An architect must choose the wall structure for a small passive-solar house located…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
An architect must choose the wall structure for a small passive-solar house located in a cold climate. The wall cross-section will have the following geometry: total area A=25m2 and length (thickness) L=0.25m. The indoor air temperature is maintained at 20∘C while the outdoor air temperature remains at −5∘C for long winter nights.
Two construction options are under consideration.
• Option I: one solid layer of reinforced concrete (k=1.4Wm−1K−1, density 2400kgm−3).
• Option II: a composite wall consisting of 0.05m of pine (k=0.12Wm−1K−1) on the interior side and 0.20m of high-density fiberglass insulation (k=0.040Wm−1K−1) on the exterior side.
Neglect thermal contact resistance between layers.
(a) Rank the three materials (concrete, pine, fiberglass) from greatest to least ability to conduct thermal energy. Explain your reasoning based on the given numerical values.
(b) For Option II, describe qualitatively how swapping the positions of the pine and fiberglass layers (putting fiberglass on the inside and pine on the outside) would affect the overnight energy loss, if at all. Support your answer with physical reasoning rather than calculations.
(c) Calculate the steady-state rate at which thermal energy is conducted through the wall for each construction option. Express each result in W and clearly show your reasoning, including how you treat the composite wall in Option II.
(d) Residential building codes often impose additional criteria such as material cost, structural strength, and environmental impact. Discuss two trade-offs the architect should consider when choosing between Option I and Option II, referencing both the quantitative results from part (c) and qualitative factors.