Astronomy quiz question: applying the Stefan-Boltzmann law

Astronomy 10 Quiz 8, Fall Semester 2007
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q8.5

[Version 1]

[3.0 points.] Consider two stars with the same luminosity. Which one of the following choices best describes the star that is larger in size?
(A) The star with the higher surface temperature.
(B) The star with the lower surface temperature.
(C) The star with the brighter apparent magnitude.
(D) The star with the dimmer apparent magnitude.
(E) (None of the above choices (A)-(D), as these two stars must have the same size.)

Correct answer: (B)

The Stefan-Boltzmann law states that luminosity is proportional to size and (temperature)^4. For two stars with the same luminosity, the larger size star must have a lower surface temperature.

Student responses
Section 0135
(A) : 7 students
(B) : 17 students
(C) : 3 students
(D) : 2 students
(E) : 0 students

[Version 2]

[3.0 points.] Consider two stars with the same size. Which one of the following choices best describes the star that has the higher surface temperature?
(A) The star with the brighter apparent magnitude.
(B) The star with the dimmer apparent magnitude.
(C) The star with the brighter luminosity.
(D) The star with the dimmer luminosity.
(E) (None of the above choices (A)-(D), as these two stars must have the same surface temperature.)

Correct answer: (C)

The Stefan-Boltzmann law states that luminosity is proportional to size and (temperature)^4. For two stars of the same size, the brighter luminosity star must have the higher surface temperature.

Student responses
Section 1073
(A) : 6 students
(B) : 1 student
(C) : 31 students
(D) : 3 students
(E) : 1 student