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Heat required to heat water and ice

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  1. Apr 16, 2017 #1
    Is the answer in my physics book wrong or did I miss something?
    1. The problem statement, all variables and given/known data
    A vessel whose walls are thermally insulated contains 2.40 kg of water and 0.450 kg of ice, all at 0.0°C. The outlet of a tube leading from a boiler in which water is boiling at atmospheric pressure is inserted into the water. How many grams of steam must condense inside the vessel (also at atmospheric pressure) to raise the temperature of the system to 28.0°C? You can ignore the heat transferred to the container.

    mw = 2.4 kg
    mi = 0.45 kg
    ΔT = 28 C°
    c = 4190
    Lf 334 * 10^3 J/kg
    Lv 2256 * 10^3 J/kg

    2. Relevant equations
    Q = mcΔT
    Q = ±mL

    3. The attempt at a solution
    Heat required to melt ice and warm water to 28 C°:
    Qreq = miLf + (mi + mw)cΔT

    Condensing steam of amount Qreq = -msLv
    ms = -(miLf + (mi + mw)cΔT)/Lv
    ms = -215 grams

    My physics book tells me the answer is 190 grams, which I get if I don't account for mi in (mi + mw)cΔT. This seems wrong to me but I wanted to ask and make sure, every other time I've claimed that I found an error in my physics book I have been incorrect.
     
  2. jcsd
  3. Apr 16, 2017 #2

    gneill

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    Staff: Mentor

    When the steam condenses, is it at the final temperature?
     
  4. Apr 16, 2017 #3
    Oops, thank you I got it right now.
     
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