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Specific heat / latent heat

  1. May 12, 2009 #1
    1. The problem statement, all variables and given/known data

    An insulated cup contains 1kg of water initially at 20 C. 0.50 kg of ice, initially at
    0 C is added to the cup of water. The water and ice are allowed to come to thermal equilibrium. The specific heat of ice is 2000 J/kg oC, the specific heat of water 4186 J/kg oC, the latent heat of fusion of water is 33.5x104J/kg. What is the final temperature of the water?

    (A) 0 C
    (B) 1.2 C
    (C) 4.6 C
    (D) 9.2 C
    (E) 15.2 C

    2. Relevant equations
    Q_gain(ice) = Q_lost(water)
    mc(Ti-Tf) = mLf + mc(Tf-0)

    3. The attempt at a solution
    Q_gain(ice) = Q_lost(water)
    mc(Ti-Tf) = mLf + mc(Tf-0)
    (1.0)(4186)(20 - Tf) = (.5)( 33.5x104 ) + (.5)(4186)(Tf)
    83,720 – 4186Tf = 167,500 + 2093 Tf
    -83780= 6279 Tf
    -13.3 = Tf
  2. jcsd
  3. May 12, 2009 #2


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    Correct method
    But what is the total energy needed to melt the ice?
    How much energy can you get from the initial water before it cools to 0c?
    Last edited: May 12, 2009
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