Question

For a steel alloy it has been determined that a carburizing heat treatment of 15 h duration will raise the carbon concentration to 0.35 wt% at a point 2.0 mm from the surface. Estimate the time necessary to achieve the same concentration at a 6.0-mm position for an identical steel and at the same carburizing temperature.

Answer 1

135 hour

Step-by-step explanation:

It is given that a carburizing heat treatment of 15 hour will raise the carbon concentration by 0.35 wt% at a point of 2 mm from the surface.

We have to find the time necessary to achieve the same concentration at a 6 mm position.

we know that
`(x_1^2)/(Dt)=constant` where x is distance and t is time .As the temperature is constant so D will be also constant

So
`(x_1^2)/(t)=constant`

then
`(x_1^2)/(t_1)=(x_2^2)/(t_2)` we have given
`x_1=2 mm\ ,t_1=15 hour\ ,x_2=6\ mm` and we have to find
`t_2` putting all these value in equation

`(2^2)/(15)=(6^2)/(t_2)`

so
`t_2=135\ hour`