A sheet of -iron is exposed to a carbon-rich (carburizing) atmosphere on one sid

Question

A sheet of -iron is exposed to a carbon-rich (carburizing) atmosphere on one side and a carbon-deficient (decarburizing) atmosphere on the other side at 700°C. A steady state condition is achieved. The carbon concentrations at the carburizing and decarburizing surfaces of the sheet are 1.13 kg/m3 and 0.59 kg/m3 , respectively. The temperature dependence of the diffusion coefficient of carbon in -iron is determined by the preexponential constant D0 = 6.210-7 m 2 /s and activation energy Qd = 80 kJ/mol. What is the mass of carbon that passes per hour through the iron sheet, if the thickness of the sheet is 1.5 mm and its area is 1 m 2 ? Assume a linear concentration profile. Explain all notations used.

Explanation / Answer

From Arhenius Equation D= Doe-Qd/RT

D =diffusivity at temperature 700 Deg.c T= 700+273.15

Qd= 80 Kj/mol =80*1000 j/mol

Do= 6.2X10-7 m2/s

D= 6.2X10-7 e- 80*1000/(8.314*(700+273.15)=6.2X10-7*6,63*10-13=4.114*10-19 m2/s

Mass of iron passing per hours = D*Concentration difference *Area /thicknesss = 4.114*10-19* (1.13-0.59) * 1/(1.5X10-3) kg/sec=1.481X10-16 kg/ec =1.481X10-16*60*60 =5.33X10-13 kg/hr

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