Physics quiz question: comparing temperature changes

Physics 205A Quiz 7, fall semester 2018
Cuesta College, San Luis Obispo, CA

A 0.50 kg iron sample (600 K initial temperature) and a 0.75 kg iron sample (300 K initial temperature) are brought in contact with each other to reach thermal equilibrium. Ignore heat exchanged with the environment. Specific heat of iron is 452 J/(kg·K). After thermal equilibrium is reached, the __________ iron sample will have experienced the larger change (increase/decrease) in temperature. (A) 0.50 kg.
(B) 0.75 kg.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

The transfer/balance energy conservation equation for this system is given by:

Q_ext = ∆E_{0.50 kg} + ∆E_{0.75 kg},

and since there is no heat exchanged with the environment, Q_ext = 0, such that:

0 = m_{0.50 kg}·c_iron·ΔT_{0.50 kg} + m_{0.75 kg}·c_iron·ΔT_{0.75 kg},

and:

–m_{0.50 kg}·ΔT_{0.50 kg} = m_{0.75 kg}·ΔT_{0.75 kg}.

From inspection, since m_{0.50 kg} < m_{0.75 kg}, then –ΔT_{0.50 kg} > ΔT_{0.75 kg}, and thus the 0.50 kg iron sample will under a larger temperature change (which would be a decrease in temperature) than the 0.75 kg iron sample (which would increase in temperature).

Sections 70854, 70855
Exam code: quiz07PeA7
(A) : 28 students
(B) : 3 students
(C) : 19 students
(D) : 0 students

Success level: 56%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.72