Physics final exam question: calorimetry experiment

Physics 205A Final Exam, Fall Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Comprehensive Problem 14.107

[20 points.] A 0.500 kg block of copper at 100.0° C is placed into 0.750 kg of water in a 0.0500 kg aluminum calorimeter. The water and the aluminum calorimeter are at 25.0° C just before the copper block is placed inside. What is the final temperature of the water, assuming negligible heat flow to the environment? The top of the calorimeter is open to let steam (if any) escape. Show your work and explain your reasoning.

(The specific heat of copper is 0.385 kJ/(kg*K); the specific heat of water is 4.19 kJ/(kg*K); the specific heat of aluminum is 0.900 kJ/(kg*K); the latent heat of vaporization for water is 2,256 kJ/kg.)

Solution and grading rubric:

• p = 20/20:
  Correct. Net heat exchange with the environment is set to zero, and equates this to sum of the heat taken in by the water and the aluminum can to warm up from 25.0 degrees C to T_f, and the heat released by the copper block as it cools down from 100.0 degrees C to T_f. Solves for T_f, which is 29.3 degrees C.
  
• r = 16/20:
  Nearly correct, but includes minor math errors.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least systematically identifies and sets up each heat exchange term with the correct mass, specific heats, and temperature changes.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some progress at setting up m*c*delta(T) terms.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Sections 70854, 70855
p: 9 students
r: 3 students
t: 10 students
v: 13 students
x: 4 students
y: 0 students
z: 0 students

A sample "p" response (from student 1214):

Another sample "p" response (from student 1977):

A sample "t" response, which is a good start (from student 4916):

A sample "v" response (from student 4657), with a final temperature that is remarkably hotter than the initial temperature of the copper block: