From the curves shown in Animated Figure and using the following Equation, determine the rate of recrystallization for pure copper at the several temperatures. Make a plot of $ln(rate)$ versus the reciprocal of temperature $($in $K^{-1}).($a$)$ Determine the activation energy for this recrystallization process. $($See Section FACTORS THAT INFLUENCE DIFFUSION.$)($b$)$ By extrapolation, estimate the length of time required for $50\%$ recrystallization at room temperature, $20C(293K).$

$($a$)k\frac{J}{m}ol$

$($b$)$ tays