Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Example 14.10, Practice Problem 14.10, Problem 14.57
A 0.50 m long copper bar has a square cross-section of 0.020 m by 0.020 m. A temperature difference of 20° C is applied to the left and the right edges of the bar. Another copper bar has a 0.25 m length, but has the same volume (and corresponding wider cross-section). Discuss why this shorter 0.25 m long copper bar will require a smaller temperature difference between its ends in order to conduct the same amount of heat per time as the 0.50 m long copper bar. (Ignore the very slight thermal expansion of these bars). Explain your reasoning using the properties of heat, temperature, and heat transfer.
Solution and grading rubric:
- that for the two bars to conduct the same rate of heat per time, the bar with the lower thermal resistance will require a smaller temperature difference;
- and second bar has a lower thermal resistance due both its shorter length and greater cross-sectional area.
Nearly correct, but includes minor math errors.
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Only discusses how either shorter length or greater cross-sectional area results in the second bar having a lower thermal resistance.
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at applying Fourier's law of conduction.
Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying Fourier's law of conduction.
Irrelevant discussion/effectively blank.
Sections 70854, 70855, 73320
Exam code: finalm34T
p: 27 students
r: 9 students
t: 11 students
v: 4 students
x: 8 students
y: 2 students
z: 1 student
A sample "p" response (from student 8984):