Cuesta College, San Luis Obispo, CA
An astronomy question on an online discussion board[*] was asked and answered:
??: Can a red dwarf have the same size as a white dwarf?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.
Bpt: They can have the same size if the red dwarf was dimmer than the white dwarf.
Solution and grading rubric:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how a red dwarf can be the same size as a white dwarf by recognizing that:
- from Wien's law, the red dwarf is cooler than the white dwarf;
- from the Stefan-Boltzmann law (or interpreting an H-R diagram), the lower temperature red dwarf must have a lower luminosity than a white dwarf of the same size.
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
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.
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.
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-Boltzmann law.
Irrelevant discussion/effectively blank.
Exam code: midterm02sLoX
p: 37 students
r: 8 students
t: 4 students
v: 3 students
x: 2 students
y: 0 students
z: 0 students
A sample "p" response (from student 0796), using the "box method" to fill in relative Stefan-Boltzmann law parameters:
A sample "p" response (from student 5713), using the diagonal lines on an H-R diagram to compare size:
A sample "p" response (from student 8041):