20180428

Astronomy midterm question: red dwarf larger than a white dwarf with same luminosity?

Astronomy 210 Midterm 2, spring semester 2018
Cuesta College, San Luis Obispo, CA

The following claim was made on an online discussion board[*]:
csmo: A red dwarf must be larger than a white dwarf if they have the same luminosity.
Discuss whether this claim is correct or 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=20180325165311AAfRex5.

Solution and grading rubric:
  • p:
    Correct. From Wien's law, determines red dwarfs are cooler than white dwarfs, and uses the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate that in order for red dwarfs and white dwarfs to have the same luminosity, the cooler red dwarf must be larger in size than the hotter white dwarf.
  • 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.
  • 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, 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 Wien's law, the Stefan-Boltzmann law, and/or H-R diagram.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Section 30674
Exam code: midterm02nVd4
p: 16 students
r: 2 students
t: 2 students
v: 4 students
x: 0 students
y: 0 students
z: 0 students

Section 30676
Exam code: midterm02StWr
p: 28 students
r: 2 students
t: 3 students
v: 9 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 7717), using a graphical "box method" to indicate relative quantities in the Stefan-Boltzmann law:

A sample "p" response (from student 1999), using an H-R diagram:

A sample "p" response (from student 2123), using both an H-R diagram and the "box method":

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