Physics final exam question: temperature changes during heat exchange

Physics 205A Final Exam, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Practice Problem 14.5, Comprehensive Problem 14.75

A 0.50 kg aluminum sample at a temperature of 25° C, and a 0.50 kg iron sample at a temperature of 50° C are brought together in contact to reach thermal equilibrium. After reaching thermal equilibrium, which sample had the greatest change in temperature? Show your work and explain your reasoning using the properties of heat, temperature, and thermal equilibrium. Specific heat of aluminum is 900 J/(kg·K). Specific heat of iron is 440 J/(kg·K).

Solution and grading rubric:

• p:
  Correct. The heat transferred from the iron sample is equal to the heat transferred to the aluminum sample as they attain thermal equilibrium. Because they have the same mass, then the iron sample, which has the smaller specific heat, will have the greater temperature change. May have explicitly solved for the final temperature of the aluminum-iron system.
  
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Recognizes that iron has a smaller specific heat in arguing that it must have the greater temperature change, but does not explicitly note that the heat or change in internal energy is the same for both samples as they attain thermal equilibrium.
  
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least discussion involves heat, specific heats, and temperature changes.
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit.
  y: Irrelevant discussion/effectively blank.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: finalB0xs
p: 20 students
r: 9 students
t: 16 students
v: 1 student
x: 1 student
y: 1 student
z: 0 students

A sample "p" response (from student 0864):
Another sample "p" response (from student 1123):