Physics quiz question: thermal resistance of wall insulation

Physics 205A Quiz 7, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e Problem 14.55, Comprehensive Problem 14.85

"Speedy Installation"
CertainTeed Corporation
certainteed.com/products/insulation/fiber-glass-insulation/317371

A 0.91 m² area section of CertainTeed SMARTBATT™ fiberglass insulation with a thickness of 8.9×10^–2 m has a thermal conductivity of 4.2×10^–3 watts/(m·K)[*]. The thermal resistance of this section of insulation is:
(A) 3.4×10^–4 K/watt.
(B) 23 K/watt.
(C) 2.4×10² K/watt.
(D) 2.9×10³ K/watt.

[*] certainteed.com/resources/30-45-062.pdf.

Correct answer (highlight to unhide): (B)

The thermal resistance R of an object can be related to its thermal conductivity κ by:

R = d/(κ·A),

where d is the thickness of the object that heat must conduct through, and A is the cross-sectional area, such that:

R = (8.9×10^–2 m)/((4.2×10^–3 watts/(m·K))·(0.91 m²)) = 23.286237572 K/watt,

or to two significant figures, the thermal resistance of the wall is 23 K/watt.

(Response (A) is κ·A·d; response (C) is 1/κ; response (D) is 1/(κ·A·d).)

Sections 70854, 70855, 73320
Exam code: quiz07cO4t
(A) : 1 student
(B) : 60 students
(C) : 3 students
(D) : 0 students

Success level: 94%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.21