Physics quiz question: equally-heated aluminum samples

Physics 205A Quiz 7, fall semester 2016
Cuesta College, San Luis Obispo, CA

"Aluminum Cube"
Cliff Hutson
flic.kr/p/rzdiCW

Two aluminum samples (0.50 kg and 0.75 kg) at 15.0° C are each separately given 15,000 J of heat. The two samples are then brought in contact with each other, and allowed to reach thermal equilibrium. Ignore heat exchanged with the environment. Specific heat of aluminum is 900 J/(kg·K). While reaching thermal equilibrium when brought in contact with each other (after each has separately been given 15,000 J of heat), heat flows from the __________ aluminum sample to the __________ aluminum sample.
(A) 0.50 kg; 0.75 kg.
(B) 0.75 kg; 0.50 kg.
(C) (No heat is exchanged.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

The transfer/balance energy conservation equation for each block is given by:

Q_ext = ∆E_small = m_small·c_Al·∆T_small,

Q_ext = ∆E_big = m_big·c_Al·∆T_big.

Since both blocks have been given the same amount of heat Q_ext = +15,000 (the positive sign denoting thermal energy added into the block) and the same specific heat c_Al, then the smaller 0.50 kg block will experience a greater increase in temperature, and be at a higher temperature than the 0.75 kg block after both have been heated up.

Thus when these two blocks are subsequently brought in contact with each other, then since the smaller 0.50 kg block is at a higher temperature than the 0.75 kg block, heat will then flow from the 0.50 kg block to the 0.75 kg block.

Sections 70854, 70855, 73320
Exam code: quiz07p4sT
(A) : 30 students
(B) : 14 students
(C) : 8 students
(D) : 0 students

Success level: 58%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.93