Answer:
The temperature is 2584.5 K
Explanation:
Given:
Activation energy [tex]Q = 80000[/tex] [tex]\frac{J}{mol}[/tex]
Preexponential [tex]D= 6.2 \times 10^{-7}[/tex] [tex]\frac{m^{2} }{s}[/tex]
Diffusion flux [tex]J = 6.4 \times 10^{-10}[/tex] [tex]\frac{kg}{m^{2} s}[/tex]
Thickness of plate [tex]\Delta x = 11 \times 10^{-3}[/tex] m
Concentration of carbon at two faces [tex]\Delta C = (0.88 - 0.41 ) = 0.47[/tex] [tex]\frac{kg}{m^{3} }[/tex]
From the formula of temperature in terms of diffusion flux,
[tex]T = (\frac{Q}{R} ) \frac{1}{\ln (\frac{D\Delta C}{J\Delta x} )}[/tex]
Where [tex]R =[/tex] 8.314 [tex]\frac{J}{mol.K}[/tex] ( gas constant )
Put the values and find the temperature,
[tex]T = (\frac{80000}{8.314} ) \frac{1}{\ln (\frac{6.2 \times 10^{-7} \times 0.47 }{6.4 \times 10^{-10}\times 11 \times 10^{-3} } )}[/tex]
[tex]T = 2584.5[/tex] K
Therefore, the temperature is 2584.5 K
