24-Bld-A4 Building Environmental Control Systems · May 2017

Question 14 of 14: External Wall R-Value

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams May 2017 — 07-Bld-A4, Building Environmental Control Systems (Building Engineering). 3-hour closed-book exam: Section 1 (four 20-mark essay/calculation questions) + Section 2 (ten 2-mark multiple-choice questions).

Reference texts: ASHRAE Handbook — Fundamentals (2021 ed.); ASHRAE Standard 62.1, Ventilation for Acceptable Indoor Air Quality (2022 ed.); McQuiston, Parker & Spitler, Heating, Ventilating, and Air Conditioning: Analysis and Design (6th ed.); National Building Code of Canada 2020 (NBCC); National Energy Code of Canada for Buildings 2020 (NECB).

Question 2.10: External Wall R-Value (2 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.

Given/Find. Series thermal resistance: $R_{total}=\sum L_i/k_i + R_{ext}+R_{int}$.

Layer resistances. Brick: $0.200/0.62=0.323$; EPS panel: $0.050/0.035=1.429$; Gypsum board: $0.012/0.16=0.075$ (all m²·°C/W).
Add surface films. $$R_{total}=0.323+1.429+0.075+0.06+0.12=2.01\ \text{m}^2\cdot^{\circ}\text{C/W}$$

Check — source data gap: the question states the wall "is consisted of four layers," but the printed table lists only THREE material layers (brick, EPS, gypsum) plus the separately-stated surface resistances. Computed strictly from the three layers given, R = 2.01 m²·°C/W, which is below all five offered choices — consistent with a fourth material layer (e.g. an air space or additional insulation course) being described in the question but never printed in this exam's table. Since any missing layer can only ADD resistance, the true wall R-value must exceed 2.01 m²·°C/W; among the offered choices we select the closest, (a) 2.786 m²·°C/W, as the best-supported answer, but flag this selection as based on incomplete source data rather than a fully closed derivation.

Final Result
Answer (best judgment, flagged): (a) 2.786 m²·°C/W — computed from the three given layers (R = 2.01) plus surface films; the source's stated fourth layer is not printed in the table.

Topic: Series thermal resistance (R-value) of a multi-layer wall assembly.

Key relations: $R_{layer}=L/k$; total assembly R = sum of all layer resistances plus interior and exterior air-film (surface) resistances.

Why this works: heat flow through a flat multi-layer wall under steady state is a series thermal circuit, so resistances simply add — exactly analogous to series electrical resistors carrying the same "current" (heat flux) through each layer in turn.

Common pitfall: forgetting to include the interior AND exterior surface (air-film) resistances, which are small individually but matter for a wall this well-insulated; and, as this question demonstrates, always cross-check the stated layer COUNT against the table actually printed before assuming the data set is complete.

Source: ASHRAE Handbook — Fundamentals, Ch. 26 (Heat, Air, and Moisture Control in Building Assemblies); NECB 2020, prescriptive envelope R-value requirements.

← Question 13 Back to the paper →