Physics quiz question: comparing final temperatures

Physics 205A Quiz 7, fall semester 2017
Cuesta College, San Luis Obispo, CA

An aluminum sample and an iron sample have the same mass and same initial temperature, and are kept separated from each other. Specific heat of aluminum is 900 J/(kg·K); specific heat of iron is 452 J/(kg·K). If the same amount of heat is transferred to each sample, the __________ sample will have a higher final temperature.
(A) aluminum.
(B) iron.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (B)

The transfer/balance energy conservation equation for each of these systems are given by:

Q_ext = ∆E_aluminum = m_aluminum·c_aluminum·ΔT_aluminum,

and:

Q_ext = ∆E_iron = m_iron·c_iron·ΔT_iron.

For each sample and its corresponding equation, the mass m and heat Q_ext transferred is the same, so:

Q_ext = Q_ext,

m_aluminum·c_aluminum·ΔT_aluminum = m_iron·c_iron·ΔT_iron,

c_aluminum·ΔT_aluminum = c_iron·ΔT_iron,

and since c_aluminum > c_iron, then ΔT_aluminum < ΔT_iron, and:

ΔT_aluminum < ΔT_iron,

(T_aluminum,f – T_aluminum,0) < (T_iron,f – T_iron,0),

and since both samples have the same initial temperature T_aluminum,0 = T_iron,0:

T_aluminum,f < T_iron,f,

thus the iron sample will have the higher final temperature.

Sections 70854, 70855
Exam code: quiz07Whu7
(A) : 25 students
(B) : 13 students
(C) : 4 students
(D) : 0 students

Success level: 31%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.36