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Thermodynamics: Mixing ice and water

  1. May 5, 2014 #1
    10 g of ice at -20C and 100g of water at +5C is mixed together. How much water and ice will there be once the system reaches equilibrium (assuming no heat is lost)?

    Specific heat of water and ice: [tex]4.186*10^3, 2.108*10^3 [/tex]
    Latent heat of fusion of ice: [tex]333.55*10^3 [/tex]

    All in units [tex](kg^{-1} * C^{-1})[/tex]

    My try:

    [tex]Energy_{water} = (0.1 * 5 * 4.186 * 10^3) = 2093 J [/tex]
    [tex]Energy_{water} - Heating_{ice} = 2093 - (0.01 * 2.108 * 10^3 * 20) = 2071.92J [/tex]

    Melting the ice with the remaning energy:

    [tex]2071.92 = 333.55*10^3 * x [/tex]
    [tex]x ≈ 0.062 grams [/tex]

    But the right answer is supposed to be 5 grams of ice melted.

    Where did I go wrong? I thought it was a bit to simple to be correct.

    Edit: +5 not -5 for water.

    Thank you!
     
    Last edited: May 5, 2014
  2. jcsd
  3. May 5, 2014 #2
    Are you sure about that -5C for the water?
     
  4. May 5, 2014 #3
    Thank you. It is supposed to be +5 C for the water.
     
  5. May 5, 2014 #4
    The following is incorrect arithmetic: 2093−(0.01∗2.108∗103∗20)=2071.92J

    Also, you should be dividing by 333 J/gm, not 333000.

    Chet
     
  6. May 5, 2014 #5
    Oh, I see. Thanks!
     
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