Physics quiz question: expansion of prototype meter

Physics 205A Quiz 7, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 13.101

"Platinum-Iridium meter bar"
National Institute of Standards and Technology
commons.wikimedia.org/wiki/File:Platinum-Iridium_meter_bar.jpg

The international prototype meter[*][**] was set by the distance between two markings on a platinum-iridium alloy bar (α = 8.7×10^–6 K^–1) at 0° C. To increase the distance between these markings by 0.01 mm, the temperature should be raised by:
(A) 0.001° C.
(B) 0.01° C.
(C) 0.1°.
(D) 1° C.

[*] "Differences...lie within 0.01 millimetre," bipm.org/en/CGPM/db/1/1/.
[**] "Pt90/Ir10 coefficient of thermal expansion @20-100° C," goodfellow.com/E/Platinum-Iridium.html.

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) = (0.01×10^–3 m)/((8.7×10^–6 K^–1)·(1 m)) = 1.14942528736 K,

or to one significant figure, the change in temperature is 1 K or 1° C.

Sections 70854, 70855
Exam code: quiz07Di5k
(A) : 5 students
(B) : 6 students
(C) : 4 students
(D) : 35 students

Success level: 70%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.09