Physics quiz question: thermal contraction of James Webb Space Telescope mirror segment

Physics 205A Quiz 7, fall semester 2015
Cuesta College, San Luis Obispo, CA

"Reflections on JWST - May 4, 2016"
James Webb Space Telescope (JWST)

The James Webb Space Telescope will use beryllium mirror segments (linear expansion coefficient 7.0×10–6 K–1), each 1.32 m wide.[*][**] During testing it is cooled from room temperature (293 K) down to its operational temperature of 53 K. The width of a mirror segment will contract by:
(A) 2.2×10–3 m.
(B) 2.7×10–3 m.
(C) 3.2×10–3 m.
(D) 4.2×10–3 m.

[*] P. Hidnert, W. T. Sweeney, "Thermal Expansion of Beryllium and Aluminum Beryllium Alloys," Scientific Papers of the Bureau of Standards, vol. 22 (1927), p. 533, dx.doi.org/10.6028/nbsscipaper.251.
[**] jwst.nasa.gov/mirrors.html.

Correct answer (highlight to unhide): (A)

The relation between the change ∆L of a linear dimension L (here, width) due to a temperature change ∆T is given by:

α·∆T = ∆L/L,

such that:

L = L·α·∆T = (1.32 m)·(7.0×10–6 K–1)·(53 K – 293 K) = –2.2176×10–3 m,

or to two significant figures, the width of the mirror segment decreases by 2.2×10–3 m.

(Response (B) is L·α·(293 K); response (C) is L·α·(53 K + 293 K); response (D) is 1/∆T.)

Sections 70854, 70855, 73320
Exam code: quiz07zSOL
(A) : 62 students
(B) : 5 students
(C) : 1 student
(D) : 1 student

Success level: 90%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.22

No comments: