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:
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.
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.
Nearly correct, but argument has conceptual errors, or is incomplete.
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.
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.
Irrelevant discussion/effectively blank.
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: