Physics final exam problem: sous-vide cooking steak

Physics 205A Final Exam, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Practice Problem 14.5, Comprehensive Problem 14.95

J. Kenji López-Alt

A sous-vide recipe calls for raw meat (0.91 kg of steak, starting at a chilled 10° C) in air-evacuated plastic bags, placed in an insulated container with 66° C water.[*][**] Find the amount of water to be placed in the container such that the temperature of the meat is 52° C once thermal equilibrium has been reached, assuming that 10,000 J of heat is lost to the environment during this process. Ignore the effects of evaporation and phase changes, and heat exchanged with the plastic bags. Show your work and explain your reasoning using the properties of heat, temperature, and thermal equilibrium.

Specific heat of steak[***] is 2,340 J/(kg·K). Specific heat of water is 4,190 J/(kg·K).

[*] "125° F for a rare steak," "[cooler] loses about 1 degree per hour when it's in the 140° F to 150° F range," J. Kenji López-Alt, "Cook Your Meat in a Beer Cooler: The World's Best (and Cheapest) Sous-Vide Hack," seriouseats.com/2010/04/cook-your-meat-in-a-beer-cooler-the-worlds-best-sous-vide-hack.html.
[**] "4 steaks, 1/2 pound each," J. Kenji López-Alt, "Sous-Vide Steaks," seriouseats.com/recipes/2010/03/sous-vide-steaks-recipe.html.
[***] "Beef, flank," engineeringtoolbox.com/specific-heat-capacity-food-d_295.html.

Solution and grading rubric:
  • p:
    Correct. Sets up an energy transfer/balance equation with changes in the thermal internal energies of the meat and water summing to –10,000 J (as heat is removed from the meat/water system, transferred out to environment), and solves for the amount of water required to cook the meat.
  • r:
    Nearly correct, but includes minor math errors. Typically has +10,000 J of heat being added to the meat/water from the environment.
  • t:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has energy transfer/balance equation but typically has meat and water exchanging heat with each other, and does not account for transfers to (or from) the environment.
  • v:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. At least some attempt at setting up change in internal energy terms and/or an energy transfer/balance equation, but typically does not set up ∆T terms correctly.
  • x:
    Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying an energy transfer/balance equation.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Sections 70854, 70855, 73320
Exam code: finalm34T
p: 6 students
r: 16 students
t: 12 students
v: 11 students
x: 6 students
y: 5 students
z: 6 students

A sample "p" response (from student 9950):

A sample "r" response (from student 4455), with 10,000 J of heat added into to container:

A sample "t" response (from student 1412), with no heat leaving or entering the container:

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