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.
Correct answer: (B)
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
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment