Astronomy in-class activity: star sizes

Astronomy 210 In-class activity 16 v.13.06.10, fall semester 2013
Cuesta College, San Luis Obispo, CA

Students find their assigned groups of three to four students, and work cooperatively on an in-class activity worksheet on applying Wien's law and the Stefan-Boltzmann law to determine the relative sizes of select pairs of stars.

(For the purposes of this in-class activity, the proportionality constant in the Stefan-Boltzmann law is omitted, as only relative rather than absolute values of star luminosities, temperatures, and sizes are compared.)

Astronomy quiz question: blue main sequence star vs. blue supergiant

Astronomy 210 Quiz 4, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

[4.0 points.] A blue main sequence star is known to be smaller than a blue supergiant because it is:
(A) same temperature as, but more luminous than a blue supergiant.
(B) same temperature as, but less luminous than a blue supergiant.
(C) same luminosity as, but hotter than a blue supergiant.
(D) same luminosity as, but cooler than a blue supergiant.

Section 70158
(A) : 9 students
(B) : 50 students
(C) : 8 students
(D) : 2 students

Correct answer: (B)

From Wien's law, the main sequence star and the supergiant must have the same temperature, because they have the same color. From the Stefan-Boltzmann law, for two stars of the same temperature, the less luminous star must be smaller in size.

"Difficulty level": 75%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.38

Astronomy quiz question: red supergiant vs. red giant

Astronomy 210 Quiz 4, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

[4.0 points.] A red supergiant is known to be larger in size than a red giant because it is:
(A) same temperature as, but more luminous than a red giant.
(B) same temperature as, but less luminous than a red giant.
(C) same luminosity as, but hotter than a red giant.
(D) same luminosity as, but cooler than a red giant.

Section 70160
(A) : 29 students
(B) : 0 students
(C) : 1 student
(D) : 1 student

Correct answer: (A)

From Wien's law, the supergiant and the giant must be the same temperature, because they have the same color. From the Stefan-Boltzmann law, for two stars of the same temperature, the more luminous star must be larger in size.

"Difficulty level": 93%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.25

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Astronomy clicker question: the Stefan-Boltzmann law

Astronomy 10, Summer Session 2007
Cuesta College, San Luis Obispo, CA

Astronomy 10 learning goal Q8.5

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

[0.3 points.] Why is a white dwarf star smaller than a main-sequence star that has the same white-hot color?
(A) It is less luminous than the main-sequence star.
(B) It is more luminous than the main-sequence star.
(C) It is cooler than the main-sequence star.
(D) It is hotter than the main-sequence star.

Correct answer: not revealed yet (see discussion).

This is the follow-up question after a short lecture (20 minutes) and an in-class activity (20 minutes) on how Wien's law and the Stefan-Boltzmann law describe blackbody radiation. Initial responses below:

Student responses
Section 8027
(A) : 3 students
(B) : 0 students
(C) : 3 students
(D) : 7 students

A leading question for the students: "Which star is hotter, and why?" Some students will have already realized that because these two stars have the same color, then they must be at the same temperature (application of Wien's law), and the class discusses why this must be the case. The same question is asked again, after the students collectively come to realization that both responses (C) and (D) cannot be true.

[0.3 points.] Why is a white dwarf star smaller than a main-sequence star that has the same white-hot color?
(A) It is less luminous than the main-sequence star.
(B) It is more luminous than the main-sequence star.
(C) It is cooler than the main-sequence star.
(D) It is hotter than the main-sequence star.

Correct answer: (A)

Student responses
Section 8027
(A) : 12 students
(B) : 1 student
(C) : 0 students
(D) : 0 students

The Stefan-Boltzmann law states that luminosity is proportional to size (that is, surface area) and temperature (T^4). Since they are the same temperature, then the less luminous star must be smaller in size than the more luminous star, which is larger in size.

Astronomy clicker question: why are white dwarfs small?

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

Astronomy 10 learning goal Q8.5

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

[0.3 points.] Why is a white dwarf star smaller than a main-sequence star that has the same white-hot color?
(A) It is less luminous than the main-sequence star.
(B) It is more luminous than the main-sequence star.
(C) It is cooler than the main-sequence star.
(D) It is hotter than the main-sequence star.

Correct answer: (A).

The fact that both stars have the same white-hot color tells you that they must have the same temperature (Wien's law). From the Stefan-Boltzmann law, luminosity is proportional to size and temperature^4, thus with both stars having the same temperature, the less luminous star is the smaller star.

Student responses
Section 4136
(A) : 9 students
(B) : 4 students
(C) : 7 students
(D) : 11 students

Section 5076
(A) : 2 students
(B) : 1 student
(C) : 10 students
(D) : 3 students