An iron-carbon alloy initially containing 0.255 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1130°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 0.191 wt% after a 6 h treatment? The value of D at 1130°C is 6.0 x 10:10 m²/s. erf(z) z erf(z) Z erf(z) 0.9340 0.00 0.0000 0.55 0.5633 1.3 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 0.1680 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 0.7707 1.9 0.9928 0.30 0.3286 0.90 0.7970 2.0 0.9953 0.35 0.3794 0.95 0.8209 2.2 0.9981 0.4284 1.0 0.8427 0.9993 0.45 0.4755 1.1 0.8802 2.6 0.9998 0.50 0.5205 1.2 0.9103 2.8 0.9999 z 0.15 0.40 E 2.4

Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
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### Educational Resource: Diffusion in Iron-Carbon Alloys

**Overview:**
An iron-carbon alloy initially containing 0.255 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1130°C. Under these circumstances, carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; thus, the carbon concentration at the surface position is maintained essentially at 0.00 wt% C. The objective is to determine the position at which the carbon concentration will be 0.191 wt% after a 6-hour treatment. The diffusion coefficient (D) at 1130°C is given as 6.0 × 10⁻¹⁰ m²/s.

**Table Explanation:**
The table below provides values of the error function (erf(z)) for various values of the variable z.

| z     | erf(z)  | z     | erf(z)  | z   | 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  | 0.7707  | 1.9 | 0.9929  |
| 0.30  | 0.3286  | 0
Transcribed Image Text:### Educational Resource: Diffusion in Iron-Carbon Alloys **Overview:** An iron-carbon alloy initially containing 0.255 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1130°C. Under these circumstances, carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; thus, the carbon concentration at the surface position is maintained essentially at 0.00 wt% C. The objective is to determine the position at which the carbon concentration will be 0.191 wt% after a 6-hour treatment. The diffusion coefficient (D) at 1130°C is given as 6.0 × 10⁻¹⁰ m²/s. **Table Explanation:** The table below provides values of the error function (erf(z)) for various values of the variable z. | z | erf(z) | z | erf(z) | z | 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 | 0.7707 | 1.9 | 0.9929 | | 0.30 | 0.3286 | 0
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