Physics quiz question: radiating concrete columns cooling

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

Kelly Nighan

Two concrete columns (emissivity 0.85[*]) are at a temperature of 293 K, and are exposed all around their sides to an environment at a temperature of 273 K. The two columns have the same cross-sectional area, but the shorter column is one-half the length of the taller column. The __________ concrete column cools off faster due to the net amount of radiative heat per time transferred to/from the environment.
(A) shorter.
(B) taller.
(C) (There is a tie.)
(D) (Not enough information is given.)

[*] engineeringtoolbox.com/emissivity-coefficients-d_447.html.

Correct answer (highlight to unhide): (B)

The power (rate of heat per time) radiated is given by:

Power = –e·σ·A·((Tobj)4 – (Tenv)4),

Since both the short and tall concrete columns have the same emissivity e and temperature Tobj), and are both surrounded by the same environment temperature Tenv), the net rate of heat simultaneously radiated to and absorbed from the environment them differs only because of their surface areas:

Powershort = –(0.85)·σ·Ashort·((293 K)4 – (273 K)4),

Powertall = –(0.85)·σ·Atall·((293 K)4 – (273 K)4).

Since the taller column has more surface area (Atall > Ashort), then the taller column will have a greater net rate of heat radiated per time, thus cooling off faster than the shorter column (Powertall > Powershort).

(Note the negative values for power here, corresponding to a net amount of heat being removed (radiated) from the object, while a positive value corresponds to a net amount of heat being put into (absorbed) by the object (in order to be consistent with the ±Q convention for removing heat from (–) or putting heat into (+) a thermodynamic system).)

Sections 70854, 70855, 73320
Exam code: quiz07p4sT
(A) : 14 students
(B) : 23 students
(C) : 15 students
(D) : 0 students

Success level: 44%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.72

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