Physics quiz question: thermal contraction of lid and pot

Physics 205A Quiz 7, fall semester 2016
Cuesta College, San Luis Obispo, CA

"Pot Lid"
Mike Shoup
flic.kr/p/bjbrwB

A tempered glass lid (linear expansion coefficient 3.3×10^–6 K^–1) fits exactly with no gaps on an aluminum pot (linear expansion coefficient 23×10^–6 K^–1) at room temperature (20° C). If both the lid and the pot decrease in temperature to 10° C, the lid will:
(A) have a gap all around it.
(B) still fit exactly.
(C) be squeezed by the pot.
(D) (Not enough information.)

Correct answer (highlight to unhide): (C)

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

α·∆T = ∆L/L,

such that for the lid and the pot:

∆L_lid = L·α_glass·∆T,

∆L_pot = L·α_Al·∆T.

The original diameter of the lid and the pot at the initial temperature of 20° C is the same, and both lid and pot experience the same temperature decrease ∆T. Since the linear expansion coefficient for aluminum is greater than that of glass (α_Al > α_glass), then the diameter of the pot will contract more than the diameter of the lid (∆L_pot > ∆L_lid), such that the lid will be compressed by the pot.

Sections 70854, 70855, 73320
Exam code: quiz07p4sT
(A) : 11 students
(B) : 7 students
(C) : 34 students
(D) : 0 students

Success level: 65%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50