Physics quiz question: rate of heat radiated by the sun

Physics 205A Quiz 7, fall semester 2017
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. The sun has a surface temperature of 5,772 K and a surface area of 6.09×1018 m2. The sun radiates heat per time at a rate of:
(A) 3.45×1011 watts.
(B) 1.11×1015 watts.
(C) 1.99×1015 watts.
(D) 3.83×1026 watts.

Correct answer (highlight to unhide): (D)

The net power radiated by the sun (where the negative sign indicates that heat is continuously leaving the surface of the sun) is given by:

Power = –e·σ·A·((T)4 – (Tenv)4),

where the emissitivity e = 1 (for an ideal blackbody), the Stefan-Boltzmann constant σ = 5.670×10–8 watts/(m2·K4), the surface area A = 6.09×1018 m2, the surface temperature T = 5,772 K, and the temperature of the environment is assumed to be Tenv = 0 K, such that the rate of heat radiated by the sun can be solved for:

Power = –(1)·(5.670×10–8 watts/(m2·K4)·(6.09×1018 m2)·((5,772 K)4 – (0)4),

Power = –3.832707188×1026 watts,

or to three significant figures, the rate of hate radiated per time from the sun is 3.83×1026 watts.

(Response (A) is A·σ; response (B) is T4; response (C) is e·σ·A·T.)

Sections 70854, 70855
Exam code: quiz07Whu7
(A) : 1 student
(B) : 3 students
(C) : 18 students
(D) : 20 students

Success level: 48%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.66

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