Physics final exam question: cooling a liquid-filled glass

Physics 205A Final Exam, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 13.14, 13.15

A glass container is filled to the brim with a liquid when the system is at 40° C. After the system is cooled to 15° C, the liquid level is slightly below the top of the container. There are no phase changes. Which material (glass or liquid) has a larger coefficient of volume expansion? Explain your answer using the properties of temperature and thermal expansion.

Solution and grading rubric:

• p:
  Correct. Argues that since liquid contracted more than the glass, then the liquid must have a greater volume expansion coefficient than the glass.
  
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete.
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit.
  y: Irrelevant discussion/effectively blank.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: finalB0xs
p: 37 students
r: 8 students
t: 0 students
v: 1 student
x: 1 student
y: 1 student
z: 0 students

A sample "p" response (from student 3737):
A sample "p" response (from student 4242):