Answer:[tex]8.76\times 10^{-3} min^{-1}[/tex]
Explanation:
Given
n=5
0.3 fraction recrystallize after 100 min
According to Avrami equation
[tex]y=1-e^{-kt^n}[/tex]
where y=fraction Transformed
k=constant
t=time
[tex]0.3=1-e^{-k(100)^5} [/tex]
[tex]e^{-k(100)^5} =0.7[/tex]
Taking log both sides
[tex]-k\cdot (10^{10}=\ln 0.7[/tex]
[tex]k=3.566\times 10^{-11}[/tex]
At this Point we want to compute [tex]t_{0.5}\ i.e.\ y=0.5[/tex]
[tex]0.5=1-e^{-kt^n}[/tex]
[tex]0.5=e^{-kt^n}[/tex]
[tex]0.5=e^{-3.566\times 10^{-11}\cdot (t)^5}[/tex]
taking log both sides
[tex]\ln 0.5=-3.566\times 10^{-11}\cdot (t)^5[/tex]
[tex]t^5=1.943\times 10^{10}[/tex]
[tex]t=114.2 min[/tex]
Rate of Re crystallization at this temperature
[tex]t^{-1}=8.76\times 10^{-3} min^{-1}[/tex]
