Answer:
844°C
Explanation:
The problem can be easily solve by using Fick's law and the Diffusivity or diffusion coefficient.
We know that Fick's law is given by,
[tex]J = - D \frac{\Delta c}{\Delta x}[/tex]
Where [tex]\frac{\Delta c}{\Delta x}[/tex] is the concentration of gradient
D is the diffusivity coefficient
and J is the flux of atoms.
In the other hand we have, that
[tex]D= D_0 e^{\frac{E_d}{RT}}[/tex]
Where [tex]D_0[/tex] is the proportionality constant,
R is the gas constant, T the temperature and [tex]E_d[/tex] is the activation energy.
Replacing the value of diffusivity coefficient in Fick's law we have,
[tex]J = -D_0 ^{\frac{E_d}{RT}}\frac{\Delta c}{\Delta x}[/tex]
Rearrange the equation to get the value of temperature,
[tex]T=\frac{Ed}{Rln(\frac{J\Delta x}{D_0 \Delta c})}[/tex]
We have all the values in our equation.
[tex]\Delta c = 0.664-0.339 = 0.325 C. cm^{-1}[/tex]
[tex]\Delta x = 9.7*10^{-3}m[/tex]
[tex]E_d = 82000J[/tex]
[tex]D_0 = 6.5*10^{-7}m^2/s[/tex]
[tex]J = 3.2*10^{-9}m^2/s[/tex]
[tex]R= 8.31Jmol^{-1}K[/tex]
Substituting,
[tex]T=\frac{Ed}{Rln(\frac{J\Delta x}{D_0 \Delta c})}[/tex]
[tex]T=-\frac{-82000}{(8.31)ln(\frac{3.2*10^{-9}(9.7*10^{-3})}{6.5*10^{-7} (0.325)})}[/tex]
[tex]T=1118.07K=844\°C[/tex]
