$2\mathrm{.}9$ A young engineer is asked to design a thermal protection barrier for a sensitive electronic device that might be exposed to irradiation from a high$-$powered infrared laser. Having learned as a student that a low thermal conductivity material provides good insulating characteristics, the engineer specifies use of a nanostructured aerogel, characterized by a thermal conductivity of $k_a=0\mathrm{.}005\frac{W}{m}*K,$ for the protective barrier. The engineer's boss questions the wisdom of selecting the aerogel because it has a low thermal conductivity. Consider the sudden laser irradiation of $($a$)$ pure aluminum, $($b$)$ glass, and $($c$)$ aerogel. The laser provides irradiation of $G=10{10}^6\frac{W}{m^2}.$ The absorptivities of the materials are $=0\mathrm{.}2,0\mathrm{.}9,$ and $0\mathrm{.}8$ for the aluminum, glass, and aerogel, respectively, and the initial temperature of the barrier is $T_i=300K.$ Explain why the boss is concerned. Hint: All materials experience thermal expansion $($or contraction$),$ and local stresses that develop within a material are, to a first approximation, proportional to the local temperature gradient.