Cuesta College, San Luis Obispo, CA
An astronomy question on an online discussion board[*] was asked and answered:
Pdg: What is an example of a cooler star being smaller than a hotter star?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.
nin: The sun and a red star like Barnard's star.
Solution and grading rubric:
Correct. Uses Wien's law to determine that the sun would be the hotter (yellow) star, while Barnard's star would be the (red) cooler star. Then uses the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how Barnard's star would need to be a red dwarf in order to be cooler and smaller than the sun, a medium-mass main-sequence star.
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Compares two stars (hotter, larger vs. cooler, smaller), where the hotter star is more luminous than the cooler star, but does not explicitly compare the sun versus a red (dwarf) star.
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least discussion demonstrates understanding of Wien's law, but the Stefan-Boltzmann law and/or H-R diagram discussion is garbled, with a hotter, larger sun having the same luminosity as a cooler, smaller red (dwarf) star; or may have erroneously claimed that the two stars have the same temperature, but Stefan-Boltzmann law and/or H-R diagram discussion is consistent with this mistake in Wien's 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, the Stefan-Boltzmann law, and/or H-R diagram.
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on Wien's law, the Stefan-Boltzmann law, and/or H-R diagram.
Irrelevant discussion/effectively blank.
Exam code: midterm02sL0w
p: 22 students
r: 4 students
t: 9 students
v: 5 students
x: 3 students
y: 0 students
z: 0 students
A sample "p" response (from student 3428):