A spherical Pyrex glass shell has inside and outside diameters of \(D_{1}=0.15 \mathrm{~m}\) and \(D_{2}=0.30 \mathrm{~m}\), respectively. The inner surface is at \(T_{s, 1}=150^{\circ} \mathrm{C}\) while the outer surface is at \(T_{s, 2}=30^{\circ} \mathrm{C}\).

(a) Determine the temperature at the midpoint of the shell thickness, \(T\left(r_{m}=0.1125 \mathrm{~m}\right)\).

(b) For the same surface temperatures and dimensions as in part (a), show how the midpoint temperature would change if the shell material were aluminum.