Astronomy midterm question: red supergiants versus red giants

Astronomy 210 Midterm 2, spring semester 2015
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was answered:

Yg: Red supergiants can be the same size as red giants.

Discuss why this answer is incorrect, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

[*] answers.yahoo.com/question/index?qid=20150326215251AATYkHE.

Solution and grading rubric:

• p:
  Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to discuss how a red supergiant cannot be the size as a red giant by either arguing:
  1. that from Wien's law, a red supergiant must have the same temperature as a red giant, and from the H-R diagram a supergiant must be more luminous than a giant, such that from the Stefan-Boltzmann law, for two stars that have the same temperature, the more luminous supergiant must be larger than the less luminous giant, which makes it not possible for the supergiant to have the same size as the giant; or instead argues
  2. that from the Stefan-Boltzmann law, for two stars that have the same size, the more luminous supergiant must have a hotter surface temperature, which makes it not possible to have the same color as the less luminous giant.
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. At last discussion demonstrates understanding of Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Section 30674
Exam code: midterm02N4ra
p: 20 students
r: 1 student
t: 11 students
v: 4 students
x: 1 student
y: 1 student
z: 0 students

Section 30676
Exam code: midterm02s0Ju
p: 30 students
r: 5 students
t: 12 students
v: 2 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 2194):
A sample "t" response (from student 1175):