mid+term+2

# mid+term+2 - Louisiana State University Mechanical...

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Louisiana State University Mechanical Engineering Department ME 2733- Materials of Engineering; Spring 2003 (Section 2) Midterm Exam Part II March 25, 2003 Name:_________________________ SOLUTIONS Problem 1 . Consider a copper sample with the energy for vacancy formation Q v =0.9eV/atom. Knowing that at 400 o C the equilibrium concentration of vacancies is 1.46x10 22 vacancies/m 3 what is the vacancy concentration at 900 o C? The Boltzmann’s constant is k=8.62x10 -5 eV/atom K. Solution: In general the equilibrium concentration of vacancies N v is given by: ) exp( kT Q N N v v = (1) where N=number of atomic sites per cubic meter and Q v =activation energy By writing this relation for two different temperatures: T 1 =400 o C +273 o C =673 o K and T 2 =900 o C +273 o C =1173 o K we get: ) exp( 1 1 kT Q N N v v = (2) ) exp( 2 2 kT Q N N v v = (3) By taking the ratio of Eqs (2) and (3) we get: = + = 2 1 1 2 2 1 2 1 ( exp ) exp( T kT T T Q kT Q kT Q N N v v v v v (4) = 2 1 1 2 1 2 ) ( exp T kT T T Q N N v v v (5) knowing N v1 =1.46x10 22 m -3 we get: = × × × × = K

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## This note was uploaded on 01/22/2012 for the course ME 2733 taught by Professor Meng during the Fall '10 term at LSU.

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mid+term+2 - Louisiana State University Mechanical...

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