Physics quiz question: cooling a brim-filled container

Physics 5A Quiz 7, spring semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 13.14

[3.0 points.] A cylindrical aluminum container is filled to the brim with water when the system is at 30.0° C. The temperature of the container and the water is lowered to 5.0° C. The volume expansion coefficient of aluminum is 69 ×10^-6 K^–1. The volume expansion coefficient of water is 210×10^-6 K^–1. What happens to the water when the temperature of the container and the water is lowered to 5.0° C?
(A) Some water will overflow the container.
(B) No water will overflow, and the water level will still be at the brim of the container.
(C) No water will overflow, and the water level will be below the brim of the container.
(D) (Not enough information is given to determine this.)

Correct answer: (C)

The volume expansion coefficient for water is greater than the volume expansion coefficient for aluminum. If they experience the same decrease in temperature, the water will decrease in volume more than the interior of the aluminum container, and thus will no longer be up at the brim of the container. Response (A) would occur if the water and the aluminum container experience the same increase in temperature, starting with the water at the brim of the container. Response (B) would only occur if water and aluminum had the same volume expansion coefficient.

Student responses
Sections 4987, 4988
(A) : 12 students
(B) : 8 students
(C) : 12 students
(D) : 0 students