Astronomy midterm question: hotter giant same size as cooler supergiant?

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

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

??: Can a giant be the same size as a supergiant if the giant were hotter than the supergiant?
MirJ: No.

Discuss why this answer is correct, 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=20151031174552AAVPVMx.

Solution and grading rubric:

• p:
  Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how a supergiant and a giant with the same size is not possible if the giant is hotter by discussing either that:
  1. for a supergiant and giant with the same size, the supergiant must be hotter than the giant (thus the giant cannot be hotter than the supergiant);
  2. for a giant hotter than a supergiant of the same size, the giant would be more luminous than the supergiant (which is not possible, as all supergiants are more luminous than giants);
  3. for a giant hotter than a supergiant, the giant must be smaller than the supergiant (thus the giant cannot be the same size as the supergiant).
• 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 least 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 70160
Exam code: midterm02n1N0
p: 18 students
r: 2 students
t: 1 student
v: 3 students
x: 6 students
y: 1 student
z: 0 students

A sample "p" response (from student 4321) discussing how a supergiant must be hotter than the giant of the same size (thus the giant cannot be hotter than the supergiant):
A sample "p" response (from student 6392) how giant that is hotter than a supergiant of the same size would be more luminous than the supergiant (which is not possible, as all supergiants are more luminous than giants):
A sample "p" response (from student 1996) how a giant hotter than a supergiant must be smaller than the supergiant (thus the giant cannot be the same size as the supergiant):