Physics final exam question: comparison of radiating object temperatures

Physics 205A Final Exam, fall semester 2015
Cuesta College, San Luis Obispo, CA

A dark-colored cube (emissivity 0.80) and a light-colored cube (emissivity 0.20) radiate the same rate of heat per time in all directions to the environment (assumed to be 0 K). The light-colored cube has four times more surface area than the dark-colored cube. Determine which cube has a hotter temperature (or if there is a tie). Explain your reasoning using the properties of temperature and radiative heat transfer.

Solution and grading rubric:

• p:
  Correct. Discusses:
  1. that the smaller, darker cube has an emissivity four times that of the lighter, larger cube; and
  2. the smaller, darker cube has a surface area one-fourth that of the lighter, larger cube; and
  3. since both cubes radiate the same rate of heat per time, their temperatures must be equal.
• 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 different emissivity and area values.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Typically only compares just emissivity, or just area, or somehow does not recognize that they have the same rate of heat radiated out to the environment.
• 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/application 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: final7rUk
p: 49 students
r: 9 students
t: 6 students
v: 2 students
x: 2 students
y: 1 student
z: 1 student

A sample "p" response (from student 0048):