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

rate = 7.580 ×
`10^(-3)` /min

Step-by-step 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 =
`-(ln (1-y))/(t^n)`

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

k =
`-(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)` =
`[(-ln(1-y))/(k)]^(1/n)`

`t^(0.5)` =
`[\frac{-ln(1-0.5)}{5.65* 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