1) If a superalloy jet engine is heated so that its length in cach direction exp
ID: 714757 • Letter: 1
Question
1) If a superalloy jet engine is heated so that its length in cach direction expands by 1%, what is its percentage change in volume (assume it is roughly cubic)? Hint: Calculate its volume before and after heating, assuming that its length, height, and width are the same, i.c., a cubic engine. 2) Calculate the density of Al in g/'cm*, given that it forms an FCC crystal structure with an atomic radius of 0.143 nm (10 cm) and a mass of 27 g/mole. Avogadro's number is 6.02 x 103 atoms/mole. Hint: calculate the number of atoms in cach cell carefully. 3) Compute the packing fraction P of a BCC crystal (hint: P = total volume of spheres in the cubic cell volume of the cubic cell, assuming that spheres touch along the body diagonal) 4) Calculate the vacancy concentration in aluminum at 50%, 70%, and 90% of TM-923 K. G-0.66 eV, and k = 8.62 x 10SeV/K. Calculate In (o/N) and 1/T, and plot on a linear scale (hint: should be a straight line). 5) a) If the vacancy concentration in Cu is measured to be 105 at 1300K (near its melting point), what is ? (assume the pre-exponential factor is 1; R OvN-exp (-6/RT) b) What would be the concentration at 650 K? ) Determine the largest size of an interstitial hole in FCC Fe. B0.124 nm. Could a C atom sit in an interstitial site (-0.077 nm? Why or why not?Explanation / Answer
1. The volume of a cube = a^3 where a is the side. If the side is increased by 1%, the side becomes, a+0.01a = 1.01a
New volume= (1.01a)^3 = 1.030301 a^3
Change in volume = 1.030301a^3 - a^3 = 0.030301
Percentage increase = 3.0301 %
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