Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 14.49
A steel bar has twice the cross-sectional area as another steel bar of the same length. The bottom of each bar is immersed in 0° C water, while the top of each bar is heated to 75° C. (Ignore the very slight thermal expansion of these bars). The wider bar has ________ the thermal resistance of the narrower bar. (A) one-fourth.
(B) one-half.
(C) twice.
(D) four times.
(E) (There is a tie.)
Correct answer: (B)
The thermal resistance R is given by:
R = d/(Κ·A),
where d corresponds to the (identical) length of these bars, Κ is the (identical) thermal conductivity of these bars, and A is the cross-sectional area of the bars. With Awide = 2·Anarrow, then for these two bars:
Rwide = d/(Κ·Awide),
Rnarrow = d/(Κ·Anarrow),
The wider bar will have one-half the thermal resistance of the narrower bar:
Rwide = d/(Κ·Awide) = d/(Κ·(2·Anarrow)) = (1/2)·Rnarrow.
Sections 70854, 70855
Exam code: quiz07Di5k
(A) : 0 students
(B) : 24 students
(C) : 18 students
(D) : 3 students
(E) : 5 students
Success level: 48%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50
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