Question

An iron-carbon alloy initially containing 0.258 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1120°C. Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at 0.0 wt% C. At what position will the carbon concentration be 0.194 wt% after a 6 h treatment? The value of D at 1120°C is 6.9 × 10-11 m2/s.

Answer 1

1.95 mm

Step-by-step explanation:

Let's calculate the carbon conc. 0.194 wt% after a 6 h treatment using the expression:

`(C_x - C_0)/(C_s - C_0) = 1 - erf ((x)/(2 √(Dt)))`

`(0.194 - 0.258)/(0 - 0.258) = 1 - erf ((x)/(2 √(Dt)))`

`0.248 = 1 - erf ((x)/(2 √(Dt)))`

`erf((x)/(2 √(Dt)) = 0.752`

From the erf z table, at erf(z) = 0.752

z = 0.80

Thus,

`(x)/(2 √(Dt)) = 0.80`

Where d =
`6.9*10^-^1^1`

Time, t = 6 hrs = (6 * 60mins * 60secs)

Substituting values:

`(x)/(2 √(6.9*10^-^1^1 * (6*60mins*60sec))) = 0.80`

`(x)/(2 √(1.49*10^-^6))) = 0.80`

`(x)/(2.44*10^-^3) = 0.80`

Solve for x:

`x = 0.80 * 2.44*10^-^3`

`x = 1.95*10^-^3`

x = 1.95 mm

The position will the carbon concentration be 0.194 wt% after a 6 h treatment is at 1.95 mm