Cuesta College, San Luis Obispo, CA
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.
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,
∆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