Astronomy quiz question: applications of the Stefan-Boltzmann law

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

Astronomy 10 learning goal Q8.5

[Version 1]

[3.0 points.] Which one of the following statements best describes the relationship between a main sequence star and a supergiant that have the same luminosity?
(A) The main sequence star is cooler and smaller than the supergiant.
(B) The main sequence star is cooler and larger than the supergiant.
(C) The main sequence star is hotter and smaller than the supergiant.
(D) The main sequence star is hotter and larger than the supergiant.
(E) (None of the above choices (A)-(D), as it is not possible for a main sequence star to have the same luminosity as a supergiant.)

Correct answer: (C)
From an H-R diagram, a main sequence star must be hotter in order to have the same luminosity as a supergiant. From the Stefan-Boltzmann law, since luminosity is proportional to size and temperature^4, and with both stars having the same luminosity, the hotter star must be smaller in size.

Student responses
Section 4136
(A) : 6 students
(B) : 3 students
(C) : 22 students
(D) : 1 student
(E) : 0 students

[Version 2]
[3.0 points.] Which one of the following statements best describes the relationship between a main sequence star and a white dwarf that have the same luminosity?
(A) The main sequence star is cooler and smaller than the white dwarf.
(B) The main sequence star is cooler and larger than the white dwarf.
(C) The main sequence star is hotter and smaller than the white dwarf.
(D) The main sequence star is hotter and larger than the white dwarf.
(E) (None of the above choices (A)-(D), as it is not possible for a main sequence star to have the same luminosity as a white dwarf.)

Correct answer: (B)
From an H-R diagram, a main sequence star must be cooler in order to have the same luminosity as a supergiant. From the Stefan-Boltzmann law, since luminosity is proportional to size and temperature^4, and with both stars having the same luminosity, the cooler star must be larger in size.

Student responses
Section 5076
(A) : 3 students
(B) : 10 students
(C) : 1 student
(D) : 4 students
(E) : 2 students