A homeowner installs a new wall assembly consisting of a 0.5 mm–thick sheet of…
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
A homeowner installs a new wall assembly consisting of a 0.5 mm–thick sheet of aluminum attached to the interior side of a 40 mm–thick layer of expanded polystyrene (EPS) foam. The wall area of interest is 1.0 m². The indoor air is maintained at 21 °C, and the exterior surface of the EPS is in contact with outdoor air at 0 °C. The aluminum and EPS are in perfect thermal contact with each other.
Assume a steady state has been reached and that energy transfer occurs only by conduction normal to the wall surfaces.
(a) Without performing any numerical calculation, compare the relative thermal resistances of the aluminum sheet and the EPS layer. Provide a brief justification based on the intrinsic properties of the two materials.
(b) Describe qualitatively how the addition of the thin aluminum sheet affects (i) the overall rate at which energy leaves the house through that 1.0 m² portion of wall and (ii) the temperature of the interior surface of the EPS compared with the case where no aluminum sheet is present.
(c) The homeowner is considering replacing the 40 mm thickness of EPS with a 4 mm thickness of high-conductivity graphite foam, which is ten times more expensive per unit volume but has the same mass. Explain why this substitution is unlikely to reduce the home’s heating cost, even though the graphite foam is more thermally conductive than EPS.