Astronomy midterm question: same size supergiant and giant stars

Astronomy 210 Midterm 2, fall semester 2010
Cuesta College, San Luis Obispo, CA

Discuss whether or not a supergiant and a giant star with the same size could have the same temperature, and why. Support your answer using the Stefan-Boltzmann law and/or an H-R diagram.

Solution and grading rubric:

• p:
  Correct. Uses either the H-R diagram and/or the Stefan-Boltzmann law to show that since all supergiants are more luminous than giants, then it is not possible for a supergiant and a giant to have the same size and same temperature (as that would result in the same luminosity).
  
• 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. Attempts to use H-R diagram and/or Stefan-Boltzman law with stars of same size and same temperature, while realizing that supergiants and giants have different luminosities, but does not adequately resolve that these two arguments are inconsistent with each other (or resolves this with a plausible overlapping range of sizes/temperatures).
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use H-R diagram and/or Stefan-Boltzman law.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 70160
p: 21 students
r: 7 students
t: 6 students
v: 7 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1204):

Another sample "p" response (from student 0002):