Physics quiz question: aluminum vs. uranium contraction

Physics 205A Quiz 7, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e Problems 13.14, 13.21

"A nuclear fuel pellet..."
Idaho National Laboratory

A cylindrical uranium fuel pellet used in the Oak Ridge National Laboratory Graphite Reactor is 2.5 cm in diameter, and is encased in a jacket of aluminum[*]. Assume that this measurement is at the maximum reactor operating temperature of 535 K. To ensure that the uranium fuel pellet will have a smaller diameter than the interior diameter of the aluminum jacket as they both gradually cool down, aluminum was selected as it has a linear expansion coefficient __________ the linear expansion coefficient of uranium.
(A) less than.
(B) exactly equal to.
(C) greater than.
(D) (Not enough information is given.)

[*] C. D. Cagle, The ORNL Graphite Reactor, U.S. Atomic Energy Commission (1957), p. 11, web.ornl.gov/info/reports/1957/3445605702068.pdf.

Correct answer (highlight to unhide): (A)

The relative amount of linear expansion is given by:

L/L = α·∆T,

where L is the original linear dimension (in this case, diameter) at the original temperature, and ∆L is the amount of linear expansion (if temperature increases) or contraction (if temperature decreases).

A linear expansion coefficient α of zero means that the object will neither expand nor contract with changes in temperature. A small linear expansion coefficient means the object will experience a small amount of expansion/contraction for a given change in temperature, and a large linear expansion coefficient means the object will experience a large amount of expansion/contraction for the same change in temperature. Since the uranium pellet experiences a larger amount of contraction than the aluminum jacket as temperature decreases for both of them, then uranium has a larger linear expansion coefficient, and aluminum must have a smaller linear expansion coefficient.

Sections 70854, 70855, 73320
Exam code: quiz07b0o7
(A) : 30 students
(B) : 4 students
(C) : 25 students
(D) : 0 students

Success level: 51%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.32

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