Physics final exam question: hot coffee plus frozen coffee

Physics 5A Final Exam, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 14.40

[20 points.] A Physics 5A student is going to make iced coffee by first brewing hot coffee, at a temperature of 85.0° C, and pouring it into a glass containing 0.300 kg of frozen coffee from a freezer at –15.0° C. How much hot coffee should the student pour into the glass, in order to result in a final temperature of 10.0° C? Assume that coffee is essentially water. Neglect the temperature change of the glass. Show your work and explain your reasoning.

(The specific heat of ice is 2.10 kJ/(kg*K); the specific heat of water is 4.19 kJ/(kg*K); the latent heat of fusion for water is 334 kJ/kg.)

Solution and grading rubric:

• p = 20/20:
  Correct. Net heat exchange with the environment (or glass) is set to zero, and equates this to sum of the heat taken in by the ice to warm up from -15.0 degrees C to 0 degrees C, the heat taken in to melt this ice completely, the heat taken in by the melted ice (as water) to warm up from 0 degrees C to 10 degrees C, and the heat given up by the coffee to cool down from 85.0 degrees C to 10.0 degrees C. Solves for the mass of the hot coffee, which is 0.389 kg.
  
• r = 16/20:
  Nearly correct, but includes minor math errors. May neglect the specific heat capacity for ice and water being different, or may have converted temperature changes in Celsius into absolute temperatures in Kelvins.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has energy balance equation with systematic application of Q = m*c*delta(T) and Q = m*L heat exchanges.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  
• 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:
p: 3 students
r: 3 students
t: 10 students
v: 15 students
x: 0 students
y: 1 student
z: 0 students

A sample of a "p" response (from student 1484) is shown below:
An "r" response (from student 7937) that uses the same heat capacity for ice and for liquid coffee:
An "x" response (from student 1337) that ends on a friendly note: