20160622

Physics quiz question: surface temperature of Bellatrix

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. Bellatrix is a star that radiates heat per time at a rate of 2.5×1030 watts, and has a surface area of 2.2×1020 m2. The surface temperature of Bellatrix is:
(A) 4.2×103 K.
(B) 2.1×104 K.
(C) 1.1×105 K.
(D) 6.1×105 K.

The net power radiated by Bellatrix (–2.5×1030 watts, where the negative sign indicates that heat is continuously leaving the surface of the star) 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 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),

T = (–(–2.5×1030 watts)/((1)·(5.670×10–8 watts/(m2·K4))·(2.2×1020 m2)))(1/4),

T = 2.11584362479×104 K,

or to two significant figures, the surface temperature of Bellatrix is 2.2×104 K.

(Response (A) is σ(–1/2); response (C) is (Power/A)(–1/2); response (D) is (Power·σ)(1/4).)

Sections 70854, 70855
Exam code: quiz07zSOL
(A) : 12 students
(B) : 31 students
(C) : 15 students
(D) : 10 students

Success level: 45%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.35