Physics final exam problem: metal sample specific heat capacity

Physics 205A Final Exam, fall semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 14.83

A 1.20 kg slab of metal is taken from a container of 100.0° C boiling water, where it was in thermal equilibrium. The metal slab is then placed into a thermally insulated vessel containing 5.00 kg of 25.0° C water. The metal slab and water reach thermal equilibrium at a temperature of 26.2° C. What is the specific heat of this metal, in kJ/(kg·K)? Show your work and explain your reasoning using the properties of heat, temperature, and thermal equilibrium.

Solution and grading rubric:

• p :
  Correct. Sets up an energy balance equation with the internal energy decrease of the metal slab and the internal energy increase of the water summing to zero, or sets them equal to each other (with the appropriate handling of ± signs).
  
• r:
  Nearly correct, but includes minor math errors. As (p), but has a negative specific heat for the metal.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least sets up an energy balance equation.
  
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Attempts to derive total heat capacity from C = Q/∆T.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Section 72177
p: 10 students
r: 0 students
t: 0 students
v: 1 student
x: 0 students
y: 2 students
z: 0 students

Sections 70854, 70855
p: 34 students
r: 2 students
t: 2 students
v: 9 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 5555):
Another sample "p" response (from student 8128):
A sample "r" response (from student 5685):
A sample "v" response (from student 1448):
Another sample "v" response (from student 4581):