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 – (T_env)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 T_env = 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