing 0.268 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1040°C. Under these circumstances, the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere. This process maintains the carbon concentration at the surface essentially at 0.0 wt% C.**Objective:** Determine the position at which the carbon concentration will be 0.201 wt% after a 7-hour treatment. The diffusion coefficient, D, at 1040°C is given as \(2.5 \times 10^{-11} \, \text{m}^2/\text{s}\).**Error Function Values:**The following table provides values of the error function, erf(z), which are used in calculating diffusion equations.| \(z\) | \(\text{erf}(z)\) | \(z\) | \(\text{erf}(z)\) | \(z\) | \(\text{erf}(z)\) ||-------|------------------|-------|------------------|-------|------------------|| 0.00 | 0.0000 | 0.55 | 0.5633 | 1.3 | 0.9340 || 0.025 | 0.0282 | 0.60 | 0.6039 | 1.4 | 0.9523 || 0.05 | 0.0564 | 0.65 | 0.6420 | 1.5 | 0.9661 || 0.10 | 0.1125 | 0.70 | 0.6778 | 1.6 | 0.9763 || 0.15 | 0.1680 | 0.75 | 0.7112 | 1.7 | 0.9838 || 0.20 | 0.2227 | 0.80 | 0.7421 | 1.8 | 0.9891 || 0.25 | 0.2763 | 0.85 | 0

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An iron-carbon alloy initially containing 0.268 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1040°C. Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at 0.0 wt% C. At what position will the carbon concentration be 0.201 wt% after a 7 h treatment? The value of D at 1040°C is 2.5 × 10-11 m²/s.

An iron-carbon alloy initially containing 0.268 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1040°C. Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at 0.0 wt% C. At what position will the carbon concentration be 0.201 wt% after a 7 h treatment? The value of D at 1040°C is 2.5 × 10-11 m²/s.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

**Iron-Carbon Alloy Carbon Diffusion Analysis**

An iron-carbon alloy initially containing 0.268 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1040°C. Under these circumstances, the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere. This process maintains the carbon concentration at the surface essentially at 0.0 wt% C.

**Objective:** Determine the position at which the carbon concentration will be 0.201 wt% after a 7-hour treatment. The diffusion coefficient, D, at 1040°C is given as \(2.5 \times 10^{-11} \, \text{m}^2/\text{s}\).

**Error Function Values:**

The following table provides values of the error function, erf(z), which are used in calculating diffusion equations.

| \(z\) | \(\text{erf}(z)\) | \(z\) | \(\text{erf}(z)\) | \(z\) | \(\text{erf}(z)\) |
|-------|------------------|-------|------------------|-------|------------------|
| 0.00 | 0.0000 | 0.55 | 0.5633 | 1.3 | 0.9340 |
| 0.025 | 0.0282 | 0.60 | 0.6039 | 1.4 | 0.9523 |
| 0.05 | 0.0564 | 0.65 | 0.6420 | 1.5 | 0.9661 |
| 0.10 | 0.1125 | 0.70 | 0.6778 | 1.6 | 0.9763 |
| 0.15 | 0.1680 | 0.75 | 0.7112 | 1.7 | 0.9838 |
| 0.20 | 0.2227 | 0.80 | 0.7421 | 1.8 | 0.9891 |
| 0.25 | 0.2763 | 0.85 | 0

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