Astronomy midterm question: same luminosity, same size, different temperature stars?

Astronomy 210 Midterm 2, fall semester 2015
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

??: Can two stars with the same luminosity have the same size, but different temperatures?
Lodar: If the temperatures are different, the sizes would also have to be different for their luminosities to be the same.

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.

[*] answers.yahoo.com/question/index?qid=20150810205550AAgBvqF.

Solution and grading rubric:

• p:
  Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how same luminosity stars with different temperatures would have to have different sizes. May also demonstrate that same luminosity stars with different temperatures cannot have the same temperatures.
• 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 clearly based on Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Section 70158
Exam code: midterm02sP3c
p: 34 students
r: 3 students
t: 1 student
v: 2 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 5635) discussing how same luminosity stars with different temperatures would have to have different sizes:
A sample "p" response (from student 1022), discussing how same luminosity stars with different temperatures cannot have the same temperatures: