Astronomy midterm question: giant hotter or cooler to be bigger than a supergiant?

Astronomy 210 Midterm 2, fall semester 2016
Cuesta College, San Luis Obispo, CA

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

Pdg: Does a giant need to be cooler or hotter in order to be bigger in size than a supergiant?
non: Hotter.

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=20161004185806AAV5fBU.

Solution and grading rubric:

• p:
  Correct. Uses the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how a giant cannot be hotter in order to be bigger than a supergiant, by arguing that since a giant must be dimmer than a supergiant, in order for the giant to be bigger than a supergiant, the giant must have a cooler temperature. (Using Wien's law is not necessary to answer this question.)
• 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 the Stefan-Boltzmann law and/or H-R diagram.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use the Stefan-Boltzmann law and/or H-R diagram.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on the Stefan-Boltzmann law and/or H-R diagram.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Section 70158
Exam code: midterm02sU6A
p: 15 students
r: 8 students
t: 9 students
v: 3 students
x: 1 student
y: 0 students
z: 0 students

Section 70160
Exam code: midterm02NbnW
p: 10 students
r: 3 students
t: 6 students
v: 3 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 0301):