## 20151128

### 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.

• 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):