Physics final exam question: heat conduction comparison

Physics 205A Final Exam, fall semester 2012
Cuesta College, San Luis Obispo, CA

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

A 0.50 m long steel bar has twice the cross-sectional area as a 1.00 m long steel bar. The bottom of each bar is immersed in 20° C water, while the top of each bar is heated to 80° C. (Ignore the very slight thermal expansion of these bars). Discuss why the 0.50 m bar will conduct more heat per time than the 1.00 m bar. 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 bar, at a rate (1) proportional to the cross-sectional area, and (2) inversely proportional to the length, such that the wider, shorter bar will conduct heat at a rate four times faster than the narrower, longer bar.
• 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 bar will conduct heat faster than the narrower, longer bar.
• 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 bars.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: finalPr0p
p: 16 students
r: 18 students
t: 4 students
v: 9 students
x: 1 student
y: 1 student
z: 2 students

A sample "p" response (from student 1337):
Another sample "p" response (from student 1391), explicitly discussing thermal resistance:
A sample "r" response (from student 4568), only discussing the difference in cross-sectional area: