Physics quiz question: expansion of aluminum rod

Physics 205A Quiz 7, fall semester 2017
Cuesta College, San Luis Obispo, CA

An aluminum bar (linear expansion coefficient 2.3×10^–5 K^–1) has a length of 1.0000 m at 20.0° C. It will have a length of 1.0001 m at:
(A) 4° C.
(B) 16° C.
(C) 20.4° C.
(D) 24° C.

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 with an increase in length of ∆L = +0.0001 m, then:

∆T = ∆L/(α·L) = (+0.0001 m)/((2.3×10^–5 K^–1)·(1 m)) = +4.347826087 K,

or to one significant figure, the change in temperature is +4 K or +4° C, and so the bar will stretch by 0.0001 m when the temperature is 20.0° C + 4° C = 24° C.

(Response (A) is ΔT; response (B) is 20.0° C – ΔT; response (C) is 20.0° C + (ΔT/10).)

Sections 70854, 70855
Exam code: quiz07Whu7
(A) : 6 students
(B) : 2 students
(C) : 12 students
(D) : 22 students

Success level: 52%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.59