Answer:
t = 1456.8 sec
Explanation:
given data:
contant k = 2.60*10^{-6}
rate of crystallization is 0.0013 s-1
rate of transformation is given by
[tex]r = \frac{1}{t_0.5}[/tex]
use specifies value to solve [tex]t_0.5[/tex]
it is ime required for 50% tranformation
[tex]r = \frac{1}{.0013}=769.2 sec[/tex]
Avrami equation is given by
[tex]y = 1 - e^{-kt^n}[/tex]
[tex]0.5 = 1 - e^{-kt_0.5^n}[/tex]
[tex]1-0.5 = e^{-kt_0.5^n}[/tex]
[tex]ln (1 - 0.5) = -kt_0.5^n[/tex]
[tex]ln \frac{ln (1 - 0.5)}{-k} = nln t_0.5[/tex]
[tex]n = \frac{ ln \frac{ln (1 - 0.5)}{-k}}{ln t_0.5}[/tex]
[tex]n = \frac{ ln \frac{ln (1 - 0.5)}{-2.60*10^{-6}}}{ln 769.2}[/tex]
n = 1.88
second degree of recrystalization may be determine by rearranging original avrami equation
[tex]t = [\frac{-ln(1-y)}{k}]^{1/n}[/tex]
for 90%completion
[tex]t = [\frac{-ln(1-0.9)}{2.60*10^{-6}}]^{1/1.88}[/tex]
t = 1456.8 sec
