Recrystallization is a thermally activated process. As such we can take a look at a series of temperatures to see the fraction of recrystallized material. Please determine the activation energy for the recrystallization process using values of the 50% recrystallized portion at each temperature.

Complete Question

Re crystallization is a thermally activated process. As such, can be characterized by the Arrhenius expression (Equation 1). As a first approximation we can treat   where is the time necessary to fully recrystallize  the micro structure. For a 50% cold-worked aluminum alloy,  t_R is 100 hours at 250° C  and 10 hours at 280°C .Calculate the activation energy for the Re crystallization  process  

Equation 1

The Activation energy is  

Explanation:

From the question we are given the Arrhenius expression for the growth rate(Z) as

Where    Q is the activation energy

              C  is known as the pre-exponential constant

               R   is the universal gas constant

                T is the absolute temperature

From the question according to the first approximation the  rate is inverse of time to fully recrystallize the micro structure(t_R)

   We are told that at 250°C that = 100 hours

        Now substituting into the  Arrhenius expression

          -----(2)

 We are told that at 280°C that = 10 hours        

Now substituting into the  Arrhenius expression                

          ----(3)

Dividing the second equation by the first one

Substituting for R

answer:

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explanation: