Physics final exam question: heat conducted through different-orientation bricks

Physics 205A Final Exam, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Example 14.10, Practice Problem 14.10, Problem 14.57

A brick can be placed in either of two orientations. The bottom of each brick is immersed in 20° C water, while the top of each brick is heated to 80° C. (Ignore the very slight thermal expansion of these bricks.) Discuss why these two bricks will not conduct the same amount of heat per time. Explain your answer using the properties of heat, temperature, and heat transfer.

Solution and grading rubric:

• p:
  Correct. Heat is conducted from the top to the bottom of each brick, at a rate (1) proportional to the cross-sectional area, and (2) inversely proportional to the length (in this case, height), such that the wider, shorter brick will conduct heat at a rate faster than the narrower, taller brick.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically argues only (1) area, or only (2) length as a factor in why the wider, shorter brick will conduct heat faster than the narrower, taller brick.
• 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. At least recognizes different factors (1)-(2) and attempts to discuss heat conduction along the length of the bars.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion based on phenomena other than heat conduction along the length of the bricks.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855, 73320
Exam code: finaln0M3
p: 24 students
r: 31 students
t: 1 student
v: 3 students
x: 0 students
y: 1 student
z: 1 student

A sample "p" response (from student 0494):
Another sample "p" response (from student 2395):
A sample "r" response (from student 0825), discussing only how the cross-sectional area A affects the flow of heat conducted through the bricks:
A sample "r" response (from student 1025), discussing only how the length (height) d affects the flow of heat conducted through the bricks: