Cuesta College, San Luis Obispo, CA
An astronomy question on an online discussion board(*) was asked and answered:
Pd: Is it possible that a small hot star and a cool big star [located the same distance from us] can be equally bright?Discuss why this answer is not correct, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.
Star Dust: Small-hot is [always] more luminous than cool-big.
*Adapted from: http://answers.yahoo.com/question/index?qid=20120928201352AA8dDbB.
Solution and grading rubric:
- p = 20/20:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to show that small, hot stars can be either (a) equally luminous, or (b) less luminous than cool, big 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.
- 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:
Exam code: midterm02NuF7
p: 20 students
r: 5 students
t: 1 student
v: 1 student
x: 0 students
y: 0 students
z: 0 students
A sample "p" response (from student 5411) demonstrating how a small hot star could be as luminous as a large cool star:
Another sample "p" response (from student 0716) demonstrating how a small hot star could be less luminous than a large cool star: