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For a steel alloy it has been determined that a carburizing heat treatment of 10 h duration will raise the carbon concentration to 0.45% wt% at a point 2.5mm from the surface. Estimate the time necessary to achieve the same concentration at a 5.0mm position for an identical steel and at the same carburizing temperature.

Answer :

Answer:

T2=40hrs

Explanation:

Heat carburizing treatment is T1=10hrs

T2=?

Carbon concentration 0.45%

Position 1 X1=2.5mm

Position 2 X2=5mm

Recall that X^2/DT= constant

But since temperature is constant also D is constant

Hence

X1^2/D1=X2^2/D2

2.5^2/10=5^2/T2

T2=40hrs

The required time is 40 hours.

We need to estimate the time necessary to achieve a carbon concentration of 0.45 wt% at a point 5.0 mm from the surface.

We know that

[tex]\frac{x^2}{Dt} =constant[/tex]

Since the temperature is constant, so D is constant,

[tex]\frac{x^2}{t} =constant\\\frac{x_{1}^{2}}{t_1}=\frac{x_{2}^{2}}{t_2}[/tex]

Here [tex]x_1[/tex] = 2.5 mm

[tex]t_1[/tex] = 10 h

[tex]x_2[/tex] = 5 mm

[tex]t_2=\frac{x_{2}^{2}t_1}{x_{1}^{2}} \\=\frac{5^2\times10}{2.5^2}\\=40 hours[/tex]

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