GATE 2021 MT – Question 61

Physical Metallurgy · Diffusion in solids · 2 marks · Numerical answer

A thick steel plate with 0.1 wt.% C is carburized at 950 °C, keeping surface C at 1.1 wt.%. After 9 hours, the depth where C reaches 0.6 wt.% is ______ mm (two decimal places). Carbon diffusivity in γ-Fe at 950 °C is $1.6\times10^{-11}$ m$^2$/s.

z	0.35	0.40	0.45	0.50	0.55	0.60
erf(z)	0.3794	0.4284	0.4755	0.5205	0.5633	0.6039

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 0.65 to 0.75

Explanation

For constant surface concentration, erf[z]=(Cs−Cx)/(Cs−C0)=(1.1−0.6)/(1.1−0.1)=0.5. Interpolation gives z≈0.477.

Thus x=2z√Dt=2(0.477)√(1.6×10⁻¹¹×32400)=0.000687 m, or **0.69 mm**.