Question

Question 125 pts An FCC nickel-carbon alloy initially containing 0.20 wt% carbon is carburized at an elevated temperature and in an atmosphere in which the surface carbon concentration is maintained at 1.0 wt%. Given: Do = 2.3 x 10-5 m2/s, Qd = 111,000 J/mol. If, after 49.5 h, the concentration of carbon is 0.35 wt% at a position 4.0 mm below the surface, determine the temperature at which the treatment was carried out. Boltzmann constant, k = 8.617x10-5 eV/(atom-K)= 1.38x10-23 J/(atom-K) and Avogadro’s number, NA=6.022×1023 atom/mol. Group of answer choices 1300 K 1375 K 975 K 1027 K

Answer 1

975 K

Step-by-step explanation:

Here, given :

The alloy is a FCC nickel-carbon.

`$D_o= 2.3 * 10^(-5) \ m^2/s$`

`$Q_d=111,000 \ J/mol$`

Boltzmann Constant,
`$k=8.617 * 10^(-5) \ eV/(atom-K)$`

Therefore,

`$(C_x-C_o)/(C_s-C_o)= (035-0.20)/(1.0-0.20)$`

= 0.1875

`$=1-\text{erf}\left((x)/(2√(Dt))\right)$`

So,
`$\text{erf}\left((x)/(2√(Dt))\right) = 0.8125$`

Therefore,

w erf w

0.92 0.80677

y 0.8125

0.96 0.82542

Now,

`$(y-0.92)/(0.96-0.92) = (0.8125-0.80677)/(0.82542-0.80677)$`

y = 0.93228

`$\text{erf}\left((x)/(2√(Dt))\right) = 0.93228$`

`$D=(x^2)/(4t(0.93228)^2)$`

`$D=((4* 10^(-3))^2)/(4* 49.5 * 3600 * (0.93228)^2)$`

`$= 2.58 * 10^(-11)$`

`$T=(Q_d)/(R(\ln D_o - \ln D))$`

`$T=(111000)/(8.31(\ln (2.3 * 10^(-5)) - \ln (2.58 * 10^(-11))))$`

T = 974.84 K

T = 975 K