## 20150105

### Physics final exam question: temperature differences for heat conducted through different bars

Physics 205A Final Exam, fall semester 2014
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.

• p:
Correct. Discusses:
1. 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;
2. and second bar has a lower thermal resistance due both its shorter length and greater cross-sectional area.
• r:
Nearly correct, but includes minor math errors.
• t:
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.
• v:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at applying Fourier's law of conduction.
• x:
Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying Fourier's law of conduction.
• y:
Irrelevant discussion/effectively blank.
• z:
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):