Answer:
[tex]T=899.849K=626.7\°c[/tex]
Explanation:
We need to use Fick's Law to resolve this problem.
We know for this Law that:
[tex]J=-D\frac{\Delta c}{\Delta x}[/tex]
And we know as well that the diffusivity coefficient can be expressed as follows,
[tex]D=D_0 e^{-\frac{Ed}{RT}}[/tex]
Where J is the flux of atoms, D is the diffusivity, R is the gas constant, Ed is the activation energy and \frac{\Delta c}{\Delta x} is the concentration of gradient.
To calculate the temperature we need to remplace the equation of diffusivity coefficient in the Fick's law equation.
[tex]J=-D\frac{\Delta c}{\Delta x} = -D_0 e^{-E_d/RT}\frac{\Delta c}{\Delta x}[/tex]
Rearrange the equation to get the value of temperature
[tex]ln(\frac{J\Delta x}{D_0 \Delta c})=(-\frac{E_d}{RT})[/tex]
[tex]T=-\frac{E_d}{Rln(\frac{J\Delta x}{D_0 \Delta c})}[/tex]
We have all the values,
[tex]\Delta x= 10*10^{-3}m\\\Delta c= 0.85-0.40 =0.45kg.c.cm^{-1}[/tex]
[tex]Ed=-80000Jmol^{-1}K^{-1}\\R=8.31Jmol^{-1}K^{-1}\\J=6.3*10^{-10}kg.m^{-2}\\D_0 = 6.2*10^{-7}m^2s^{-1}[/tex]
So substituting,
[tex]T=\frac{-80000}{8.31*ln(\frac{(6.3*10^{-10})(10*10^{-3})}{6.2*19^{-7}*0.45})}[/tex]
[tex]T=899.849K=626.7\°c[/tex]
