Answer:
The total time (in seconds) for the transformation to reach 95% completion is 516.783 secs
Explanation:
Given Data:
n=1.5
Time to reach 30% completion=125 Secs
Required:
Total Time for the transformation to reach 95% completion=?
Solution:
Avrami Equation:
[tex]y=1-e^{-kt^n}[/tex]
where:
k is time constant
t is the time
y is the remaining amount of reaction.
First Calculate K:
[tex]0.3-1=-e^{-k*125^1.5}\\-0.7=-e^{-k*125^1.5}\\[/tex]
Taking "ln"on both sides
ln(0.7)=-k*(125^1.5)
k=0.000255
At 95 % completion:
Avrami Equation Can be rearranged as:
[tex]y-1=-e^{-kt^n}\\ln(-y+1)=-k*t^n\\\frac{ln(-y+1)}{-k}=t^n\\ ln(\frac{ln(-y+1)}{-k})=n*lnt\\\frac{ln(\frac{ln(-y+1)}{-k})}{n}=lnt \\e^{\frac{ln(\frac{ln(-y+1)}{-k})}{n}}=t[/tex]
[tex]e^{\frac{ln(\frac{ln(-0.95+1)}{-0.000255}))}{1.5}}=t\\t=516.783 \ secs[/tex]
The total time (in seconds) for the transformation to reach 95% completion is 516.783 secs
