Physics final exam question: larger versus smaller surface area coolers

Physics 205A Final Exam, Fall Semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Multiple-Choice Question 14.5

[10 points.] A large styrofoam ice chest has warm temperatures outside, compared to its cold temperature contents. A small styrofoam ice chest has the same wall thickness, and the same warm temperatures outside and cold temperature inside. Which ice chest will have the greatest rate of heat entering its contents per time? Explain your answer using the properties of heat
conduction.

Solution and grading rubric:

• p = 10/10:
  Correct. Both coolers have the same temperature difference and thickness, but the larger cooler has more surface area, and thus has the smaller thermal resistance, and the greater rate of heat entering its contents per time. (Assuming that the larger cooler contains more cool substance that the smaller cooler, the larger cooler would take longer to warm up, due to the mass factor in Q = m*c*delta(T), but the relative amount of contents in the larger cooler does not affect the rate of heat entering its contents.)
  
• r = 8/10:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  
• t = 6/10:
  Nearly correct, but argument has conceptual errors, or is incomplete.
  
• v = 4/10:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Argues that the larger cooler will have a lesser rate of heat entering it per time, based on the mass of its conents.
  
• x = 2/10:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 1/10:
  Irrelevant discussion/effectively blank.
  
• z = 0/10:
  Blank.
  

Grading distribution:
Section 72177
p: 11 students
r: 1 student
t: 0 students
v: 0 students
x: 0 students
y: 1 student
z: 0 students

Sections 70854, 70855
p: 31 students
r: 6 students
t: 0 students
v: 11 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1337):

Another sample "p" response (from student 2962):

Yet another sample "p" response (from student 5051):

A sample "v" response (from student 1448):