Question 13.6

On the basis of the SiO₂-Al₂O₃ phase diagram (Figure 12.27 in the sixth edition), for each pair of the following list of compositions, which would you judge to be the more desirable refractory? Justify your choices.

1. 99.8 wt% SiO₂-0.2 wt%Al₂O₃ and 99.0 wt% SiO₂-1.0 wt%Al₂O₃
2. 30 wt% SiO₂-70 wt%Al₂O₃ and 26 wt% SiO₂-74 wt%Al₂O₃
3. 10 wt% SiO₂-90 wt%Al₂O₃ and 5 wt% SiO₂-95 wt%Al₂O₃

Question 13.11

Soda and lime are added to a glass batch in the form of soda ash (Na₂CO₃ and limestone (CaCO₃). During heating, these two ingredients decompose to give off carbon dioxide, the resulting products being soda and lime. Compute the weight of soda ash and limestone that must be added to 100 kg of quartz (SiO₂) to yield a glass of composition 75%wt SiO₂, 15%wt Na₂O and 10% wt CaO.

Question 13.17

For many viscous materials, the viscosity may be defined in terms of the expression

viscosity = sigma / (d(epsilon)/dt)

where sigma and d(epsilon)/dt are, respectively, the tensile strength and the strain rate. A cylindrical specimen of soda-lime glass of diameter 5 mm and length 100 mm is subjected to a tensile force of 1N along its axis. If its deformation is to be less than 1 mm over a week's time, using Figure 13.6, determine the maximum temperature to which the specimen may be heated.

Question 14.3

Compute mer molecular weights for the following:

1. polytetrafluoroethylene
2. polymethyl methacrylate
3. nylon 6,6
4. polyethylene terephthalate

Question 14.8

Is it possible to have a polyvinyl chloride homopolymer with the following molecular weight data and a number-average degree of polymerization of 1120? Why or why not?

Mol. Wt. range (g/mol)	wi	xi
8,000-20,000	0.02	0.05
20,000-32,000	0.08	0.15
32,000-44,000	0.17	0.21
44,000-56,000	0.29	0.28
56,000-68,000	0.23	0.18
68,000-80,000	0.16	0.10
80,000-92,000	0.05	0.03

Question 14.12

Using the definitions for total chain molecule length L (Equation 14.11, sixth edition) and average chain end-to end distance r, (Equation 14.12), for a linear polytetrafluoroethylene determine:

1. the number-average molecular weight for L = 2000 nm
2. the number-average molecular weight for r = 15 nm

Question 14.20

Calculate the number-average molecular weight of a random nitrile rubber [poly (acrylonitrile butadiene) co-polymer] in which the fraction of butadiene mers is 0.3; assume that this concentration corresponds to a number-average degree of polymerization of 2000.

Question 14.29

The density of totally crystalline nylon 6,6 at room temperature is 1.213 g/cm³. Also at room temperature the unit cell of this material is tri-clinic with lattice parameters:

a = 0.497 nm, alpha = 48.4 degrees

b = 0.547 nm, beta = 76.6 degrees

c = 1.729 nm, gamma = 62.5 degrees

If the volume of a triclinic unit cell is given by the following expression:

abc(1 - cos²(alpha) - cos²(beta) - cos²(gamma) + 2 cos(alpha)cos(beta)cos(gamma))^0.5

determine the number of mer units per unit cell.