## 20160503

### Astronomy midterm question: same luminosity, but different temperature and size stars

Astronomy 210 Midterm 2, spring semester 2016
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?
qcp: Yes, that's true. A cooler star means that it must be bigger to be of equal  luminosity.
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.

Solution and grading rubric:
• p:
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.
• 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. At least discussion demonstrates understanding of Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
• 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, H-R diagram and/or the Stefan-Boltzmann law.
• x:
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:
Irrelevant discussion/effectively blank.
• z:
Blank.
Section 30674
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: