Cuesta College, San Luis Obispo, CA
Astronomy 10 learning goal Q8.3
[15 points.] Consider the blackbody (continuous) spectra of two different objects, on the same intensity versus wavelength graph shown below. Explain using Wien's law and/or the Stefan-Boltzmann law why object X is smaller than object Y.
Solution and grading rubric:- p = 15/15:
Correct. Wien's law says that Object X (peak intensity at a shorter wavelength) must be hotter than Object Y. The Stefan-Boltzmann law says that luminosity (related to the intensity of the peak) is proportional to size and temperature^4. Since Object X is hotter, in order for it to be less luminous than Object Y is for Object X to be much smaller than Object Y. May only implicitly utilize Wien's law in discussion. - 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 understands the Stefan-Boltzmann law. - 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. - y = 1.5/15:
Irrelevant discussion/effectively blank. - z = 0/15:
Blank.
Section 1073
p: 14 students
r: 4 students
t: 14 students
v: 9 students
x: 0 students
y: 0 students
z: 1 student
A sample of a "p" response (from student 4888) is shown below:
Another "p" response appeals to analyzing the Stefan-Boltzmann equation (from student 7276):
A few students (7635 shown here), upon immediately receiving the midterm at the start of class, had written down from short-term memory on the cover page the six special comparison cases discussed in class using the Stefan-Boltzmann law:
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