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
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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.
erf(z)
erf(z)
0.55 0.5633 1.3
0.025 0.0282 0.60 0.6039 1.4 0.9523
0.0564 0.65 0.6420 1.5
Z
0.00
0.05
0.15
0.0000
0.10 0.1125 0.70 0.6778
0.20
Z
0.1680 0.75 0.7112 1.7
0.2227 0.80 0.7421 1.8
0.45 0.4755 1.1
0.50 0.5205
Z
1.6
1.2 0.9103
erf(z)
0.9340
2.8
0.9661
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
0.40 0.4284 1.0
0.8427 2.4
0.9763
0.9838
0.9891
0.9981
0.8802 2.6 0.9998
0.9993
0.9999
Transcribed Image Text: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. erf(z) erf(z) 0.55 0.5633 1.3 0.025 0.0282 0.60 0.6039 1.4 0.9523 0.0564 0.65 0.6420 1.5 Z 0.00 0.05 0.15 0.0000 0.10 0.1125 0.70 0.6778 0.20 Z 0.1680 0.75 0.7112 1.7 0.2227 0.80 0.7421 1.8 0.45 0.4755 1.1 0.50 0.5205 Z 1.6 1.2 0.9103 erf(z) 0.9340 2.8 0.9661 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 0.40 0.4284 1.0 0.8427 2.4 0.9763 0.9838 0.9891 0.9981 0.8802 2.6 0.9998 0.9993 0.9999
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