Physics quiz question: comparing changes in internal energies

Physics 205A Quiz 7, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e Practice Problem 14.5, Comprehensive Problem 14.75

A 0.50 kg iron sample at 90.0° C is placed into a container with 5.00 kg of water. The iron and water are allowed to reach a final temperature of 80.0° C. Ignore the effects of evaporation and phase changes, and heat exchanged with the environment and container. Specific heat of iron is 440 J/(kg·K). Specific heat of water is 4,190 J/(kg·K). After reaching thermal equilibrium, the __________ had the greatest change in internal energy.
(A) iron sample.
(B) water.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

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

Q_ext = ∆E_iron + ∆E_water,

where for an isolated system, Q_ext = 0, such that:

0 = m_iron·c_iron·(80.0° C – 90.0° C) + m_water·c_water·(80.0° C – T_{water, i}),

which can be subsequently solved for the initial water temperature T_{water, i} = 79.894988067° C, or 79.9° C to three significant figures. While this means that the iron experienced a much larger temperature change than the water, the iron experienced the same amount of thermal internal energy change (a decrease) as the change in thermal internal energy of the water (an increase). This can be seen by looking back on the transfer/balance energy conservation equation:

0 = ∆E_iron + ∆E_water,

–∆E_iron = ∆E_water.

Sections 70854, 70855, 73320
Exam code: quiz07b0o7
(A) : 17 students
(B) : 24 students
(C) : 17 students
(D) : 1 student

Success level: 29%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.62