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Lilit [14]
3 years ago
11

For some metal alloy it is known that the kinetics of recrystallization obey the Avrami equation, and that the value of k in the

exponential is 2.60 x 10-6, for time in seconds. If, at some temperature, the rate of recrystallization is 0.0013 s-1, what total time (in s) is required for the recrystallization reaction to go to 90% completion?
Engineering
1 answer:
JulsSmile [24]3 years ago
5 0

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

r = \frac{1}{t_0.5}

use specifies value to solve t_0.5

it is ime required for 50% tranformation

r = \frac{1}{.0013}=769.2 sec

Avrami equation is given by

y = 1 - e^{-kt^n}

0.5 = 1 - e^{-kt_0.5^n}

1-0.5 = e^{-kt_0.5^n}

ln (1 - 0.5) = -kt_0.5^n

ln \frac{ln (1 - 0.5)}{-k} = nln t_0.5

n = \frac{ ln \frac{ln (1 - 0.5)}{-k}}{ln t_0.5}

n = \frac{ ln \frac{ln (1 - 0.5)}{-2.60*10^{-6}}}{ln 769.2}

n = 1.88

second degree of recrystalization may be determine by rearranging original avrami equation

t = [\frac{-ln(1-y)}{k}]^{1/n}

for 90%completion

t = [\frac{-ln(1-0.9)}{2.60*10^{-6}}]^{1/1.88}

t = 1456.8 sec

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