Astronomy final exam question: main-sequence star colors vs. sizes

Astronomy 210 Final Exam, Spring Semester 2011
Cuesta College, San Luis Obispo, CA

[20 points.] An astronomy question on an online discussion board (http://answers.yahoo.com/question/index?qid=20090920095747AAfgLH2) was asked and answered:
Jayen: While looking at the H-R diagram I noticed the [bluer] stars were bigger, and the [redder] stars were smaller. Is this always the case [for] stars in the main sequence?
lithiumdeuteride: Not necessarily...
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.

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. Interprets H-R diagram to show that for main sequence stars, blue stars are larger than red stars.
  • 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. Applies Wien's law, but does not limit scope of discussion to main sequence stars.
  • 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:
Grading distribution:
Section 30674
Exam code: finaln4St
p: 12 students
r: 7 students
t: 8 students
v: 4 students
x: 4 students
y: 1 student
z: 0 students

A sample "p" response (from student 7924):

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