20161127

Physics final exam question: cool aluminum block in warm water

Physics 205A Final Exam, fall semester 2015
Cuesta College, San Luis Obispo, CA

An aluminum block is placed in a container of water. The aluminum block is initially cooler than the warm water, and they are allowed to come to thermal equilibrium. The container is not thermally isolated from the environment. For the aluminum block to experience a smaller change in thermal energy than the water while they reach thermal equilibrium, determine whether heat must enter or leave the container. Explain your reasoning using the properties of heat, temperature, and thermal equilibrium.

Specific heat of aluminum is 900 J/(kg·K). Specific heat of water is 4,190 J/(kg·K).

Solution and grading rubric:
  • p:
    Correct. Discusses:
    1. how the aluminum block (initially cooler than the water) increases in thermal energy as it reaches thermal equilibrium;
    2. how the water (initially warmer than the aluminum block) decreases in thermal energy as it reaches thermal equilibrium; and
    3. from energy conservation (either explicitly shown in a transfer-balance equation, or discussed conceptually), in order for the aluminum block to undergo a smaller thermal energy change than the water, while some heat is transferred from the water to the block, some heat from the water must also be lost to the environment.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete. May discuss how heat must leave the container based on comparing just specific heats, or comparing just temperature changes of the aluminum block and water (without knowing how their masses compare, or their respective initial temperatures).
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying energy conservation to thermal energy changes and heat transfers with the environment.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit. Approach other than applying energy conservation to thermal energy changes and heat transfers with the environment.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Sections 70854, 70855, 73320
Exam code: final7rUk
p: 29 students
r: 3 students
t: 26 students
v: 6 students
x: 3 students
y: 2 students
z: 1 student

A sample "p" response (from student 3179):

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