QUIZ -4 Solution

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Friday, 03/02/2012 “An Aggie does not lie, cheat, or steal or tolerate those who do” Page 1 of 2
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Quiz 4 Materials-Spring 2012
50 minutes, Open textbook, open class notes; no other material is allowed, use a pen (no pencils please)
1) We have a polyacrylonitrile (PAN) sample containing 8,000 chains with molecular weights between 5,000 and
10,000 g/mol, and 7000 chains with molecular weights between 10,000 and 15,000 g/mol. Determine the
weight average molecular weight.
M wi wiMi
8000 7500 0.407 3050.85
7000 12500 0.593 7415.25
15000 1.000 10466.1
̅̅̅̅̅
2) Determine the number of vacancies per cm 3 needed for a BCC iron crystal to have a density of 7.87 g/cm 3 . The
lattice parameter and molecular weight of iron are 2.866 10 -8 cm and 55.847 g/mol, respectively
Expected Theoretical Density
( )
Calculate the number of iron atoms and vacancies that would be present in each unit cell:
( )
There should be 2-1.9977 = 0.002235 vacancies per unit cell
Then the number of vacancies per cm 3
3) An iron FCC with 0.02 wt% C is to be carburized at 1200 C in 4 h, such that a point 0.6 mm beneath the
surface reaches 0.45 wt% C. Calculate the carbon wt% content required at the surface of the steel.
Cs
C0 0.02
Cx 0.45
for C in iron
FCC
Do(m2/s)
2.30E-05
Qd(J/mol)
1.48E+05
R 8.314
T(K) 1473
D(m2/s)
1.298E-10
t(s) 14400
x(m)
6.00E-04
z 0.2194
erf(0.2194) 0.2435
Cs(%C) 0.5884

Friday, 03/02/2012 “An Aggie does not lie, cheat, or steal or tolerate those who do” Page 2 of 2
4) For a given material, plastic deformation begins with a stress of 400 MPa and the modulus of elasticity is 150
GPa. For a specimen with a cross-sectional area of 200 mm 2 and 90 mm long, what is the maximum length to
which it may be stretched without causing plastic deformation