The outer surface of a steel alloy is to be hardened by increasing its carbon co

Question

The outer surface of a steel alloy is to be hardened by increasing its carbon content. The carbon is to be supplied from an external carbon-rich atmosphere, which is maintained at an elevated temperature. A diffusion heat treatment at 846°C for 10 min increases the carbon concentration to 0.70 wt% at a position 1.6 mm below the surface. Estimate the diffusion time required at 630°C to achieve this same concentration also at a 1.6 mm position. Assume that the surface carbon content is the same for both heat treatments, which is maintained constant. The preexponential and activation energy values for the diffusion of carbon in the iron are 7.5 x 107 m2/s and 70.9 kJ/mol, respectively. min

Explanation / Answer

since (Cx-CO)/CS-CO)=1-erf{ x/2*sqrt(Dt)}

Cx= concentration at position x, Co= initial concentration and Cs= surface concentration.

since LHS is same for both the temperatures given

x/Sqrt(Dt)= constant m since x is also same

D1t1= D2t2

t2= (D1t1/D2), but D= Do*exp(Ea/RT)

lnD= lnDO- Ea/RT

hence ln D1= lnDo- Ea/RT1

lnD2= lnDo-Ea/RT2, T1= 846 deg.c= 846+273= 1119, T2= 630 deg.c =630+273= 903K

lnD1-lnD2= (-Ea/R)*(1/T1-1/T2)= *-70.9*1000/8.314)*(1/1119-1//903), Ea= activation energy

D1/D2= 6.19

hence t2= 10*6.19=61.9 min

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