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Final temperature of two mixed substances (simply enthalpy math)

  1. Dec 2, 2012 #1
    1. The problem statement, all variables and given/known data

    A 100-g sample of Cu(s), initially at 100oC, is added to 140 g of water, initially at 25oC. What is the final temperature of the mixture?

    Specific heat
    (in J g-1 oC-1)
    Cu(s) 0.385
    H2O(l ) 4.184

    2. Relevant equations

    Q = m * ΔT * c

    heat lost = heat gained
    = m2 * ΔT2 * c2

    3. The attempt at a solution

    100 * (T2 - 100) * 0.385 = 140 * (T2 - 25) * 4.185
    38.5* (T2 - 100) = 585.9 * (T2 - 25)
    38.5T2 - 3850 = 585.9T2 - 14647.5
    T2 = 19.725°C


    But the temperature can't be lower than both their starting temperatures, what did I do wrong? The answer is supposed to be 29.6
     
    Last edited: Dec 2, 2012
  2. jcsd
  3. Dec 2, 2012 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    From the way you have written your equation, you are assuming that the final temperature T2 of the copper is greater than 100 C.
     
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