Physics quiz question: volume expansion of engine coolant

Physics 205A Quiz 7, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e Problem 13.15

"2013 Subaru Forester - First Drive"
NRMA Motoring and Services
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A 2014 Subaru Forester 2.0XT Premium uses 8.9×10^–4 m³ of liquid coolant[*]. Assume that the coolant is undiluted propylene glycol (volume expansion coefficient 7.3×10^–4 K^–1)[**]. If 5.0×10^–5 m³ of coolant is released into the overflow reservoir due to thermal expansion (ignoring engine volume expansion), the increase in temperature was:
(A) 44 K.
(B) 54 K.
(C) 77 K.
(D) 8.1×10² K.

[*] 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.
[**] dowac.custhelp.com/app/answers/detail/a_id/7213/related/1/session/L2F2LzEvdGltZS8xNDA2MzEyODAwL3NpZC9QVjVweWItbA%3D%3D.

Correct answer (highlight to unhide): (C)

The relation between the change in volume ∆V due to a temperature change ∆T is given by:

β·∆T = ∆V/V,

such that:

∆T = ∆V/(β·V) = (5.0×10^–5 m³)/((7<.3×10^–4 K^–1)·(8.9×10^–4 m³)) = 76.958596275 K,

or to two significant figures, the change in temperature is an increase of 77 K.

(Response (A) is 3·β/∆V; response (B) is 3·(V/∆V); and response (D) is ∆V/((6.9×10^–5 K^–1)·V), where 6.9×10^–5 K^–1 is the thermal volume expansion coefficient of the aluminum engine block, used in a subsequent problem on the same quiz.)

Sections 70854, 70855, 73320
Exam code: quiz07cO4t
(A) : 4 students
(B) : 10 students
(C) : 45 students
(D) : 5 students

Success level: 70%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.84