Question

It is known that the kinetics of recrystallization for some alloy obey the Avrami equation, and that the value of n in the exponential is 2.4. If, at some temperature, the fraction recrystallized is 0.30 after 100 min, determine the rate of recrystallization at this temperature.

Answer 1

Answer:

rate = 7.580 × $10^{-3}$   /min

Explanation:

given data

value of n = 2.4

fraction recrystallized = 0.30

time = 100 min

solution

we will get here rate of recrystallization at this temperaturewe use here avrami equation that is

y = 1 - exp (-k $t^n$ )    ................1

we get hete first k

k = $-\frac{ln (1-y)}{t^n}$

put heer value n is 2.4 and y = 0.30 and t is 100

k = $-\frac{ln (1-0.30)}{100^{2.4}}$

k = 5.65 × $10^{-6}$  

now we get here $t^{0.5}$  

value of t at y  0.5

$t^{0.5}$    = $[\frac{-ln(1-y)}{k}]^{1/n}$

$t^{0.5}$    = $[\frac{-ln(1-0.5)}{5.65\times 106{-6}}]^{1/2.4}$  

$t^{0.5}$    = 131.923 min

and

rate = 1 ÷ $t^{0.5}$  

rate = 1 ÷  131.923

rate = 7.580 × $10^{-3}$   /min