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Specific heat of a piece of metal dropped in water

  1. Nov 16, 2007 #1
    1. The problem statement, all variables and given/known data

    A metal container, which has a mass of 8.0 kg contains 14.3 kg of water. A 2.9-kg piece of the same metal, initially at a temperature of 190.0°C, is dropped into the water. The container and the water initially have a temperature of 15.1°C and the final temperature of the entire system is 17.1°C. Calculate the specific heat of the metal.

    2. Relevant equations

    Q = c* m *change in T

    3. The attempt at a solution

    The heat of the container + the heat of the water = the heat of the piece of metal

    using algebra I got the equation:

    cwater*Mwater*change in Twater / [Mpiece*change in Tpiece - Mcontainer*change in Tcontainer]

    I am having trouble figuring out the temperatures for the equation. Please help!
     
  2. jcsd
  3. Nov 16, 2007 #2

    mgb_phys

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    Nearly right, The change in T for the container and the water is the same.

    So the equation is
    Cwater * Mwater * dT water + Cmetal * MContainer * dTwater = Cmetal * Mmetal *dTmetal

    The only unknown is Cmetal.
     
  4. Nov 16, 2007 #3

    Shooting Star

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    Hi cyclonefb3,

    There's no equality sign in your eqn.

    Let t be the final temp. Then,

    (14.3*Cw+8*Cm)(17.1-15.1) = (2.9*Cm)(190-17.1).

    If Cwater is known, you can find Cm.
     
  5. Nov 16, 2007 #4
    I think I have the dTpiece wrong this is what i'm entering:

    41.86(14.3)(17.1-15.1) / [2.9*(190-15.1)] - [8*(17.1-15.1)]

    I'm not sure where to go from here...
     
  6. Nov 16, 2007 #5

    mgb_phys

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    It would help if your equations had = signs!

    Cwater * Mwater * dT water + Cmetal * MContainer * dTwater = Cmetal * Mmetal *dTmetal
    4200 * 14.3 (17.1-15.1) + C * 8 (17.1-15.1) = C * 2.9 (190-17.1)
    120120 = C (2.9*172.9 - 8*2)

    Hint C for metals is generally a few hundred J/kg/k
     
    Last edited: Nov 16, 2007
  7. Nov 16, 2007 #6
    thanks, it was just he program being really picky with digits.
     
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