Thermal insulation.

a) A piece of insulation consists of a layer of material A and a layer of material B, each of thickness L, but with different thermal conductivities. Suppose that the insulation separates a reservoir at Th from a reservoir at T_l . Derive a formula for the steady-state temperature at the A/B interface. Explain the predictions of your formula for the cases kA >> kB and kA = kB. Hint: the heat fluxes through the two materials have to be the same.

b) Most new windows are supplied as sealed modules consisting of two thin pieces of glass separated by a gap filled with nitrogen (air, basically.) Sketch the temperature profile through such a module on a hot day.

c) In practice, a highly porous material (such as is used in winter clothing) is even more effective as insulation than a layer of air of the same thickness. Suggest an explanation for this.