Cuesta College, San Luis Obispo, CA
Astronomy 10 learning goal Q8.3
[Version 1]
[15 points.] Consider the following statement: "If two stars have the same brightness, the star with the lower temperature will be bigger." Discuss whether this statement is true or not, and support your answer using Wien's law and/or the Stefan-Boltzmann law.
Solution and grading rubric:
- p = 15/15: Correct.
Wien's law: peak wavelength is inversely proportional to temperature, size is not a factor. The Stefan-Boltzmann law: luminosity (brightness) proportional to size * (Temperature)^4, such that two stars can have the same brightness if the smaller star were hotter, and the larger star were cooler. - r = 12/15:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. - t = 9/15:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least recognizes that the Stefan-Boltzmann law is applicable, but argument is garbled. - v = 6/15:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. - x = 3/15:
Implementation/application of ideas, but credit given for effort rather than merit. Agrees or disagrees with statement with no discussion. - y = 1.5/15:
Irrelevant discussion/effectively blank. - z = 0/15:
Blank.
Grading distribution:
Section 4136
p: 21 students
r: 2 students
t: 7 students
v: 7 students
x: 2 students
y: 0 students
z: 0 students
[Version 2]
[15 points.] Consider the following statement: "If two stars have the same color, the brighter star will be bigger." Discuss whether this statement is true or not, and support your answer using Wien's law and/or the Stefan-Boltzmann law.
Solution and grading rubric:
- p = 15/15:
Correct. Wien's law: temperature is inverserly proportional to peak wavelength, which is related to color. Since both stars have the same color, then they must have the same temperature. The Stefan-Boltzmann law: luminosity
(brightness) proportional to size * (Temperature)^4, such that the smaller star must be dimmer, and the larger star must be cooler, given that they are the same size. - r = 12/15:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Uses the Stefan-Boltmann law correctly, but the temperature is assumed to be the same (or implied), not explicitly derived from applying Wien's law. - t = 9/15:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least recognizes how the Stefan-Boltzmann law and Wien's law are applicable, but argument is garbled. - v = 6/15:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. - x = 3/15:
Implementation/application of ideas, but credit given for effort rather than merit. Agrees or disagrees with statement with no discussion. - y = 1.5/15:
Irrelevant discussion/effectively blank. - z = 0/15:
Blank.
Grading distribution:
Section 5076
p: 7 students
r: 3 students
t: 6 students
v: 4 students
x: 0 students
y: 0 students
z: 0 students
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