Astronomy midterm question: blue supergiants just as bright as red supergiants?

Astronomy 210 Midterm 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board(*) was asked and answered:

Pd...: Is it possible that a blue supergiant can be as bright as a red supergiant, (assuming they are the same distance from Earth)?
per..gogy: Technically the blue supergiant would be the brighter one. Blue stars are more luminous than red stars...

Discuss whether or not if this answer is correct, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

*Source: http://answers.yahoo.com/question/index?qid=20110602185220AATh4tm.

Solution and grading rubric:

• p = 20/20:
  Correct. Wien's law: blue stars are hotter, and are located on the left side of an H-R diagram, while red stars are cooler, and are located on the right side. Uses Stefan-Boltzmann law and/or interprets H-R diagram to show that either (a) blue supergiants and red supergiants can have the same size, such that the blue supergiants (being hotter) are more luminous; or (b) blue supergiants and red supergiants can have the same luminosity, but the blue supergiants (being hotter) are smaller in size.
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors.
  
• v = 8/20:
  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-Boltzman law.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzman law.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:Section 70160
Exam code: midterm02n1cT
p: 13 students
r: 6 students
t: 6 students
v: 3 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 8386), discussing how the blue supergiant while hotter, would be smaller than the red supergiant in order to have the same luminosity:
Another sample "p" response (from student 1027) instead arguing that a blue supergiant will be brighter than a red supergiant, assuming that they are the same size: