Cuesta College, San Luis Obispo, CA
An astronomy question on an online discussion board[*] was asked and answered:
??: If two stars have the same luminosity, is it always true that the star with the lower temperature must be bigger?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.
qcp: Yes, that's true. A cooler star means that it must be bigger to be of equal luminosity.
Solution and grading rubric:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how a cooler star must be bigger than a hotter star to have the same luminosity.
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: midterm02n4s5
p: 12 students
r: 3 students
t: 3 students
v: 1 student
x: 2 students
y: 1 student
z: 0 students
A sample "p" response (from student 1503), using both the "box method" to fill in relative Stefan-Boltzmann law parameters, along with using the diagonal lines on an H-R diagram to compare size:
A sample "x" response (from student 1096), appealing to recent tragic events in pop culture: