Question 1 of 6

Question 1 (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (A) — loadings on building enclosures. A building enclosure must resist several physically independent load types simultaneously, and a durable design provides a continuous path for each rather than treating the wall as a single structural problem. GRAVITY loads are the enclosure's own dead weight (cladding, glazing, insulation) plus superimposed snow, carried by anchors sized for both short-term and long-term creep behaviour. WIND loads act as fluctuating positive pressure on the windward face and negative suction on the leeward/side faces and at corners and roof edges, where local pressure coefficients spike well above the mean; cladding, glazing and fasteners must resist both the peak gust and cyclic fatigue. SEISMIC loads require the enclosure to tolerate the building's interstorey drift without cladding cracking or glazing popping from its frame. THERMAL loads have two aspects: the day–night and seasonal temperature swing across the assembly drives differential expansion between dissimilar materials (requiring movement joints), while the steady-state heat FLOW load is what insulation addresses (Questions 2 and 4). MOISTURE loads include bulk rainwater deposited on the exterior face (Question 6), capillary rise of groundwater at grade, vapour diffusing through the assembly from the warm humid side (Question 4), and construction moisture drying out over the first service years. AIR-PRESSURE loads — from stack effect, wind, and mechanical system operation — drive both bulk air leakage and, far more importantly, moisture-laden air INTO the assembly at a rate that dwarfs pure vapour diffusion wherever the air barrier is discontinuous. UV/SOLAR RADIATION loads heat exterior surfaces (Question 3) and degrade exposed cladding and sealants over time. Finally, IN-SERVICE and IMPACT loads (maintenance access, hail, wind-borne debris) round out the set. Treating each of these as a distinct load PATH problem — exactly as for the structural system — is what distinguishes durable enclosure design from a wall that merely looks complete.

Part (B)(i) — surface temperature and radiation wavelength. Every surface above absolute zero emits thermal radiation across a continuous spectrum of wavelengths, but the wavelength at which emission PEAKS is fixed by the surface's absolute temperature through Wien's Displacement Law:

Given. Wien's Displacement Law constant b = 2897.8 μm·K.

The relation is strictly INVERSE: as a surface's absolute temperature rises, the wavelength of its peak radiant emission shrinks. A cold surface (near ambient building temperatures) radiates almost entirely in the long-wave infrared; a very hot surface (a furnace, an incandescent filament, the sun) shifts its peak progressively toward the shorter-wave infrared and eventually into the visible band. This is precisely why an infrared thermal-imaging camera can distinguish building surface temperatures — it reads the peak/intensity of the LONG-WAVE emission spectrum, which shifts measurably even over the narrow 0–40 °C range found in building science.

Part (B)(ii) — wavelength range at normal building temperatures.

Find. The peak thermal-radiation wavelength range for building surfaces spanning a realistic winter-to-summer extreme, −30 °C (243.15 K) to +50 °C (323.15 K).

1. Apply Wien's law at both temperature extremes. $$\lambda_{max}(-30^\circ\text{C}) = \frac{2897.8}{243.15} = 11.9\ \mu\text{m}, \qquad \lambda_{max}(+50^\circ\text{C}) = \frac{2897.8}{323.15} = 9.0\ \mu\text{m}$$
2. Interpret the range. $$\boxed{\lambda_{max}\approx 9\text{–}12\ \mu\text{m over the realistic building-surface temperature range}}$$ This places the peak emission squarely in the LONG-WAVE (far) infrared band; the full thermal-emission spectrum of an ordinary building surface spans roughly 3–50 μm, entirely below what the human eye or ordinary glazing can see — a key reason low-emissivity coatings are tuned to reflect this specific long-wave band rather than the sun's short-wave spectrum.

Part (B)(iii) — temperature of a surface emitting visible light.

Find. The absolute temperature a surface must reach for its Wien peak to fall inside the visible band, 0.4–0.7 μm.

1. Invert Wien's law at the two ends of the visible band and at its green-light centre (≈0.50 μm, where the eye is most sensitive): $$T=\frac{b}{\lambda_{max}}:\qquad T(0.7\ \mu\text{m})=\frac{2897.8}{0.7}=4140\ \text{K},\quad T(0.5\ \mu\text{m})=\frac{2897.8}{0.5}=5796\ \text{K},\quad T(0.4\ \mu\text{m})=\frac{2897.8}{0.4}=7245\ \text{K}$$
2. State the result. $$\boxed{T\approx 4100\text{–}7200\ \text{K to peak somewhere in the visible band; }T\approx 5800\ \text{K for the peak at green-yellow light}}$$ 5800 K is, not coincidentally, essentially the sun's photosphere temperature (≈5778 K) — the sun is the reference case of a blackbody radiator whose Wien peak falls in the visible band. No ordinary building surface (which sits within roughly 200–330 K) ever approaches this; that is exactly why building surfaces are invisible in the thermal-IR sense but never self-luminous.