Physics 205A Quiz 7, fall semester 2015
Cuesta College, San Luis Obispo, CA
Stars can be modeled as spherical blackbodies that radiate heat out to an environment assumed to have a temperature of 0 K. Pollux is a star that radiates less heat per time, but is larger in size than Bellatrix. Pollux has a surface temperature __________ Bellatrix.
(A) cooler than.
(B) same as.
(C) hotter than.
(D) (Not enough information given.)
Correct answer: (A)
The net power radiated by a star with an environment assumed to be at absolute zero is given by:
Power = –e·σ·A·((T)4 – (Tenv)4) = –e·σ·A·((T)4 – (0 K)4).
where the emissitivity e = 1 (for an ideal blackbody), the Stefan-Boltzmann constant is σ = 5.670×10–8 watts/(m2·K4), A is the surface area, and the surface temperature T is unknown, and can be solved for:
(T)4 = –Power/(e·σ·A),
T = (–Power/(e·σ·A))(1/4).
This allows a ratio to be set up to compare the surface temperatures of Bellatrix and Pollux:
TBellatrix = (–PowerBellatrix/(e·σ·ABellatrix))(1/4),
TPollux = (–PowerPollux/(e·σ·APollux))(1/4),
such that:
(TBellatrix/TPollux) = (PowerBellatrix/PowerPollux))·(APollux/ABellatrix)(1/4).
Since Pollux radiates less heat per time than Bellatrix, then the ratio (PowerBellatrix/PowerPollux)) is greater than 1; and since Pollux is larger in size than Bellatrix, the ratio (APollux/ABellatrix)(1/4) is also greater than 1. Thus the ratio (TBellatrix/TPollux) must then be greater than 1, so Pollux has a cooler surface temperature than Bellatrix.
Sections 70854, 70855
Exam code: quiz07zSOL
(A) : 50 students
(B) : 12 students
(C) : 7 students
(D) : 0 students
Success level: 72%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.70
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