Cuesta College, San Luis Obispo, CA
An astronomy question on an online discussion board[*] was given the following answers:
CM: I keep thinking that a cooler star could be more luminous than a hotter star--is this true?Discuss why this answer is incorrect, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.
Okl: No, it cannot be true.
Do: There are situations in which this may be true.
[*] Adapted from https://answers.yahoo.com/question/index?qid=20090316143453AAmTD1h.
Solution and grading rubric:
- p = 20/20:
Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to show specifically how it is possible for a cooler star to be more luminous than a hotter star, provided that the cooler star is sufficiently larger than the hotter star.
- r = 16/20:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. As (p), but may instead demonstrate how a cooler star could be equally luminous as a hotter star.
- 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-Boltzmann 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-Boltzmann law.
- y = 2/20:
Irrelevant discussion/effectively blank.
- z = 0/20:
Exam code: midterm02n4iL
p: 22 students
r: 4 students
t: 1 student
v: 0 students
x: 1 student
y: 0 students
z: 0 students
z: 0 students
A sample "p" response (from student 0507) using an H-R diagram:
Another sample "p" response (from student 0794) using the "box model" of the Stefan-Boltzmann law:
Yet another sample "p" response (from student 3946) showing all the possible entries in the Stefan-Boltzmann "box model":