Physics quiz question: concrete beam contraction

Physics 205A Quiz 7, fall semester 2019
Cuesta College, San Luis Obispo, CA

A concrete beam (linear expansion coefficient 9.8×10^–6 K^–1) is 12.2 m long at room temperature (293 K). In order to contract by 0.0010 m, its temperature should be decreased by:
(A) 1.2×10^–5 K.
(B) 8.2×10^–5 K.
(C) 0.38 K.
(D) 8.4 K.

Correct answer: (D)

The relation between the change in length ∆L due to a temperature change ∆T is given by:

α·∆T = ∆L/L,

such that:

∆T = ∆L/(α·L) = (–0.0010 m)/((9.8×10^–6 K^–1)·(12.2 m)) = –8.36400133824 K,

or to two significant figures, the decrease in temperature is 8.4 K or 8.4° C.

(Response (A) is L·α; response (B) is ∆L/L; response (C) is ∆L/(α·T₀).)

Sections 70854, 70855
Exam code: quiz07VlnC
(A) : 3 students
(B) : 8 students
(C) : 3 students
(D) : 37 students

Success level: 73%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.49