Engineering, 15.04.2020 01:33 samariahopkins4

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.

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Answer from: emmagbales

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 $t^{-1}_R$ where t_R 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

$rate = Ce^{-Q/RT}$

The Activation energy is $Q = 1.85 *10^{5} J/mol$

Explanation:

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

$Z = Ce^{-Q/RT}$

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 t_R = 100 hours

Now substituting into the Arrhenius expression

$Z = Ce^{-Q/RT}$

$\frac{1}{100h} = Ce^{-Q/R(250+273)K}$

$0.010h^{-1} = Ce^{-Q/R(523K)}$ -----(2)

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

Now substituting into the Arrhenius expression

$\frac{1}{10h} = Ce^{-Q/R(280+273)K}$

$0.10h^{-1} = Ce^{-Q/R(553K)}$ ----(3)

Dividing the second equation by the first one

$\frac{0.010}{0.10h} = \frac{Ce^{-Q/R(523K)}}{ Ce^{-Q/R(553K)}}$

$ln (0.01) = \frac{-Q (1/523K)- (1/553K)}{R}$

$Q = \frac{Rln(0.10)}{(1/523K) - (1/553K)}$

Substituting 8.314 J/mol K for R

$Q = \frac{(8.314 )ln(0.10)}{(1/523K) - (1/553K)}$

$Q = 1.85 *10^{5} J/mol$

Answer from: Quest

At a roundabout you must yield to traffic already in the roundabout

Answer from: Quest

the equation above shows how temperature f, measured in degrees fahrenheit, relates to a temperature c, measured in degrees celsius. based on the equation, which of the following must be true?

a temperature increase of 1 degree fahrenheit is equivalent to a temperature increase of

degree celsius.

a temperature increase of 1 degree celsius is equivalent to a temperature increase of 1.8 degrees fahrenheit.

a temperature increase of

degree fahrenheit is equivalent to a temperature increase of 1 degree celsius.

a) i only

b) ii only

c) iii only

d) i and ii only

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Recrystallization is a thermally activated process. As such we can take a look at a series of temper...

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