91Ó°ÊÓ

For each of the following pairs of materials, decide which has the larger thermal conductivity. Justify your choices. (a) Pure silver; sterling silver \((92.5\) wt\% \(\mathrm{Ag}-7.5 \mathrm{wt} \% \mathrm{Cu})\) (b) Fused silica; polycrystalline silica (c) Linear and syndiotactic poly(vinyl chloride) \((D P=1000) ;\) linear and syndiotactic polystyrene \((D P=1000)\) (d) Atactic polypropylene \(\left(\bar{M}_{w_{5}}=10^{6} \mathrm{~g} / \mathrm{mol}\right)\); isotactic polypropylene \(\left(\bar{M}_{w}=10^{5} \mathrm{~g} / \mathrm{mol}\right)\)

We might think of a porous material as being a composite in which one of the phases is a pore phase. Estimate upper and lower limits for the room- temperature thermal conductivity of an aluminum oxide material having a volume fraction of \(0.25\) of pores that are filled with still air.

(a) Briefly explain why thermal stresses may be introduced into a structure by rapid heating or cooling. (b) For cooling, what is the nature of the surface stresses? (c) For heating, what is the nature of the surface stresses?

A steel wire is stretched with a stress of 70 MPa \((10,000 \mathrm{psi})\) at \(20^{\circ} \mathrm{C}\left(68^{\circ} \mathrm{F}\right) .\) If the length is held constant, to what temperature must the wire be heated to reduce the stress to \(17 \mathrm{MPa}\) \((2500 \mathrm{psi}) ?\)

The two ends of a cylindrical rod of nickel \(120.00 \mathrm{~mm}\) long and \(12.000 \mathrm{~mm}\) in diameter are maintained rigid. If the rod is initially at \(70^{\circ} \mathrm{C}\), to what temperature must it be cooled in order to have a \(0.023 \mathrm{~mm}\) reduction in diameter?

What measures may be taken to reduce the likelihood of thermal shock of a ceramic piece?