HW#3 solution manual PDF

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CIVE 378 Materials of Construction Homework Assignment #3 Due: February 14, 2018

1.! Copper has an FCC crystal structure and an atomic radius of 0.1278 nm. Calculate a theoretical value for the density of copper, [(mass/unit cell) / (volume/unit cell)], in mega-grams per cubic meter. The atomic mass of copper is 63.54 g/mol, and 1 mole of copper contains 6.02*1023 atoms (Avogadro’s number). Given: •! •! •! •!

n=4 (FCC structure); A= 63.54 R=0.1278nm NA=6.02x1023

So, to compute the density of copper, we have first to find Vc.

Vc = ( 2 2 R ) 3 Vc = ( 2 2 x0.1278 x10 -฀9 )3 V c = 4.7231´฀10 -฀29 Then, r is going to be:

r=

nA Vc N A

4 ´฀ 63.54 4.7231 ´฀10 -฀29 ´฀6.02 ´฀10 23 r = 8938889.522 = 8.99 Mg / m3

r=

2.! Refer to below phase diagram (equilibrium diagram) of binary alloy A-B. Temperature

Liquidus LIQUID

LIQUID+and T2

a฀

a฀

LIQUID+and

Eutectic point

a฀

and

T1

b฀ b฀

b฀ %*A

0

5

10

(a)! List phases existing in the system: Liquid, a฀, b฀ (b) Specify liquidus on the graph: see the graph (c) Mark eutectic point on the graph: see the graph (d) How much liquid and how much solid ( a฀ ) are present for an alloy of 2% A 98% B at temperature T2? % Liquid = [(2.0-0.7)/(4.6-0.7)]*100 = 33.3% % a฀ = [(4.6-2.0)/(4.6-0.7)]*100 = 66.7% 3.! Figure below shows a portion of the H2O – NaCl phase diagram. (a)! At a salt composition of 10%, what is the temperature at which ice will start melting? -21C (b)!What is the eutectic temperature of the ice and salt combination? -21C...