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Iron Cubes and Volume

  1. Mar 17, 2009 #1
    1. The problem statement, all variables and given/known data
    A physics student has two cubes of iron. One cube has three times the volume of the other. The cubes are heated over identical flames for the same amount of time. The cubes are then removed and the temperature of each cube is recorded immediately.

    How will the thermometer readings compare?



    2. Relevant equations
    Q=mc∆t


    3. The attempt at a solution
    My initial thought was that a smaller volume meant a smaller mass and that the smaller mass would have a lower temperature than that of the bigger volume.

    1. The problem statement, all variables and given/known data
    A physics student has three cubes of metal: a 100 g cube of iron, a 300 g cube of iron, and a 100 g cube of aluminum. The student puts the cubes into a beaker of boiling water. The cubes remain in boiling water until each cube is as hot as it is going to get. The cubes are then removed and the temperature of each cube is immediately recorded.

    How will the thermometer readings compare?

    Which cube reached its final temperature most quickly?

    Discuss how the answers to this exercise differ from the answers to the preceding exercise.



    2. Relevant equations
    Specific Heat of Aluminum: 0.215 cal/g/degree Celsius
    Specific Heat of Iron: 0.1 cal/g/degree Celsius
    Specific Heat of Water: 1 cal/g/degree Celsius
    Q=Q=mc∆t

    3. The attempt at a solution
    1. The 100 g iron cube would have the highest temperature because of its small mass. The 100 g aluminum cube would have the lowest temperature because of its high specific heat.
    2. The 100 g iron cube would reach its final temperature first.
    3. ???
     
    Last edited: Mar 17, 2009
  2. jcsd
  3. Mar 17, 2009 #2
    1.) For one -- I'm going to make the assumption that the iron cubes are initially at the same temperature.

    Now we can relate volume = mass / density. Since density is an intrinsic property of a material it's independent of how much of the substance we have it will always be constant. This means that a larger volume would indeed have larger mass given to samples of the same substance.

    Now you're asked about the final temperature of the two materials while giving each sample the same amount of heat, the heat capacity has to be the same because it's also intrinsic, and the initial temperature is the same.

    What can we say about the final temperature? Rewrite Q = mC∆t in terms of final temperature and the answer will really stick out.

    2.) You might want to actually compute the ratios to make sure you're correct.
     
    Last edited: Mar 17, 2009
  4. Mar 17, 2009 #3

    rl.bhat

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    Homework Helper

    My initial thought was that a smaller volume meant a smaller mass and that the smaller mass would have a lower temperature than that of the bigger volume.

    If you keep tip of a needle in a flame, it becomes red hot quickly. Now if you keep tip of a large nail of the same material as that of needle, it takes longer time to become red hot.
    Similarly what happens in the above problem?
     
  5. Mar 17, 2009 #4
    Can you assist me with the 2nd part, I don't know what ratios to compute.
     
  6. Mar 17, 2009 #5
    The cube with the less volume (less mass) would heat up first.
     
  7. Mar 17, 2009 #6
    For the second question regarding the cubes in boiling water, wouldn't they all eventually reach 100 degrees Celsius?
     
  8. Mar 17, 2009 #7

    LowlyPion

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    Homework Helper

    They all get to temperature, so they should all read the same immediately after removing from the 100° bath.
     
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