Physics final exam question: thermal expansion of different length bars

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

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 13.101, Problem 14.11

A 0.50 m long steel bar has same cross-sectional area as a 1.00 m long steel bar, and are both initially at room temperature (25° C). The same amount of heat is evenly applied to each bar. Discuss why both bars would expand by 0.0001 m from their original lengths. (Ignore heat lost to the environment.) Explain your answer using the properties of heat, internal energy, temperature, and thermal expansion.

Solution and grading rubric:

• p:
  Correct. Same heat is applied to each bar, but:
  1. the shorter bar is half the mass of the longer bar, such that the increase in temperature of the shorter bar will be twice that of the longer bar.
  2. the shorter bar has half the length, but twice the temperature change compared to the longer bar, and so the length expansion (which is proportional to both the original length and temperature increase) will be the same compared to the 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. At least recognizes that (1) bars experience different temperature changes, and (2) expansion of bars depends on both original length and temperature change.
• 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. May instead argue that same cross-sectional area is relevant factor, or same temperature change for both bars, etc. At least some discussion based on thermal expansion and/or heat capacity.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion based on phenomena other than thermal expansion or heat capacity.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: finalPr0p
p: 9 students
r: 7 students
t: 5 students
v: 25 students
x: 0 students
y: 3 students
z: 2 students

A sample "p" response (from student 1408), starting off with a few black fuzzy caterpillars: