Physics quiz question: thermal conductivity of book-insulation

Physics 205A Quiz 7, fall semester 2013
Cuesta College, San Luis Obispo, CA

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

"Artifacts of our civilization forever trapped in sedimentary layers"
David Cameron, The Blockhouse School Project
theblockhouseschool.org/2012/12/book-insulation/

In December 2012, over a thousand discarded research journals were stacked by the Blockhouse School Project to make a 0.30 m thick insulating wall 6.7 m wide and 2.0 m tall[*]. The builders claim that the thermal resistance of the wall is approximately 0.16 K/watts. The thermal conductivity of the wall is:
(A) 0.0036 watts/(m·K).
(B) 0.022 watts/(m·K).
(C) 0.14 watts/(m·K).
(D) 160 watts/(m·K)

[*] theblockhouseschool.org/2012/12/book-insulation/.

Correct answer (highlight to unhide): (C)

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 the thermal conductivity can be solved for:

κ = d/(R·A),

κ = (0.30 m)/((0.16 K/watts)·(6.7 m)·(2.0 m)) = 0.1399253731 watts/(m·K),

or to two significant figures, the thermal conductivity of the wall is 0.14 watts/(m·K).

(Response (A) is R·d/A; response (B) is d/A; response (D) is ∆T/R.)

Sections 70854, 70855, 73320
Exam code: quiz07b0o7
(A) : 13 students
(B) : 9 students
(C) : 31 students
(D) : 5 students

Success level: 53%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.55