Physics quiz question: rate of thermal loss through sleeping pad

Physics 205A Quiz 7, fall semester 2015
Cuesta College, San Luis Obispo, CA

"Therm-a-Rest® Closed-Cell Mattresses"

A Thermarest® Z Lite SOL™ polyethylene insulating sleeping pad[*] 
(area of 0.933 m2 and thickness of 0.020 m) has a thermal resistance of 0.43 K/watt. If there is a 20° C temperature difference between the top (in contact with a sleeping person) and bottom (in contact with the cold ground) of the sleeping pad, the rate of heat per time conducted through the pad will be:
(A) 1.1×10–3 watts.
(B) 2.2×10–2 watts.
(C) 8.6 watts.
(D) 47 watts.

[*] cascadedesigns.com/therm-a-rest/mattresses/fast-and-light/z-lite/product.

Correct answer (highlight to unhide): (D)

The rate of heat per time conducted is given by:

Power = ∆T/R,

where the temperature difference ∆T and the thermal resistance R of the sleeping pad are given, such that:

Power = (20° C)/(0.43 K/watt) = 46.511627907 watts,

or to two significant figures, the rate of heat conducted through the sleeping pad is 47 watts.

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

Sections 70854, 70855, 73320
Exam code: quiz07zSOL
(A) : 3 students
(B) : 4 students
(C) : 8 students
(D) : 54 students

Success level: 78%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.46

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