Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e Problem 13.15
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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.
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,
∆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