Physics quiz question: thermal expansion of different cross-section bars

Physics 205A Quiz 7, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 13.9

A 1.0 cm² cross-sectional area steel bar is heated up such that its length extends by by 0.1 mm. To extend a 2.0 cm² cross-sectional area steel bar by 0.1 mm, it must experience a temperature change __________ the temperature change of the 1.0 cm² cross-sectional area steel bar. (The bars have the same length.)
(A) smaller than.
(B) the same as.
(C) larger than.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (B)

The relative amount of linear expansion (∆L/L) is given by:

∆L/L = α·∆T,

such that the amount of expansion ∆L can be expressed as:

∆L = L·α·T,

and since ∆L does not depend on the cross-sectional area of the bar, then both bars of the same length L and same material α must experience the same temperature increase ∆T to expand by the same ∆L amount.

Sections 70854, 70855
Exam code: quiz07h3A7
(A) : 15 students
(B) : 20 students
(C) : 17 students
(D) : 0 students

Success level: 38%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.71