GATE 2024 MT – Question 55
During carburization at 950 °C, carbon concentration reaches 0.8 wt.% at depth 0.3 mm after one hour. The time to obtain the same concentration at 0.6 mm at the same temperature is ______ hours (nearest integer).
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Correct answer: 4 to 4
Explanation
With unchanged boundary and initial concentrations, the diffusion profile depends on $x/\sqrt{Dt}$.
The same concentration fixes this ratio.
At the same temperature $D$ is unchanged, so $t_2=t_1(x_2/x_1)^2=1(0.6/0.3)^2=\boxed{4\ \mathrm{hours}}$.