Astronomy clicker question: same luminosity main sequence vs. giant star

Astronomy 210, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Students were asked the following clicker question (Classroom Performance System, einstruction.com) at the end of their learning cycle:

A main sequence star will be ___________ compared to a giant star that has the same luminosity.
(A) cooler and smaller.
(B) cooler and larger.
(C) hotter and smaller.
(D) hotter and larger.
(E) (I'm lost, and don't know how to answer this.)

Section 70158 (pre-)
(A) : 11 students
(B) : 2 students
(C) : 31 students
(D) : 2 students
(E) : 0 students

This question was asked again after displaying the tallied results with the lack of consensus, with the following results. No comments were made by the instructor, in order to see if students were going to be able to discuss and determine the correct answer among themselves.

Section 70158 (post-)
(A) : 3 students
(B) : 0 students
(C) : 38 students
(D) : 3 students
(E) : 0 students

Correct answer: (C)

From an H-R diagram, main sequence stars are hotter than giants that have the same luminosity. From the Stefan-Boltzmann law (luminosity proportional to size and temperature^4), since the main sequence star has the same luminosity as, but is hotter than the giant, then the main sequence star must be smaller in size.

Pre- to post- peer-interaction gains:
pre-interaction correct = 67%
post-interaction correct = 86%
Hake (normalized) gain <g> = 58%

Section 70160 (pre- only)
(A) : 3 students
(B) : 0 students
(C) : 22 students
(D) : 1 student
(E) : 0 students

Correct = 85%