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Calorimetry - Water & Ice Problem

  1. Nov 1, 2009 #1
    1. The problem statement, all variables and given/known data

    A 10 gram quantity of water at 25 degrees Celsius is poured onto a 400 gram block of ice which is at -10 degrees Celsius. Assume that all the heat is contained within these two objects. Determine the final equilibrium temperature.
    Specific heat of water is 4186 J/kgK
    Specific heat of ice is 2100 J/kgK
    Latent heat of fusion of ice is 334,000 J/kgK


    2. Relevant equations

    Q = mc[tex]\Delta[/tex]T
    Q = mLf

    3. The attempt at a solution

    Qwater + Qice = 0

    Water cools to 0[tex]\cdot[/tex]C
    Q = mc[tex]\Delta[/tex]T
    Q = (0.010 kg)(4186 J/kgK(0[tex]\cdot[/tex] - 25[tex]\cdot[/tex]C)
    Q = -1046.5 J

    Water freezes at 0[tex]\cdot[/tex]C
    Q = mLf
    Q = (0.010 kg)(334,000 J/kgK)
    Q = 3340 J

    Water, which is now ice, cools to final temperature Tf
    Q = mc[tex]\Delta[/tex]T
    Q = (0.010 kg)(2100 J/kgK)(Tf - 0[tex]\cdot[/tex]C)
    Q = 21(Tf)

    Ice heats up to final temperature Tf
    Q = mc[tex]\Delta[/tex]T
    Q = (0.400 kg)(2100 J/kgK)(Tf - -10[tex]\cdot[/tex]C)
    Q = 840(Tf) + 8400 J

    Putting everything together...
    Qwater + Qice = 0
    -1046.5 J + 3340 J + 21(Tf) + 840(Tf) + 8400 J = 0
    861(Tf) = -10,693.5 J
    Tf = -12.4[tex]\cdot[/tex]C

    This can't be the right temperature for Tf because the ice starts at -10 [tex]\cdot[/tex]C and it's supposed to heat up! (Isn't it?)

    If someone could please give me a hint as to what I'm doing wrong, I would greatly appreciate it.

    Thank you!
     
  2. jcsd
  3. Nov 2, 2009 #2

    alphysicist

    User Avatar
    Homework Helper

    Hi catspajamas,

    I have not checked all of your numbers, but this does not look right to me. Notice in the previous quantity, Q is negative when heat leaves the water (as it cools to zero degrees). If water is freezing, is heat entering or leaving the water?


     
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