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W3.1 Energy Use in Buildings

Created October 19, 2026

Key points

Heat loss through the envelope: layers in series → $R_{tot}$ → $U$ ; window/frame side by side → area-weighted $U$ → Thermal resistance
$\dot Q_{loss} = U A \Delta T$ is a rate [W]; energy over a period = rate × time
Heating needed = losses − internal gains (people, equipment)
Design (max) power → coldest temperature; annual energy → average temperature

Chain

Layers ( $d/k$ , $1/h$ ) → $R_{tot}$ → $U$ → $U_{avg}$ (area fractions) → $\dot Q = U_{avg} A \Delta T$ → − gains → × time → annual energy

Typical traps

“rate”, “thermal power” → W; “heat”, “thermal energy”, “annual” → J or kWh
“half of a sphere” → $A = 2\pi r^2$
$E = P \times t$ : the time unit decides the energy unit (kW × h = kWh, kW × s = kJ); 3600 only for kWh ↔ kJ
Max → lowest temperature; annual → average temperature
Sanity check: one building ≈ 10⁵ kWh/yr, not 10⁹

Exam

Oct 2025 Task 2a–e: Mars dome (glass + argon windows, metal frame, half sphere): $R_{window}$ 0.65, $U_{avg}$ 1.27, $\dot Q$ 111.9 / 63.9 kW, max extra heat 101.9 kW, annual 4.73·10⁵ kWh
MCQ: Oct 2025 5.1–5.4 (U, heat pump, wall layers), Nov 2023 5.3–5.4 (auditorium walls, COP)

Concepts