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An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere wherein the surface carbon concentration is maintained at 1.0 wt%. If after 51 h the concentration of carbon is 0.35 wt% at a position 3.5 mm below the surface, determine the temperature at which the treatment was carried out. You will need to use data in the two tables below to solve this problem. Diffusing Species Fe Table 5.1 Tabulation of Error Function Values erf(z) 0 0.0282 0.0564 0.1125 Fe Z 0 0.025 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Table 5.2 A Tabulation of Diffusion Data Host Metal a-Fe (BCC) y-Fe (FCC) a-Fe 0.1680 0.2227 0.2763 0.3286 0.3794 y-Fe 0.4284 0.4755 0.5205 Z 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.0 1.1 1.2 Do(m²/s) 2.8 x 10-4 5.0 x 10-5 6.2 x 10-7 2.3 x 10-5 erf(z) 0.5633 0.6039 0.6420 0.6778 0.7112 0.7421 0.7707 0.7970 0.8209 0.8427 0.8802 0.9103 80 284 Z 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Activation Energy Qa kJ/mol eVlatom 251 2.60 148 2.0 2.2 2.4 2.6 2.8 2.94 0.83 1.53 erf(z) 0.9340 0.9523 0.9661 0.9763 0.9838 0.9891 0.9928 0.9953 0.9981 0.9993 0.9998 0.9999 Calculated Value T(°C) 500 900 900 1100 500 900 900 1100 D(m²/s) 3.0 x 10-21 1.8 x 10-15 1.1 x 10-17 7.8 x 10-16 2.4 x 10-12 1.7 x 10-10 5.9 x 10-12 5.3 × 10-11

An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere wherein the surface carbon concentration is maintained at 1.0 wt%. If after 51 h the concentration of carbon is 0.35 wt% at a position 3.5 mm below the surface, determine the temperature at which the treatment was carried out. You will need to use data in the two tables below to solve this problem. Diffusing Species Fe Table 5.1 Tabulation of Error Function Values erf(z) 0 0.0282 0.0564 0.1125 Fe Z 0 0.025 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Table 5.2 A Tabulation of Diffusion Data Host Metal a-Fe (BCC) y-Fe (FCC) a-Fe 0.1680 0.2227 0.2763 0.3286 0.3794 y-Fe 0.4284 0.4755 0.5205 Z 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.0 1.1 1.2 Do(m²/s) 2.8 x 10-4 5.0 x 10-5 6.2 x 10-7 2.3 x 10-5 erf(z) 0.5633 0.6039 0.6420 0.6778 0.7112 0.7421 0.7707 0.7970 0.8209 0.8427 0.8802 0.9103 80 284 Z 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Activation Energy Qa kJ/mol eVlatom 251 2.60 148 2.0 2.2 2.4 2.6 2.8 2.94 0.83 1.53 erf(z) 0.9340 0.9523 0.9661 0.9763 0.9838 0.9891 0.9928 0.9953 0.9981 0.9993 0.9998 0.9999 Calculated Value T(°C) 500 900 900 1100 500 900 900 1100 D(m²/s) 3.0 x 10-21 1.8 x 10-15 1.1 x 10-17 7.8 x 10-16 2.4 x 10-12 1.7 x 10-10 5.9 x 10-12 5.3 × 10-11

Elements Of Electromagnetics
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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Table 5.2 A Tabulation of Diffusion Data Diffusing Species Fe Fe C C Cu Zn Al Cu Mg Cu Host Metal a-Fe (BCC) y-Fe (FCC) a-Fe y-Fe Cu Cu Al Al Al Ni Do(m²/s) 2.8 x 10-4 5.0 x 10-5 6.2 x 10-7 2.3 x 10-5 7.8 x 10-5 2.4 x 10-5 2.3 x 10-4 6.5 x 10-5 1.2 x 10-4 2.7 x 10-5 Activation Energy Qa eVlatom 2.60 kJ/mol 251 284 80 148 211 189 144 136 131 256 2.94 0.83 1.53 2.19 1.96 1.49 1.41 1.35 2.65 Calculated Value T(°C) 500 900 900 1100 500 900 900 1100 500 500 500 500 500 500 D(m²/s) 3.0 x 10-21 1.8 x 10-15 1.1 x 10-17 7.8 x 10-16 2.4 x 10-12 1.7 x 10-10 5.9 x 10-12 5.3 × 10-11 4.2 × 10-19 4.0 × 10-18 4.2 × 10-14 4.1 x 10-14 1.9 × 10-13 1.3 x 10-22
Transcribed Image Text:Table 5.2 A Tabulation of Diffusion Data Diffusing Species Fe Fe C C Cu Zn Al Cu Mg Cu Host Metal a-Fe (BCC) y-Fe (FCC) a-Fe y-Fe Cu Cu Al Al Al Ni Do(m²/s) 2.8 x 10-4 5.0 x 10-5 6.2 x 10-7 2.3 x 10-5 7.8 x 10-5 2.4 x 10-5 2.3 x 10-4 6.5 x 10-5 1.2 x 10-4 2.7 x 10-5 Activation Energy Qa eVlatom 2.60 kJ/mol 251 284 80 148 211 189 144 136 131 256 2.94 0.83 1.53 2.19 1.96 1.49 1.41 1.35 2.65 Calculated Value T(°C) 500 900 900 1100 500 900 900 1100 500 500 500 500 500 500 D(m²/s) 3.0 x 10-21 1.8 x 10-15 1.1 x 10-17 7.8 x 10-16 2.4 x 10-12 1.7 x 10-10 5.9 x 10-12 5.3 × 10-11 4.2 × 10-19 4.0 × 10-18 4.2 × 10-14 4.1 x 10-14 1.9 × 10-13 1.3 x 10-22
An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere wherein the surface carbon concentration is maintained at 1.0 wt%. If after 51 h the concentration of carbon is 0.35 wt% at a position 3.5 mm below the surface, determine the temperature at which the treatment was carried out. You will need to use data in the two tables below to solve this problem. Diffusing Species Fe Table 5.1 Tabulation of Error Function Values erf(z) 0 0.0282 0.0564 0.1125 Fe Z 0 0.025 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Table 5.2 A Tabulation of Diffusion Data Host Metal a-Fe (BCC) y-Fe (FCC) a-Fe 0.1680 0.2227 0.2763 0.3286 0.3794 y-Fe 0.4284 0.4755 0.5205 Z 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.0 1.1 1.2 Do(m²/s) 2.8 x 10-4 5.0 x 10-5 6.2 x 10-7 2.3 x 10-5 erf(z) 0.5633 0.6039 0.6420 0.6778 0.7112 0.7421 0.7707 0.7970 0.8209 0.8427 0.8802 0.9103 80 284 Z 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Activation Energy Qa kJ/mol eVlatom 251 2.60 148 2.0 2.2 2.4 2.6 2.8 2.94 0.83 1.53 erf(z) 0.9340 0.9523 0.9661 0.9763 0.9838 0.9891 0.9928 0.9953 0.9981 0.9993 0.9998 0.9999 Calculated Value T(°C) 500 900 900 1100 500 900 900 1100 D(m²/s) 3.0 x 10-21 1.8 x 10-15 1.1 x 10-17 7.8 x 10-16 2.4 x 10-12 1.7 x 10-10 5.9 x 10-12 5.3 × 10-11
Transcribed Image Text:An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere wherein the surface carbon concentration is maintained at 1.0 wt%. If after 51 h the concentration of carbon is 0.35 wt% at a position 3.5 mm below the surface, determine the temperature at which the treatment was carried out. You will need to use data in the two tables below to solve this problem. Diffusing Species Fe Table 5.1 Tabulation of Error Function Values erf(z) 0 0.0282 0.0564 0.1125 Fe Z 0 0.025 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Table 5.2 A Tabulation of Diffusion Data Host Metal a-Fe (BCC) y-Fe (FCC) a-Fe 0.1680 0.2227 0.2763 0.3286 0.3794 y-Fe 0.4284 0.4755 0.5205 Z 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.0 1.1 1.2 Do(m²/s) 2.8 x 10-4 5.0 x 10-5 6.2 x 10-7 2.3 x 10-5 erf(z) 0.5633 0.6039 0.6420 0.6778 0.7112 0.7421 0.7707 0.7970 0.8209 0.8427 0.8802 0.9103 80 284 Z 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Activation Energy Qa kJ/mol eVlatom 251 2.60 148 2.0 2.2 2.4 2.6 2.8 2.94 0.83 1.53 erf(z) 0.9340 0.9523 0.9661 0.9763 0.9838 0.9891 0.9928 0.9953 0.9981 0.9993 0.9998 0.9999 Calculated Value T(°C) 500 900 900 1100 500 900 900 1100 D(m²/s) 3.0 x 10-21 1.8 x 10-15 1.1 x 10-17 7.8 x 10-16 2.4 x 10-12 1.7 x 10-10 5.9 x 10-12 5.3 × 10-11
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