Physics final exam question: smaller, hotter, and more luminous star

Physics 205A Final Exam, fall semester 2016
Cuesta College, San Luis Obispo, CA

Stars can be modeled as spherical blackbodies (emissivity 1.0) that radiate heat out to an environment assumed to have a temperature of 0 K. Discuss why a smaller star must have a higher temperature than a larger star in order to radiate more heat per time than the larger star. Explain your reasoning using the properties of temperature and radiative heat transfer.

Solution and grading rubric:

• p:
  Correct. Discusses:
  1. that the size of the smaller star (if the only differing factor) would result in a lower rate of heat radiation per time;
  2. that the smaller size must then have a hotter temperature to result in a higher rate of heat radiation of per time.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. At least compares both surface area and temperature values. (May also have set the rate of heat radiated per time equal for the two stars.)
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Typically only compares just surface area, or just temperature.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying Stefan's law of radiation.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying Stefan's law of radiation.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: finali0w4
p: 37 students
r: 8 students
t: 1 student
v: 1 student
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 0424):
Another sample "p" response (from student 6436):