Physics final exam question: volume expansion coefficients of engine vs. coolant

Physics 205A Final Exam, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 13.14, 13.15

"2013 Subaru Forester - First Drive"
NRMA Motoring and Services
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A 2014 Subaru Forester 2.0XT Premium[*] uses undiluted propylene glycol coolant, which is released into an overflow reservoir due to its thermal expansion when the engine is running. Discuss why the volume expansion coefficient of the coolant must be greater than the expansion coefficient of the engine for this overflow to happen. Explain your reasoning using the properties of temperature and thermal expansion.

[*] 2014 Forester Owner Manual (Ver. B), Fuji Heavy Industries Ltd. (2013), p. 12-8, techinfo.subaru.com/proxy/71914/pdf/ownerManual/071914_2014_Forester/MSA5M1403BrevSTIS_18.pdf.

Solution and grading rubric:

• p:
  Correct. Compares the volume expansion equations for the coolant and the engine:
  1. recognizing that the increase in temperature ΔT and the initial volumes of the coolant and the engine are the same;
  2. and for the coolant to overflow the engine, the ΔV increase in volume of the coolant must be greater than the ΔV increase in volume of the engine;
  3. thus the volume expansion coefficient of the coolant must be greater than the volume expansion coefficient of the engine.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. May present a completely qualitative argument on relative expansion condition for overflow, without specifically noting that the coolant and engine start with the same volume, and experience the same increase in temperature.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at discussing thermal expansion.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying thermal expansion concepts.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: finalm34T
p: 30 students
r: 7 students
t: 16 students
v: 6 students
x: 0 students
y: 2 students
z: 1 student

A sample "p" response (from student 0619):